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This 14-lesson series introduces each concept in an easy-to-understand way and by using example problems that are worked out step-by-step and line-by-line to completion. Includes Permutations (79 minutes); Combinations #11;(4..
Having trouble engaging your algebra students? This set of PowerPoint® slides highlights student-centered situations to teach algebra. The problems are rigorous enough to require true problem-solving and accessible enough to allow all stude..
Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understanding of key concepts. 13..
GRADES 9-12. Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understandi..
Everything you need for a class of up to 30 students. Kit contains: 30 Algebra Tile™ Student Sets (each set includes a 35-piece, two-color set of Algebra Tiles™), a 70-piece overhead set of Algebra Tiles™, an instructional ..
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. |
This is the first of two courses designed to emphasize topics which are fundamental to the study of calculus. Emphasis is placed on equations and inequalities, functions (linear, polynomial, rational), systems of equations and inequalities, and parametric equations. Upon completion, students should be able to solve practical problems and use appropriate models for analysis and predictions.
This course has been approved to satisfy the Comprehensive Articulation Agreement general education core requirement in natural sciences/mathematics. |
MAA Review
[Reviewed by Fernando Q. Gouvêa, on 05/20/2010]
Lie groups play such a central role in mathematics and its applications that all mathematics students should be aware of them. From computer graphics to quantum theory, from differential equations to number theory, Lie groups and algebras are everywhere. Nevertheless, most mathematics undergraduates have never heard of them.
Of course, the reason for this is that even the definition of a Lie group (i.e., a differentiable manifold which is also a group and whose group operations are smooth functions) seems to require more background knowledge than most undergraduates have. In a famous article on "Very Basic Lie Theory" (American Mathematical Monthly, 1983), Roger Howe argued that the absence of the theory of Lie groups from most undergraduate programs was both scandalous and unnecessary. Since then, several books attempting to respond to Howe's challenge have appeared. Harriet Pollatsek's Lie Groups is her entry in this list.
Howe's article, and many of the books that it inspired, still laid a heavy emphasis on the underlying topology and analysis, with the result that only advanced undergraduates (in fact, probably only rather strong advanced undergraduates) could really understand the material. Pollatsek is not satisfied with that approach. At Smith College, she has been teaching Lie Groups to sophomores, using a problem-driven approach that only assumes knowledge of linear algebra and multivariable calculus. From that course was born this book.
Lie Groups is fundamentally a problem book: each chapter presents a sequence of problems that students should solve. In each chapter, the main sections are followed by a summary section called "Putting the pieces together." Finally, a section called "A broader view" tries to give a wider context to the material in that chapter. Everything important is done through problems. Thus, this is a book to be used, not a book to be read.
I must admit that I find teaching this material to sophomore mathematics majors to be a little bit too much of a reach. Instead, I used the book in a seminar course that followed our standard one-semester introduction to abstract algebra. In the class were six seniors, three juniors, and (yes!) a sophomore; all had taken algebra, either in the previous semester or a year before. Most, but not all, had taken other advanced courses as well, including Real Analysis. My students were assigned problems to solve and present in class, and we developed the theory in that way. Every once in a while, I would step in and give a broader view.
Did it work? Yes, it mostly did, though in the process I discovered that some aspects have to be tweaked a little bit. Because Pollatsek doesn't want to assume any algebra background, there are lots of "check that SL(2,R) is a group" problems — more than I or my students wanted. Because she doesn't want to assume much knowledge of topology, she does not have the chance to make much of connectedness, compactness, covering spaces, and (most significant in this context) simple connectedness. This seems like an opportunity lost.
Some choices I just don't understand. Why, for example, is there a section on differential equations? It seems totally unrelated to the rest of the book. Why make such a meal of continuity versus differentiability in the definition of one-parameter subgroups? In this setting, one might as well just state that all one-parameter subgroups are differentiable and be done with it. Why not do more with the fact that SU(2) is a three-sphere? (My students were fascinated.) Why work only with the one-dimensional Lorenz group? Why not have more pictures? After all, it's easy to draw pictures of the one-dimensional Lie groups.
In many of the problems, there is more handholding than I wanted my students to have; at some points, this included "hints" that led towards unnecessarily messy ways of doing things. Pollatsek clearly thinks that students at this level prefer computation to theory. She is probably right, but I would rather not indulge that preference.
Some issues had to do with the fact that my students knew some things that her students didn't (what a group is, what a normal subgroup is) but did not have a sure grasp of some things that her students clearly do have well under control (the example that stands out in my mind is the Jacobian matrix of a differentiable map). The bibliography is also a little strange, too selective for my taste. This proved significant towards the end, when my students were working on term papers and all of them wanted the same books… which were not in our library.
There is no representation theory at all. The adjoint representation is described, but not put into any sort of context. With no representation theory, one cannot do much more than say "the physicists use this a lot," without showing how or why. That seems like a pity.
Pollatsek's book faces stiff competition. Perhaps the closest competitor is John Stillwell's Naïve Lie Theory, a beautiful book aimed at upper-level undergraduates that is very much in the same spirit. Kristopher Tapp's Matrix Groups for Undergraduates is also in a similar spirit. The main difference, of course, is that Stillwell and Tapp have written textbooks, while Pollatsek gives us a problem book. Using it requires buy-in: you need to want to teach in this way, and you will need to convince your students that the work is worth doing. If that applies to you, give this book a try.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College. He'll be doing the Lie groups thing again soon. |
To introduce students to selected topics of combinatorics and
elementary analytic number theory.
Intended
Learning Outcomes:
On successful completion of the course students will be:
Able to use generating functions to solve a variety of combinatorial problems
Proficient in the calculation and application of continued fractions.
Pre-requisites:
None
Dependent Courses:
None
Course Description:
The combinatorial half of this course is concerned with
enumeration, that is, given a family of problems P(n), n a natural number, find a(n), the number of
solutions of P(n) for each such n. The basic device is the generating function, a
function F(t) that can be found directly from a description of the problem and for which
there exists an expansion in the form F(t) = sum {a(n)gn(t); n a
natural number}. Generating
functions are also used to prove a family of counting formulae to prove combinatorial
identities and obtain asymptotic formulae for a(n).
In Number Theory we look at the
question of identifying irrational numbers and approximating them by rationals. We
introduce continued fractions which we study in detail. These lead also to solutions of
certain equations (Pell's equations) in integers. When identifying irrational numbers we
find criteria which guarantee that a number is transcendental.
Teaching Mode:
2 Lectures per week
1 Tutorial per week
Private Study:
5 hours per week
Recommended Texts:
H S Wilf, Generatingfunctionology, Academic Press. 2nd ed.,
1994.
A Baker, A Concise Introduction to the Theory of Numbers,
CUP, 1984.
Niven, Zuckerman and Montgomery, An Introduction to the
Theory of Numbers, (5th edition), 1991, Wiley. |
This survey of basic mathematical concepts includes both modern and historical perspectives. Emphasis is on the development and appreciation of mathematical ideas and their relationship to other disciplines. Topics include, among others: mathematical problem-solving, set theory, graph theory, an introduction to randomness, counting and probability, statistics and data exploration, measurement and symmetry, and recursion. This course satisfies the core curriculum requirement for a core-area course in mathematics and is also recommended as the first course in mathematics for prospective elementary teachers. Prerequisite: A satisfactory score on the mathematics placement exam |
This year long course provides students with the applications and concepts necessary for success in pre-algebra. Concepts addressed include number patterns and algebra, operations with decimals, percents and fractions, data analysis and probability, integers, geometry and measurement.
This year long course provides students with the applications and concepts necessary for success in pre-algebra. Concepts addressed include algebraic concepts, operations with decimals, percents and fractions, real world applications, data analysis, algebraic concepts, geometry and measurement.
This year long course provides students with pre-algebra skill development necessary for success in Algebra 1. Concepts addressed include algebraic concepts such as expressions, equations, functions, real world applications, and data analysis.
Textbook(s): Glencoe or Algebraic Thinking Pt. 2
Algebra 1:
Prerequisites:Pre Algebra and Orleans Hanna test
Algebra 1 provides students with the materials outlined in the Maryland Core Learning Goals in Algebra 1 and Data Analysis. These goals include indicators that require experiences with problem solving and patterns, graphing linear equations, finding quadratics and other non-linear functions. Students will take the Algebra/Data Analysis High School Assessment at the end of this course as a part of the high school graduation requirement. The middle school Algebra 1 student will also take their grade level MSA assessment.
Textbook(s): Algebra 1, Prentice Hall
Geometry:
Prerequisite:Successful completion of Algebra 1, Grade 7
Geometry provides students with the skills outlined in the Maryland Core Learning Goals for Geometry. These skills include using logic to develop arguments, working with postulates and theorems of Euclidian geometry, applying rules for parallel and perpendicular lines, identifying congruent and similar figures, classifying polygons, measuring angles and writing proofs of triangle congruence, drawing, constructing and performing plane transformations.
Textbook(s): Geometry, Prentice Hall
Last modified: 9/5/2007 10:01:07 PM
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Overview The workbook provides teachers and students with 143 pages of challenging worksheets for practice to help develop Geometry skills. The workbook includes all topics covered throughout a Geometry course. The worksheets contained in this workbook consist of several different formats to provide a variety of exercises. Formats include multiple choice questions, fill-in the blank, problem solving, puzzle worksheets, and more.
Geometry Workbook Teacher Edition 1.0 - Loose Leaf Bound This version is loose leaf bound for easy removal/replacement of worksheets from the workbook. This binding method allows for flexible use of the worksheets including copying as needed under license by the author as specified in the copyright notice. This edition of the workbook contains answers to all of the problems as a key in the back of the workbook.
Geometry Workbook Teacher Edition 1.0 - Spiral Bound This version is spiral bound to prevent loss of worksheets from the workbook. This binding method allows for easy access to the worksheets with protection against loss of individual pages. This edition of the workbook contains answers to all of the problems as a key in the back of the workbook.
Geometry Workbook Student Editions 1.0 This version can be ordered either in the loose leaf bound version or in spiral bound version. This edition contains all workbook pages, however there is not an answer key located in the back of the workbook. |
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The amount of time Lesson Planet will save me is going to be mind blowing!
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Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez.
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, �Calculus Derivatives 2� and �Calculus Derivatives 2.5 (HD).� Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
This video is the 4th in a series of videos that explains derivatives. First, Sal shows another example of differentiating a polynomial and then shows two examples using the chain rule. Sal continues the chain rule in the next video.
This video continues with examples of differentiating functions using the chain rule including examples that use negative exponents and more complicated nested parenthesis. Note: Additional practice on using the chain rule is available.
Continuing to use the chain rule, Sal shows more examples of finding the derivative, this time, by looking at composite functions. Note: The current set of practice problems titled �Chain rule 1� cannot be solved until one knows how to find the derivative of ex and trigonometric functions
In the first example, instead of actually using the quotient rule, Sal rewrites the denominator as a negative exponent and uses the product rule. In subsequent examples, Sal shows, but does not prove, the derivative of several interesting functions including ex, ln x, sin x, cos x, and tan x.
After defining L�Hopital�s rule, Sal shows an example of using the rule to solve for the limit as x approaches 0 of (sin x) / x. He also describes what it means for a fraction to have indeterminate form.
After applying L�Hopitals Rule once and showing that the limit is still indeterminate, Sal applies the rule a second and third time before arriving at a limit that exists. He then shows that given that the final limit exits, so do the previous ones including the limit of the first original problem. Note: Practice problems on L�Hopital�s rule are available and can be practiced now or after watching the other example videos. |
Foundation Maths MyMathLab Global pack
Description
Foundation Maths has been written for students taking higher or further education courses, who have not specialised in mathematics on post-16 qualifications and need to use mathematical tools in their courses. It is ideally suited for those studying marketing, business studies, management, science, engineering, computer science, social science, geography, combined studies and design. It will be useful for those who lack confidence and need careful, steady guidance in mathematical methods. Even for those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study or distance learning.
Features Manual on the website) allow lecturers and tutors to set regular assignments or tests throughout the course.
New to this Edition
· A new chapter on Vectors
· New sections on integration and differentiation techniques
· Online video tutorials
· Access to MyMathLab
Table of Contents
Preface
Guided Tour
Mathematical symbols
1. Arithmetic of whole numbers
2. Fractions
3. Decimal Fractions
4. Percentage and Ratio
5. Algebra
6. Indices
7. Simplifying algebraic expressions
8. Factorisation
9. Algebraic fractions
10. Transposing formulae
11. Solving equations
12. Sequences and series
13. Sets
14. Number bases
15. Elementary logic
16. Functions
17. Graphs of functions
18. The straight line
19. The exponential function
20. The logarithm function
21. Measurement
22. Introduction to trigonometry
23. The trigonometrical functions and their graphs
24. Trigonometrical equations and identities
25. Solution of triangles
26. Vectors
27. Matrices
28. Tables and charts
29. Statistics
30. Probability
31. Correlation
32. Regression
33. Gradients of curves
34. Techniques of differentiation
35. Integration and areas under curves
36.Techniques of integration
37. Functions of more than one variable and partial differentiation
Solutions
Index
Back Cover
Foundation Mathshas been written for students taking higher and further education courses who have not specialised in mathematics on post-16 qualifications and need to use mathematical tools in their courses. It is ideally suited to those studying marketing, business studies, management, science, engineering, social science, geography, combined studies and design. It will be useful for those who lack confidence and who need careful, steady guidance in mathematical methods. For those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study and distance learning.
Features of the book Solutions Manual on the website) allow lecturers and tutors to set regular assignments or tests throughout the course.
· Companion website containing a student support pack, video tutorials, and PowerPoint slides and a Solutions Manual for lecturers, and can be found at
· Video tutorials on the companion website for selected exercises and examples.
· New chapter on vectors.
· Completely revised chapter on measurement.
· New sections on partial fractions and techniques of differentiation and integration.
Anthony Croft has taught mathematics in further and higher education institutions for over thirty years. He is currently Professor of Mathematics Education and Director of sigma - the Centre for Excellence in Teaching and Learning based in the Mathematics Education Centre at Loughborough University. He teaches mathematics and engineering undergraduates, and has championed mathematics support for students who find the transition from school to university difficult. He has authored many very successful mathematics textbooks, including several for engineering students. In 2008 he was awarded a National Teaching Fellowship in recognition of his work in these fields.
Robert Davison has thirty years experience teaching mathematics in both further and higher education. He is currently Head of Quality in the Faculty of Technology at De Montfort University, where he also teaches mathematics. He has authored many very successful mathematics textbooks, including several for engineering students |
The essential guide to MATLAB as a problem solving tool This text presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. The fundamentals of MATLAB are illustrated throughout with many examples from a wide range of familiar scientific and engineering areas, as well as from everyday life. The new edition has been updated to include coverage of Symbolic Math and SIMULINK. It also adds new examples and applications, and uses the most recent release of Matlab.
Audience First time users of Matlab. Undergraduates in engineering and science courses that use Matlab. Any engineer or scientist needing an introduction to MATLAB. |
The Cartoon Guide to Calculus Cartoon Guide to Calculus
Calculus is the mathematics of change...and The Cartoon Guide to Calculus represents a big change from previous books on this subject. Using graphics and humor to lighten what is often perceived as a challenging discipline, Larry Gonick teaches all of the essentials, from functions and limits to derivatives and integrals.
The cartoon's unnamed narrator, with the help of his friend Delta Wye, guides us through a vast range of concepts. We see, for example, how calculus was initially conceived by Isaac Newton and Gottfried Leibniz as a way of resolving age-old mysteries involving the calculation of motion. Newton and Leibniz make several cameo appearances within the book, sometimes to quibble with each other regarding who invented calculus first, but mostly to explain a new concept to us. It's fun to learn about instantaneous velocity with an example involving Newton jumping up and down on a trampoline.
We go on to study a vast range of functions—Gonick invents a function creature to show how they work. We also are treated to a visual definition of the limit that is significantly easier to understand than the algebraic version that has traditionally been taught to generations of students. Learning derivatives in calculus has always involved diagrams, but not quite as vividly as in this book. For example, at one point, the narrator finds himself in a rapidly filling pool of water in order to calculate the instantaneous rate of flow. Equally refreshing is the way the book shows us a sphere literally being cut up into slices in a section that illustrates how to calculate its volume.
Complete with end-of-chapter exercises, The Cartoon Guide to Calculus will inspire even the most math-phobic among |
Book Description: Teacher's Edition. This edition balances the investigative approach that is the heart of the Discovering Mathematics series with an emphasis on developing students' ability to reason deductively. If you are familiar with earlier editions of Discovering Geometry, you'll still find the original and hallmark features, plus improvements based on feedback from many of your colleagues in geometry classes. |
Working with charts, graphs and tables
Your course might not include any maths or technical content but, at... you how to use charts, graphs and tables to present your own information.
After studying this unit:
you will learn how to reflect on your mathematical history and existing skills, set up strategies to cope with mathematics and assess which areas need improving;
through instruction, worked examples and practice activities, you will gain an understanding of the following mathematical concepts:
reflecting on mathematics,
reading articles for mathematical information,
making sense of data,
interpreting graphs and charts;
you will be provided with a technical glossary, plus a list of references to further reading and sources of help, which can help you improve your maths skills.
Working with charts, graphs and tables
Introduction openlearn unit LDT_4 More working with charts, graphs and tables, which looks into more ways to present statistical information and shows you how to use charts, graphs and tables to present your own information.
Comments
This might sound stupid but i am trying out a free maths intro...
Trouble is, the articles we need to read and review are so small. How do i zoom out so that i can read the article ??? |
Our users:
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As a student I was an excellent maths student but due to scarcity of time I couldnt give attention to my daughters math education. It was an issue I could not resolve and then I came across this software. Algebrator was of immense help for her. She could now learn the basics of algebra. This was shown in her next term grades. Maria Chavez, TX
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My son used to hate algebra. Since I have purchased this software, it has surprisingly turned him to an avid math lover. All credit goes to Algebrator04-08:
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Math Study Skills-workbook - 4th edition
Summary: This workbook helps learners identify their strengths, weaknesses, and personal learning styles--and then presents an easy-to-follow system to increase their success in mathematics. With helpful study tips and test-taking strategies, this workbook can help reduce ''math anxiety'' and help readers become more effective at studying and learning mathematics |
This 14-lesson series introduces each concept in an easy-to-understand way and by using example problems that are worked out step-by-step and line-by-line to completion. Includes Permutations (79 minutes); Combinations #11;(4..
Having trouble engaging your algebra students? This set of PowerPoint® slides highlights student-centered situations to teach algebra. The problems are rigorous enough to require true problem-solving and accessible enough to allow all stude..
Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understanding of key concepts. 13..
GRADES 9-12. Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understandi..
Challenge students to aim higher in mathematics by exploring advanced-level equations and theories. The approachable and engaging format of this 6-part series conveys simple #11;techniques, how to simplify equations, solution checking, different..
From mean, median, and mode to distribution curves and random variables, students will learn everything necessary to become comfortable and confident statisticians. This 9-title series will aid in the retention of key concepts by making statistics a..
Grade 4 and up. Understanding equations and solving word problems has never been easier or more fun! Introducing algebra through balanced scales is a natural and exciting way to conceptually master fundamental algebraic ideas. The book's visuPrices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. |
MAA Review
[Reviewed by Peter Rabinovitch, on 09/22/2011]
A rule I have found to be true is that any book claiming to be suitable for beginners and yet leading to the frontiers of unsolved research problems does neither well. This book is the exception to that rule.
A glance at the table of contents reveals many of the standard combinatorics topics. As the title implies, they are generally explored via bijections. As a user of combinatorics, rather than a dyed in the wool combinatorialist, I find bijections to be the central core of the subject and so I found this book engaging.
The proofs are very clear, and in many cases several proofs are offered. For example, there may be an algebraic proof of an identity, followed by a bijective proof.
This book could serve several purposes. By focussing on the first half of the book, it could be an excellent choice for a first course in cominatorics for senior undergraduates. By selecting topics and/or moving quickly, it could work well for a more mature audience. The book is at a higher level than Stanton & White, but lower than Stanley, thus it also makes a great reference for people who use combinatorics but are not specialists.
There are many exercises. The back cover claims nearly 1000, and although I didn't count them, I have no reason to doubt this claim. Some are very simple, and some are hard — the back cover claims some are unsolved. Many of the exercises are discussed in an appendix, ranging in detail from mere hints to "draw a diagram" to full but terse solutions. Because there are so many exercises, and because the level of detail of the provided solutions varies so much, an instructor using this text could easily find appropriate problems for assignment for courses of various levels of sophistication.
There are few obvious typos.
On the negative side, the book's web site is empty, and the author uses "quantum numbers" and "quantum binomial coefficients" etc. rather than the more common "q numbers" and "q binomial coefficients."
This is a very nice book that deserves serious consideration.
Peter Rabinovitch is a Systems Architect at Research in Motion, and a PhD student in probability. He's currently thinking about applications of Mallows permutations. |
much
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing stuff. |
Unit Overview: The NCTM Algebra
Standards for Grades 9-12 indicate that "All students should generalize
patterns using explicitly defined and recursively defined functions and
identify essential quantitative relationships in a situation and determine
the class or classes of functions that might model the relationships."
This unit will
provide students with opportunities to extend various patterns in order to
find specific terms in a pattern, by exploring linear, quadratic, and
exponential functions. Investigations will include comparing the properties
of the functions such as domain and range, parameter changes, and recursive
and explicit rules for the functions.
Unit Plan:
The student will recognize, name, and analyze recursive and explicit
patterns in linear, quadratic, and exponential functions
Essential Questions to
Guide the Unit and Focus Teaching and Learning:
1. How do patterns help
us represent, analyze, make predictions, and draw and justify conclusions
from sets of data?
2. How can we use
patterns to communicate mathematical ideas?
3. How do patterns,
relations, and functions help us understand our world?
4. How do you use
patterns, relations, and functions to solve problems?
Unit Strands: 1 = Primary, 2 = Secondary
1
Algebraic Relationships
2
Data & Probability
2
Number and Operations
A1C10: Compare and contrast various forms of representations of patterns.
A1D10: Understand and compare the properties of linear, quadratic and
exponential functions (include domain and range)
A1E10: Describe the effects of parameter changes on quadratic and
exponential functions.
G4B10: Draw or use visual models to represent and solve problems.
Unit Relationship to
Grade-Level Expectations:
In this unit, students develop the
mathematics skills listed in the Targeted Learning column below. While
supporting students in the development of these skills, teachers should consider
students' previous learning and keep in mind their future learning. |
Assessment and LEarning in Knowledge Spaces (ALEKS) is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics they are most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics are also retained.
The Basic Algebra courses will be taught using the software ALEKS. It is possible for students to accelerate through the Basic Algebra sequence by completing the courses early and then following the change of section process. This process starts with printing the Math Emporium Course Section Change Form (See below) and going to see your current Basic Algebra instructor. Have the instructor fill out the top of the form and bring the signed form to the Math Department located in MSB 233 |
Summer Smarts
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Algebra Prep (8) Item #: AlgPrep-summer - The Summer Smarts course in Algebra Prep is for students who want to explore or improve their skills in mathematical concepts required for Algebra I courses. This course will provide an... [more info...]
Language Arts (3-5) Item #: LA35-summer - The Summer Smarts course in Language Arts for students in grade 3- 5 will provide an individualized study plan in the subject based on students' current level of knowledge and skills. Based on... [more info...]
Language Arts (6-8) Item #: LA68-summer - The Summer Smarts course in Language Arts for students in grade 6-8 will provide an individualized study plan in the subject based on students' current level of knowledge and skills. Based on... [more info...]
Math (3-5) Item #: M35-summer - The Summer Smarts course in Mathematics for students in grade 3-5 will provide an individualized study plan in the subject based on students' current level of knowledge and skills. Based on... [more info...]
Math (6-8) Item #: M68-summer - The Summer Smarts course in Mathematics for students in grade 6-8 will provide an individualized study plan in the subject based on students' current level of knowledge and skills. Based on... [more info...]
Math and Language Arts (2) Item #: MLA2-summer - The Summer Smarts course in Mathematics and Language Arts for students in grade 2 will provide an individualized study plan in the subject based on students' current level of knowledge and... [more info...] |
Synopsis
If you are having difficulty learning math, you already know you are not alone. Many people struggle with math. In fact, it is the one discipline in which low grades and low performance are almost universally acceptable because they are so common. For example, a parent is more likely to excuse a lower report card grade in math than in any other subject because that parent probably got lower grades in math when he or she were in school. But why is math so hard to learn? If we look at the nature of learning math it will become easy to see why it is almost a miracle that anyone (without some innate talent) ever learns math. The following "Top 10" can give you insights into how to learn math and help you understand the different pieces that must come together for you to not only learn math but enjoy the journey. 2,636 words.
Found In
eBook Information
ISBN: 9781465934 |
This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. This is intended to be a first course in linear algebra for students who are sophomores or juniors who... |
Solve equations and inequalities, both algebraically and graphically, and
Solving and model applied problems.
Math 113 - Upon successful completion of Math 113 - Finite Mathematics for Social Sciences, students will be able to engage in analyzing, solving, and computing real-world applications of finite and discrete mathematics.
Linear Algebra and Linear Programming
Students will be able to set up and solve linear systems/linear inequalities graphically/geometrically and algebraically (using matrices).
Sets and Counting
Students will be able to formulate problems in the language of sets and perform set operations, and will be able apply the Fundamental Principle of Counting, Multiplication Principle.
Probability
Students will be able to compute probabilities and conditional probabilities in appropriate ways.
Students will be able to solve word problems using combinatorial analysis.
Statistics
Students will be able to represent and statistically analyze data both graphically and numerically.
Graph theory
Students will be able to model and solve real-world problems using graphs and trees, both quantitatively and qualitatively.
Math 140 - Upon successful completion of Math 140 - Mathematical Concepts for Elementary Education I, a student will be able to:
Solve open-ended elementary school problems in areas such as patterns, algebra, ratios, and percents,
Justify the use of our numeration system by comparing it to historical alternatives and other bases, and describe the development of the system and its properties as it expands from the set of natural numbers to the set of real numbers,
Demonstrate the use of mathematical reasoning by justifying and generalizing patterns and relationships,
Display mastery of basic computational skills and recognize the appropriate use of technology to enhance those skills,
Demonstrate and justify standard and alternative algorithms for addition, subtraction, multiplication and division of whole numbers, integers, fractions, and decimals,
Identify, explain, and evaluate the use of elementary classroom manipulatives to model sets, operations, and algorithms, and
Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.
Math 228 - Upon successful completion of Mathematics 228 - Calculus II for Biologists, within the context of biological questions a student will be able, using hand computation and/or technology as appropriate, to:
Analyze first-order difference equations and first-order differential equations and small systems of such equations using analytic, graphical, and numeric techniques, as appropriate,
Analyze basic population models, including both exponential and logistic growth models,
Solve integration problems using basic techniques of integration, including integration by parts and partial fractions,
Formulate and interpret statements presented in Boolean logic. Reformulate statements from common language to formal logic. Apply truth tables and the rules of propositional and predicate calculus,
Formulate short proofs using the following methods: direct proof, indirect proof, proof by contradiction, and case analysis,
Demonstrate a working knowledge of set notation and elementary set theory, recognize the connection between set operations and logic, prove elementary results involving sets, and explain Russell's paradox,
Apply the different properties of injections, surjections, bijections, compositions, and inverse functions,
Solve discrete mathematics problems that involve: computing permutations and combinations of a set, fundamental enumeration principles, and graph theory, and
Gain an historical perspective of the development of modern discrete mathematics.
Math 239 - Upon successful completion of Math 239 - Introduction to Mathematical Proof, a student will be able to:
Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments,
Perform set operations on finite and infinite collections of sets and be familiar with properties of set operations,
Determine equivalence relations on sets and equivalence classes,
Work with functions and in particular bijections, direct and inverse images and inverse functions,
Construct direct and indirect proofs and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness, and
Explain and successfully apply all aspects of parametric testing techniques including single and multi-sample tests for mean and proportion, and
Explain and successfully apply all aspects of appropriate non-parametric tests.
Math 301 - Upon successful completion of Math 301 - Mathematical Logic, a student will be able to:
State the following theorems and outline their proofs: The Soundness Theorem, The Completeness Theorem, The Compactness Theorem, Gödel's First Incompleteness Theorem, and Gödel's Second Incompleteness Theorem,
Evaluate the development of 20th century Mathematical Logic in terms of its relation to the foundations of mathematics,
Explain basic concepts from Recursion Theory, including recursive and recursively enumerable sets of natural numbers, and apply them to theoretical and appropriate applied problems in logic,
Explain basic concepts from Proof Theory, including languages, formulas, and deductions, and use them appropriately, and
Define and give examples of basic concepts from Model Theory, including models and nonstandard models of arithmetic, and use them in appropriate settings in logic.
Math 302 - Upon successful completion of Math 302 - Set Theory, a student will be able to:
Discuss the development of the axiomatic view of set theory in the early 20th century,
Identify the axioms of a system of set theory, for example the Zermelo-Fraenkel axioms, including the Axiom of Choice,
Define cardinality, discuss and prove Cantor's Theorem and discuss the status of the Continuum Hypothesis,
Explain the concept of complementary slackness and its role in solving primal/dual problem pairs,
Classify and formulate integer programming problems and solve them with cutting plane methods, or branch and bound methods, and
Formulate and solve a number of classical linear programming problems and such as the minimum spanning tree problem, the assignment problem, (deterministic) dynamic programming problem, the knapsack problem, the XOR problem, the transportation problem, the maximal flow problem, or the shortest-path problem, while taking advantage of the special structures of certain problems.
Math 333 - Upon successful completion of Math 333 - Linear Algebra II, a student will be able to:
Analyze finite and infinite dimensional vector spaces and subspaces over a field and their properties, including the basis structure of vector spaces,
Use the definition and properties of linear transformations and matrices of linear transformations and change of basis, including kernel, range and isomorphism,
Compute with the characteristic polynomial, eigenvectors, eigenvalues and eigenspaces, as well as the geometric and the algebraic multiplicities of an eigenvalue and apply the basic diagonalization result,
Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization, and
Identify self-adjoint transformations and apply the spectral theorem and orthogonal decomposition of inner product spaces, the Jordan canonical form to solving systems of ordinary differential equations.
Math 335 - Upon successful completion of Math 335 - Foundations of Geometry, a student will be able to:
Compare and contrast the geometries of the Euclidean and hyperbolic planes,
Analyze axioms for the Euclidean and hyperbolic planes and their consequences,
Use transformational and axiomatic techniques to prove theorems,
Analyze the different consequences and meanings of parallelism on the Euclidean and hyperbolic planes,
Demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries,
Use dynamical geometry software for constructions and testing conjectures, and
Use concrete models to demonstrate geometric concepts.
Math 338 - Upon successful completion of Math 338 - Topology, a student will be able to:
Define and illustrate the concept of topological spaces and continuous functions,
Define and illustrate the concept of product topology and quotient topology,
Math 340 - Upon successful completion of Mathematics 340/Biology 340 - Modeling Biological Systems, a student will be able to:
Describe standard modeling procedures, which involve observations of a natural system, the development of a numeric and or/analytical model, and the analysis of the model through analytical and graphical solutions and/or statistical analysis,
Distinguish between analytic and numerical models,
Distinguish between stochastic and deterministic models,
Use software to quantitatively test hypotheses with data and build and evaluate mathematical and simulation models of biological systems,
Present an oral report of a semester-long group project involving the development and the analysis of a model of a biological system, and
Assess the value of model results discussed in the news and in scientific and mathematical literature.
Math 345 - Upon successful completion of Math 345 - Numerical Analysis IMath 346 - Upon successful completion of Math 346 - Numerical Analysis IIProduce a mature oral presentation of a non-trivial mathematical topic.
Math 350 - Upon successful completion of Math 350 - Vector Analysis, a student will be compute and analyze:
Scalar and cross product of vectors in 2 and 3 dimensions represented as differential forms or tensors,
The vector-valued functions of a real variable and their curves and in turn the geometry of such curves including curvature, torsion and the Frenet-Serre frame and intrinsic geometry,
Scalar and vector valued functions of 2 and 3 variables and surfaces, and in turn the geometry of surfaces,
Gradient vector fields and constructing potentials,
Integral curves of vector fields and solving differential equations to find such curves,
The differential ideas of divergence, curl, and the Laplacian along with their physical interpretations, using differential forms or tensors to represent derivative operations,
The integral ideas of the functions defined including line, surface and volume integrals - both derivation and calculation in rectangular, cylindrical and spherical coordinate systems and understand the proofs of each instance of the fundamental theorem of calculus, and
Examples of the fundamental theorem of calculus and see their relation to the fundamental theorems of calculus in calculus 1, leading to the more generalised version of Stokes' theorem in the setting of differential forms.
Math 360 - Upon successful completion of Math 360 - Probability and Statistics I, a student will be able to:
Recognize the role of probability theory, descriptive statistics and inferential statistics in the applications of many different fields,
Define and illustrate the concepts of sample space, events and compute the probability and conditional probability of events, and use Bayes' Rule,
Define, illustrate and apply the concepts of discrete and continuous random variables, the discrete and continuous probability distributions and the joint probability distributions,
Apply Chebyshev's theorem,
Define, illustrate and apply the concept of the expectation to the mean, variance and covariance of random variables,
Define, illustrate and apply certain frequently used discrete and continuous probability distributions, and
Illustrate and apply theorems concerning the distributions of functions of random variables and the moment-generating functions.
Math 361 - Upon successful completion of Math 361 - Probability and Statistics II, a student will be able to:
Recall the basic concepts in probability and statistics and understand the concept of the transformation of variables and moment-generating functions,
Define and examine the random sampling (population and sample, parameters and statistic) data displays and graphical methods with technology,
Recognize and compute the sampling distributions, sampling distributions of means and variances (S2) and the t- and F-distributions,
Explain the contribution of a scientific paper to the field of biomathematics,
Develop and lay the foundation to the solution of a problem in biomathematics, and
In addition, seniors taking this course to fulfill the seminar requirement in the biology degree program should expect to develop and write a grant proposal to do research in the area of biomathematics.
Math 390 - Upon successful completion of MATH 390 - History of Mathematics, a student will be able to:
Trace the development and interrelation of topics in mathematics up to the undergraduate level,
Be familiar with current standards (state, national, and NCTM), both content and process, for the secondary mathematics curriculum,
Be able to do both short and long term planning of lessons and units that meet current standards for the secondary mathematics curriculum,
Have taught mathematics lessons which they have planned to small groups of fellow students and/or area 7-12 students,
Be able to assess student learning in mathematics,
Be able to find research on the teaching and learning of content in the secondary mathematics curriculum and analyze teaching ideas and textbook presentations of said content in light of the found research, and
Be familiar with technology currently used in the mathematics classroom. |
Suggested Project Topics
Here are a few ideas for project topics for final year, higher diploma, and
Masters students. The only common thread is that they combine some
mathematics with compuation.
1. Program a LEGO Robot using Matlab
The goal will be to learn how to programme real-time systems,
model-based design, and develop
object oriented Matlab code. These can be applied to
contoling LEGO Mindstrom NXT robot.
2. The Singular Value Decomposition, and it's applications.
The singular value decomposition (SVD) is an important
factorization of a matrix with interesting applications to
a wide variety of areas such as image and signal processing,
data compression, computational tomography, etc..
For one example of the the SVD can be applied to problems involving in face
recognition, see Singular Value Decomposition, Eigenfaces, and 3D Reconstructions by Neil Muller, Lourenco Magaia,
B.M. Herbst
You should consider this project if you like Linear Algebra. Some
computing will be essential, but not necessarily
anything too difficult.
3. Numerical Algorithms for Parallel Computers
Many classical numerical methods were designed for single-processor computers.
Examples include Gaussian elimination
or Numerical Integration. With the advent of parallel,
multiprocessor and distributed systems, there is a need to revisit
many of these methods and to see how they can be adapted for parallel
computation.
A different example is Schwarz Methods for linear boundary
value problems. These have existed for over 100 years, but are being
``rediscovered'' because they are so suitable for parallel computers
A project on this topic would mainly involve programming and algorithm
design. Code could be tested on some Linux computers running software to
emulate parallel and distributed systems.
The student who does this project should like programming.
It would be useful
to have studied numerical analysis.
4. Simulating Small-World Networks
Many networks that occur naturally have two properties: clustering and
short average path-lengths. This is called the small world
phenomenon and is related to research activities in very diverse
areas. To verify this, check a web search engine for such topics as
Six Degrees of Separation and The Kevin Bacon Game
A student working on this project will, at the very least, read
a number of articles on the topic, learn enough mathematics to
understand some of the theorems and conjectures in the area, and write
some computer programs to simulate these networks.
The project would suit a student with interests in programming and
graph theory. Some knowledge is stochastic processes and Markov chains
would be useful.
5. Topics in Numerical Analysis
Numerical Analysis is the area of mathematics that is concerned
with the design and analysis of methods and algorithms for obtaining
useful solutions to mathematical problems. Two of the main sources of
problems are differential equations and linear algebra. The
applications are far too numerous to mention.
The interested student should browse a few books in the library. For
example
Afternotes on Numerical Analysis and
Afternotes goes to Graduate School
(G.W. Stewart),
Introduction of Numerical Analysis (Stoer and
Bulirish),
Depending on the students' interests, projects may have little or no
computing aspects, or may be strongly focused on computational
problems, or something in between.
6. Some topic of mutual interest
Why not come up with your own idea? A good place to start
would be the Education articles in
SIAM
Review. Or you could go to the
library and have a look at such titles as |
Algebra: A Self-Teaching Guide
With a "learn-by-doing" approach, it reviews and teaches elementary and some intermediate algebra. While rigorous enough to be used as a college or ...Show synopsisWith a "learn-by-doing" approach, it reviews and teaches elementary and some intermediate algebra. While rigorous enough to be used as a college or high school text, the format is reader friendly, particularly in this Second Edition, and clear enough to be used for self-study in a non-classroom environment. "Pre-test" material enables readers to target problem areas quickly and skip areas that are already well understood. Some new material has been added to the Second Edition and redundant or confusing material omitted. The first chapter has undergone major revision. Chapters feature "post-tests" for self-evaluation. Thousands of practice problems, questions and answers make this algebra review a unique and practical |
Lynn Foshee Reed
Lynn Foshee Reed has been a mathematics instructor at Maggie L. Walker Governor's School (MLWGS) in Richmond, Virginia, since 1998. Reed primarily taught calculus – AP Calculus AB as well as dual enrollment Calculus I, Calculus II, and Multivariable Calculus – in conjunction with Virginia Commonwealth University. She has also taught Algebra II, Trigonometry and Mathematical Analysis, and History of Mathematics at MLWGS. Previously, Reed taught mathematics at Virginia Tech for eight years.
Reed originates from southern Illinois and she received her Bachelor of Arts in Mathematics and minored in chemistry at the University of Evansville. After two years of teaching high school, she enrolled at Ohio State University where she received both her Master of Arts and Master of Science in Mathematics. Reed earned her Gifted Education endorsement in 2002 and achieved National Board Certification in Adolescent and Young Adult Mathematics in 2009.
Reed is Secondary Mathematics Representative on the board of the Virginia Council of Teachers of Mathematics (VCTM), and she was VCTM's representative to the Virginia Educational Technology Advisory Committee. Reed is a past president of the Greater Richmond Council of Teachers of Mathematics (GRCTM). She is one of the coordinators of the Calculus Network of Richmond, and she regularly presents at GRCTM and VCTM conferences. Reed is a more than 20-year member of both the National Council of Teachers of Mathematics and the Mathematical Association of America (MAA). Reed has experience as an AP Reader of AP Calculus exams, and she is a frequent calculus instructor for the Virginia Advanced Study Strategies review sessions.
Lynn welcomes opportunities to stretch her understanding of the world in general and mathematics in particular, and tries to demonstrate a delight in mathematics and joy in learning new things to her students and colleagues. She participated in the Institute for the History of Mathematics and Its Use in Teaching and the MAA's summer 2005 Professional Enhancement Program workshop on the "Mathematics of Asia's Past." She has participated in MAA mini-courses, most recently "Geometry and Art" and "Dance and Mathematics" at the 2012 Joint Mathematics Meetings. Lynn brought university-affiliated guest speakers to her school to expose students to mathematics in unexpected contexts like Sudoku, origami, sports, and history. "I have always been a proponent of using multidisciplinary explorations in teaching mathematics, and I emphasize to my students how mathematics opens doors to many careers and fields of interest. The mission of my school emphasizes government and international studies, and I strive to instill the viewpoint that mathematics permeates and supports nearly all other disciplines, and that as future leaders, they will benefit from studying as much mathematics as possible."
Reed is serving her Fellowship at the National Science Foundation, Arctic and Antarctic Sciences Division, Office of Polar Programs. |
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notation (e.g., 4.23e-7 as shorthand for 0.000000423) will work; do
not put a space between the digits and the letter "e."
Questions that do not have an exact numerical answer accept a small
range of answers as correct. The precision required depends on the
problem statement. When in doubt, don't round off your final answer.
In this class, there is no such thing as an answer that is "too
precise." Never round off intermediate calculations:
see Assignment 0.
Troubleshooting
Most technical problems with the online book and assignments
have one of three causes:
Clearing Cookies
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uses cookies to store your answers to assignments and to remember
your student ID when you log in to do an assignment or check your
scores.
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Tic the box to
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"Delete entire cache"), and click the "Delete"
button. |
Mathematical Modes of Thought
Overview
This is a course in modern mathematics. We will be exploring a number of topics that have been developed fairly recently in the mathematical world.
This class will be nothing like your intermediate algebra course. If you prefer equations and expressions, this is not the class for you. We will be looking at topics that might not seem like math to you. Many of these topics will be explored in context of their applications.
The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics then expressions and equations.
Technical Expectations
To be successful in this course, you will need some technical skills. Most important is access to a computer with a reliable internet connection, and the ability to operate that computer and a web browser. If you are reading this, you're probably OK for this part. There will be a couple assignments that ask you to upload files, cut-and-paste internet addresses (URLs), etc. In most cases, a non-technical alternative is available if needed.
Is this course right for you?
Math 1080 is a terminal math course, meaning it does not prepare you for any other math class. This course is intended only for people who will be seeing only one mathematics class in college.
Hopefully you went to an adviser who knows your educational goals when deciding which class to take. If you're not sure if this class is right for you, please feel free to email me and I'd be happy to discuss it with you.
Textbook
I got tired of students having to pay over $100 for the book. So instead of using a traditional textbook, a book written by a friend from graduate school, David Lippman. The textbook is available online at and is free.
Format of the Course
Each week there will be a specific set of material to learn, and assignments and tests on that material. There will be fixed due-dates for those assignments. However, the course is asynchronous, which means that you can log in any time during the week that is convenient for you and complete the assignments.
In addition to lecture, each week, you will be given a reading assignment. Attending Lectures and reading the textbook will be your primary way to learn the material for the course.
During class there will be frequent assignment, these can range from quizzes to group work. These assignments cannot be made up and make up a significant portion of your grade.
Outside of class a discussion forum will be provided where you can ask questions about the reading, and discuss the material with me and your classmates.In class you can ask me and we can discuss any problems you are having. Usually if you are having trouble, others are as well.
There will be a set of homework exercises assigned each week. The online homework exercises are required, and graded. However, if you miss a question, it will show the answer, allowing you to self-diagnose your mistake, and then you can try similar problems until you get the questions correct. You can ask questions in the discussion board about any homework questions you have difficulty with.
For each section there will be a "Skills Quiz". This will be a test consisting of problems similar, but not necessarily identical, to the homework problems, that test your understanding of the material and your ability to perform any procedures or techniques presented in that chapter. These questions will be numerical, multiple-choice, matching, or fill-in-the-blank.
Additionally, each week there will be an assignment not from the book. This assignment will be a more open-ended question that usually requires a bit more work, conceptual understanding, possibly some outside research, and may require a written solution or explanation. In some cases these may be collaborative assignments with intermediary due dates in the middle of the week. Be sure to keep track of the due dates.
Except in the case of collaborative assignments requiring feedback to fellow students, there are no graded forum response, email, or log-in frequency requirements. However, I strongly encourage you to not wait until the last day of the week to begin your assignments, as this does not allow time to seek out assistance if needed.
Midway through the course there will be a midterm exam and at the end of the course there will a final exam.
Learning Outcomes
The course learning outcomes (aka objectives) describe what abilities and skills a successful student is expected to develop and demonstrate in this course. While often related, these are separate from the course content (the specific topics we'll be covering)
Demonstrate a positive attitude towards mathematics and an appreciation for its power and uses.
Explore new and unfamiliar problems and employ critical thinking skills.
Form and communicate generalizations discovered through individual or group investigations.
Communicate methods of solutions and solutions to problems for the clarity of the receiver.
Model and solve problems using graphical methods.
Analyze and interpret data, as well as calculate statistical mean and median and use these to describe data.
Represent data using a histogram and/or other graphical forms.
Solve problems using algorithms or formulas.
Examine multicultural perspectives of at least one mathematical topic studied.
Solve, analyze, and effectively communicate the solution to problems of the instructor's choice.
Participate actively and responsibly in all course activities.
Within each sections folder, you will find a list of that sections topic-based learning outcomes, and how they related back to these course outcomes. You will be able to meet these learning outcomes by reading the book, making sure you understand the examples in the book, and working through the online exercises, seeking out assistance if you have difficulties. You will, of course, also need to apply your critical thinking skills, since part of the purpose of this course is to expand your ability apply the skills you've learned to new and different scenarios. In real life, problems rarely tell you how to solve them :)
Late Work Policy
The online Homework and Skills Test deadlines are extremely firm. The link to these assignments will actually disappear at midnight on the due date, and the assignment must be completed before midnight. Because of this, I strongly recommend that students not wait until 11:50pm to start the test, in case if they have problems logging in or something.
The Graded Assignments deadlines are also very firm, since you have the entire week to work on them. If a graded assignment is turned in late, I will never give more than 50% of the possible points.
If something major comes up (a death in the family, hospitalization, etc.), go ahead and email me or call me to let me know, and we can work something out.
Getting Help
The discussion board is a forum where you can ask questions about the reading or homework, and get help from me or your classmates. The idea is to have the class operate like a study group - with all of you working together to further your learning. This is what distinguishes an online class from a traditional distance learning or math lab course.
Use the Discussion Board to ask for help on problems you don't understand how to do. If you do understand how to do the problems, help out your classmates by answering questions on the discussion board.
I will monitor the homework discussion boards, and will respond to questions if they go unanswered, or if someone provides an incorrect response. If you have additional questions, didn't understand the answer someone gave you, or have a question that has gone unanswered, don't hesitate to email me and ask questions. However, please use the discussion boards first, so that others can benefit from your questions.
I can't stress enough that without being able to see the expression on your face, there's no way for me to judge if you understand my or a fellow student's explanation to your questions. So, you need to be proactive about your learning, and ask for more explanation when you need it. Again, you can do this via email to me, or in the discussion boards.
In addition to the discussion board and emailing me, you are also welcome to come see me on-campus if your schedule allows. See the Instructor Information to see what my office hours are this quarter.
Additionally, you can get help from the drop-in tutors at the Academic Support Center on either campus. Be aware that not all tutors have taken this math course, and may have difficulty helping you. Writing tutors are also available to help with writing assignments.
Instructor Contact
You can contact me via the discussion boards, email, messages, by phone, or in person.
If you have general questions about the course, you can ask them in the "Ask John" discussion forum. If the question is of a personal nature, feel free to email me.
If you have questions about the homework or readings, you can ask them in class. Feel free to email me, call me, or visit me in my office for additional help.
When you post a message or email me, please understand that I am not online all the time. Please allow at least 24 hours for me to respond to your questions, possibly longer on the weekends (up to 48 hours).
Grading
The first week of class there is a bio assignment and syllabus quiz.
Each week you will have online Homework.
Each section you will have a Skills Quiz.
Each section there will be a written/extended assignment.
There will be a midterm and final test.
The midterm exam will count 20% of your course grade.
In class assignments will count 20% of your course grade.
Online homework will count for 15% of your course grade.
Skills Quizzes will count for 15% of your course grade.
Written assignments will count for 15% of your course grade.
The Final will count for 20% of your course grade.
Your weighted percent in the class will be converted to a decimal grade via this scale:
90-100%: 3.5-4.0
80-89% : 2.5-3.4
75-79% : 2.0-2.4
70-74%: 1.5-1.9
60-69%: 0.7-1.4
Below 60%: 0.0
Academic Integrity
Online courses have the same academic integrity as any other college course. You can trust that I will respond to your questions and comments in a timely manner, as well as be timely and fair in grading submitted assignments.
As your instructor, I trust that you will make your best effort to complete the activities in a timely manner and to the best of your abilities. If there is an unforeseen change in your schedule feel free to contact me for alternative arrangements. I expect that the work you submit for this course will be your own work. Cheating and/or plagiarism will not be tolerated. Please refer to the college's Academic Dishonesty policy for more details.
Online Etiquette
Much has been written about online etiquette. The old saying, "Sticks and stones may break my bones, but words will never hurt me." is suddenly untrue. Words are our sole means of communication. Many times a sarcastic phrase you make to a friend is softened with a smile or eye contact. In an online situation, that same phrase can be very hurtful if read differently. Remember treat everyone the same way you would want to be treated: with respect.
There are ways to express emotions without words. These are called emoticons. You've probably seen several already in computer writing: ;-) :) :o) :-( etc., These are actually faces turned on their side to represent emotions. They take the place of body language and facial expressions that are a natural part of communication. In this setting, it's difficult sometimes to discern between sarcasm and criticism. Using emoticons can often convey the context of the comment when words can't.
Most importantly, this class will be free of sexual, verbal, and racial discrimination or harassment.
NC Policy
The NC policy has changed beginning with this semester. For a
100% refund the date is August 23 and for a 50% refund the date is
September 1. The last day to obtain an NC is Friday Oct. 23. This
is a hard deadline and will be enforced as such. The department
will not approve any late NC requests. Students must request an
NC through MetroConnect; faculty approval is no longer required.
Holidays: Observance of religious holidays follows College policy, which is
posted on the web at in the Academic
and Campus Policies for Students section. Each student is responsible
for understanding and abiding by the policy.
Accommodations for Students with Disabilities:
The Metropolitan State College of Denver is committed to making reasonable accommodations to assist individuals with disabilities in reaching their academic potential. If you have a disability that may impact your performance, attendance, or grades in this class and are requesting accommodations, then you must first register with the Access
Center, located in the Auraria Library, Suite 116, 303-556-8387. Faculty Notification Letter, I would be happy to meet with you to discuss your accommodations. All discussions will remain confidential. Further
information is available by visiting the Access Center website |
Saxon Advanced Math Home Study Kit
Prepare your students for future success in calculus, chemistry,
physics, and social sciences! The 125 incremental lessons provide
in-depth coverage of trigonometry, logarithms, analytic geometry, and
upper-level algebraic concepts. Includes continued practice of
intermediate algebraic concepts and trigonometry introduced in Algebra
2 and features new lessons on functions, matrices, statistics, and the
graphing calculator. Includes test and answer key booklets. 748 pages,
hardcover.
Wordly Wise 3000, Grade 11, 2nd Edition
Three thousand carefully selected words taken from literature,
textbooks, and SAT-prep books are the basis of this exciting vocabulary
series that teaches new words through reading, writing, and a variety
of exercises. Each lesson's alphabetized word list gives
pronunciations, parts of speech, and concise definitions, and uses each
word in a sentence. Interesting, engaging, and acting as a mnemonic
anchor for the word, sentences are anything but boring! Comprehension
of the vocabulary words is facilitated and reinforced through the five
different exercises repeated in each lesson; new for the 2nd, expanded
edition of Wordly Wise, reading first strategies as well as Greek and
Latin word studies with prefixes, suffixes, parts of speech, synonyms,
antonyms, and analogies.
Wordly Wise 3000, Grade 11, Test Booklet with Answer Key
This Wordly Wise 3000 Test Booklet, 2nd Ed. accompanies Wordly Wise 3000, Book 11, 2nd Ed.
Tests are multiple choice with questions including finding the
antonym/synonym or finding the best word to complete a sentence. Final
test questions are based upon an included passage. Line-listed answers
are included. 110 pages, softcover. Grade 11.
Daily Writing FUNdamentals, Grades 11-12
Provides a daily, systematic, approach to building writing skills
throughout grades 11-12! Thirty-two units of five daily questions and
writing applications are included, focusing on essential narrative,
persuasive, and expository writing models. Easily incorporated into
5-10 minute blocks, students will learn how to assess their own
progress and writing fluency. 110 pages, softcover. Grades 11-12.
Exploring Creation with Chemistry, 2 Volumes: Second Edition
The award-winning chemistry course that took the homeschool community
by storm is now even better! Featuring Dr. Wile's easy-to-understand
explanations---revised for extra clarity---this Christ-centered modular
course offers a rigorous foundation in high-school/college-prep
chemistry. The colorful, user-friendly text is designed specifically
for home learners and employs experiments using only readily available
chemicals and equipment. Completion of Algebra 1 is a prerequisite.
Includes a 272-page test/solutions book. 603 pages, hardcover. This
course is designed for sophomores in high school
Streams of Civilization, Volume 2
This book covers the events of world history with an emphasis on
European and American culture since the Reformation. Each chapter
traces a particular theme within a particular time period. The
principal themes include the history of Christianity and philosophy
with their results in culture, politics, economics, society, science,
and technology. A time line at the beginning of each chapter will help
the reader to see the chronological relationships between the events
discussed in the text. Throughout the text, particular points of
interest, focusing on specific individuals and events, provide further
information. Maps and photographs, as well as artwork of a particular
period, add to the overall impact of the book. Thought-provoking
questions given at the end of each chapter will encourage students to
think through the Christian implications of the material and its
relevance for today's world. In addition, a list of important words and
concepts at the end of the chapter will aid the student in focusing on
the most significant ideas discussed in the chapter. Suggested projects
can also enliven the topics being covered as a particular activity is
carried out by an individual or a class. A reading list is provided to
suggest resources for further study; an extensive index will also
enable the student to use the book for reference in years to come.
Streams of Civilization Volume 2, Tests
Streams of Civilization, Volume 2, Teacher's Manual
The answer key for Streams of Civilization, Volume 2 was developed by
the staff on Christian Liberty Press to help instructors be as
successful as possible in teaching this history course. The present
text, which was rewritten by Garry Moes, is a significant revision of
the original 1980 edition entitled Streams of Civilization: The Modern
World to the Nuclear Age, Volume 2. This answer key reflects these
comprehensive changes. |
Launched in May, 2000, with the support of an NSF grant, Project WELCOME is a new part of the
SUMMA Program. WELCOME
brings together elements of three MAA program themes: academic technology, professional development, and promoting involvement of historically underrepresented groups. The general goals include:
Developing at minority serving institutions a community of teachers who create and use interactive, computer based, explorations of mathematics
Creating an internet library of these explorations available to teachers and students everywhere
Promoting the use of interactive explorations in teaching mathematics
Technology
The interactive explorations are integrated environments which combine graphical, dynamical, symbolic, textual, and numerical representations of mathematical ideas and relations. Users interact with these environments in the familiar point and click idiom of internet web pages. The goal of each activity is to encourage students to experiment with some mathematical context by manipulating aspects of the environment and observing the results. The interactions are intended to be so natural that the environments take on a kind of virtual realism that brings mathematical constructs to life. This can take the form of moving and deforming geometric objects (in the style of Geometer's Sketchpad), but can also involve interacting with symbolic, logical, and numerical aspects of an environment.
A past MAA effort, the Interactive Mathematical Text Project (IMTP), demonstrated that empowering teachers to create these activities is both feasible and desirable. In particular, using software called Mathwright Author, IMTP participants (among others) have created a large number of educationally interesting and attractive explorations. A showcase of these activities is freely available at the Mathwright website. Visitors to that web site can also download free software called the Mathwright Library Player (2.1), necessary for using the activities.
One of the goals of Project WELCOME is to produce series of interactive explorations that are directly tied to specific courses. The materials that are produced by the project will be distributed at a WELCOME Library on the internet, starting in the summer or fall of 2001.
Mathematical Involvement of Underrepresented Groups
The MAA has an ongoing interest in increasing the participation in mathematics of historically underrepresented groups. Project WELCOME is founded on the belief that technology can make a contribution in this area. The Project Directors believe that interactive mathematical explorations are a particularly attractive and powerful lure to the investigation of mathematical ideas. It is hoped that this lure will help attract students who might otherwise not elect to study mathematics.
In order to bring interactive mathematical explorations to these students, WELCOME is enlisting the aid of their teachers. The Project will build a community of Mathwright developers among faculty in institutions which predominantly serve the target populations. The role of teachers in developing, as well as using, Mathwright activities is intentional and significant. For one thing, creating the activities themselves will give the teachers a greater sense of ownership, and will assure that the activities will be compatible with the instructional goals and philosophies of these teachers. There is another reason to involve teachers as developers. Presumably, the historical under-participation among some student populations reflects particular obstacles that these students face. If so, then faculty at institutions which serve these populations may have special insights about the nature of the obstacles and strategies for overcoming them. Such insights will be a valuable resource in developing Mathwright activities for Project WELCOME.
Professional Development
Project WELCOME has many features in common with MAA professional development programs. The faculty developers will each be teamed with an experienced Mathwright user who will serve as a mentor and collaborator. The goals of the project go beyond training new Mathwright developers. The idea is to foster a community of teachers using interactive explorations. The community will interact electronically through email and a project web page. In addition, participants will get together at national MAA meetings, where they will be encouraged to make presentations of their work. In particular, there will be several contributed paper presentations related to WELCOME at the January, 2001 meeting in New Orleans.
Project Activities
Each year of the project begins with a workshop for new faculty particpants and mentors. In 2000, the summer workshop was held in Seattle, and was attended by 6 new faculty developers, 4 mentors, as well as the project directors. During the 2000-2001 academic year the developer teams will work on Mathwright activities related to the classes of the new faculty developers. Work in progress will be shared at the winter 2001 math meetings, and more completed work at the summer meeting. At about the same time, a new class of faculty developers will be meet in a workshop, as mentioned earlier.
The materials that are produced by WELCOME participants will be reviewed and critiqued by an outside board of editors. Ultimately, the finished products will be distributed over the internet at a Project WELCOME website. |
Available Exclusively on Video
Because of the highly visual nature of the subject matter, these courses are available only on video. Mastering the Fundamentals of Mathematics features hundreds of graphics and on-screen equations that complement the professor's lessons to enhance your learning experience. The Secrets of Mental Math also contains hundreds of visual elements, including step-by-step walkthroughs of mental math problems, graphics, and illustrations.
COURSE DESCRIPTION
Course
1
of
2:
Secrets of Mental Math Professor
Professor Arthur T. Benjamin,
Harvey Mudd College Ph.D., Johns Hopkins University
Improve and expand your math potential—whether you're a corporate executive or a high-school student—in the company of Professor Arthur T. Benjamin, one of the most entertaining members of The Great Courses faculty. The Secrets of Mental Math, his exciting 12-lecture course, guides you through all the essential skills, tips, and tricks for enhancing your ability to solve a range of mathematical problems right in your head. Along the way, you'll discover how mental mathematics is the gateway to success in understanding and mastering higher fields, including algebra and statistics.
Course Lecture Titles
12
Lectures
30
minutes/lecture
1.
Math in Your Head!7.
Intermediate Multiplication2.
Mental Addition and Subtraction8.
The Speed of Vedic Division3.
Go Forth and Multiply9.
Memorizing Numbers4.
Divide and Conquer10.
Calendar Calculating
The fun continues in this lecture with determining the day of the week of any date in the past or in the future. What day of the week was July 4, 2000? How about February 12, 1809? You'd be surprised at how easy it is for you to grasp the simple mathematics behind this handy skill.
5.
The Art of Guesstimation11.
Advanced Multiplication6.
Mental Math and Paper12.
Masters of Mental MathWhether you're a high-school student preparing for the challenges of higher math classes, an adult who needs a refresher in math to prepare for a new career, or someone who just wants to keep his or her mind active and sharp, there's no denying that a solid grasp of arithmetic and prealgebra is essential in today's world. In Professor James A. Sellers' engaging course, Mastering the Fundamentals of Mathematics, you learn all the key math topics you need to know. In 24 lectures packed with helpful examples, practice problems, and guided walkthroughs, you'll finally grasp the all-important fundamentals of math in a way that truly sticks.
Course Lecture Titles
24
Lectures
30
minutes/lecture
1.
Addition and Subtraction
This introductory lecture starts with Professor Sellers' overview of the general topics and themes you'll encounter throughout the course. Then, plunge into an engaging review of the addition and subtraction of whole numbers, complete with several helpful tips designed to help you approach these types of problems with more confidence.
13.
Exponents and Order of Operations
Explore a fifth fundamental mathematical operation: exponentiation. First, take a step-by-step look at the order of operations for handling longer calculations that involve multiple tasks—complete with invaluable tips to help you handle them with ease. Then, see where exponentiation fits in this larger process.
2.
Multiplication
Continue your quick review of basic mathematical operations, this time with a focus on the multiplication of whole numbers. In addition to uncovering the relationship between addition and multiplication, you'll get plenty of opportunities to strengthen your ability to multiply two 2-digit numbers, two 3-digit numbers, and more.
14.
Negative and Positive Integers
Improve your confidence in dealing with negative numbers. You'll learn to use the number line to help visualize these numbers; discover how to rewrite subtraction problems involving negative numbers as addition problems to make them easier; examine the rules involved in multiplying and dividing with them; and much more.
3.
Long Division
Turn now to the opposite of multiplication: division. Learn how to properly set up a long division problem, how to check your answers to make sure they're correct, how to handle zeroes when they appear in a problem, and what to do when a long division problem ends with a remainder.
15.
Introduction to Square Roots
In this lecture, finally make sense of square roots. Professor Sellers offers examples to help you sidestep issues many students express frustration with, shows you how to simplify radical expressions involving addition and subtraction, and reveals how to find the approximate value of a square root without using a calculator.
4.
Introduction to Fractions
Mathematics is also filled with "parts" of whole numbers, or fractions. In the first of several lectures on fractions, define key terms and focus on powerful techniques for determining if fractions are equivalent, finding out which of two fractions is larger, and reducing fractions to their lowest terms.
16.
Negative and Fractional Powers
What happens when you have to raise numbers to a fraction of a power? How about when you have to deal with negative exponents? Or negative fractional exponents? No need to worry —Professor Sellers guides you through this tricky mathematical territory, arming you with invaluable techniques for approaching these scenarios.
5.
Adding and Subtracting Fractions
Fractions with the same denominator. Fractions with different denominators. Mixed numbers. Here, learn ways to add and subtract them all (and sometimes even in the same problem) and get tips for reducing your answers to their lowest terms. Math with fractions, you'll discover, doesn't have to be intimidating—it can even be fun!
17.
Graphing in the Coordinate Plane
Grab some graph paper and learn how to graph objects in the coordinate (or xy) plane. You'll find out how to plot points, how to determine which quadrant they go in, how to sketch the graph of a line, how to determine a line's slope, and more.
6.
Multiplying Fractions
Continue having fun with fractions, this time by mastering how to multiply them and reduce your answer to its lowest term. Professor Sellers shows you how to approach and solve multiplication problems involving fractions (with both similar and different denominators), fractions and whole numbers, and fractions and mixed numbers.
18.
Geometry—Triangles and Quadrilaterals
Continue exploring the visual side of mathematics with this look at the basics of two-dimensional geometry. Among the topics you'll focus on here are the various types of triangles (including scalene and obtuse triangles) and quadrilaterals (such as rectangles and squares), as well as methods for measuring angles, area, and perimeter.
7.
Dividing Fractions
Professor Sellers walks you step-by-step through the process for speedily solving division problems involving fractions in this lecture filled with helpful practice problems. You'll also learn how to better handle calculations involving different notations, fractions, and whole numbers, and even word problems involving the division of fractions.
19.
Geometry—Polygons and Circles
Gain a greater appreciation for the interaction between arithmetic and geometry. First, learn how to recognize and approach large polygons, including hexagons and decagons. Then, explore the various concepts behind circles (such as radius, diameter, and the always intriguing pi), as well as methods for calculating their circumference, area, and perimeter.
8.
Adding and Subtracting Decimals
What's 29.42 + 84.67? Or 643 + 82.987? What about 25.7 – 10.483? Problems like these are the focus of this helpful lecture on adding and subtracting decimals. One tip for making these sorts of calculations easier: making sure your decimal points are all lined up vertically.
20.
Number Theory—Prime Numbers and Divisors
Shift gears and demystify number theory, which takes as its focus the study of the properties of whole numbers. Concepts that Professor Sellers discusses and teaches you how to engage with in this insightful lecture include divisors, prime numbers, prime factorizations, greatest common divisors, and factor trees.
9.
Multiplying and Dividing Decimals
Investigate the best ways to multiply and divide decimal numbers. You'll get insights into when and when not to ignore the decimal point in your calculations, how to check your answer to ensure that your result has the correct number of decimal places, and how to express remainders in decimals.
21.
Number Theory—Divisibility Tricks
In this second lecture on the world of number theory, take a closer look at the relationships between even and odd numbers, as well as the rules of divisibility for particular numbers. By the end, you'll be surprised that something as intimidating as number theory could be made so accessible.
10.
Fractions, Decimals, and Percents
Take a closer look at converting between percents, decimals, and fractions—an area of basic mathematics that many people have a hard time with. After learning the techniques in this lecture and using them on numerous practice problems, you'll be surprised at how easy this type of conversion is to master.
22.
Introduction to Statistics
Get a solid introduction to statistics, one of the most useful areas of mathematics. Here, you'll focus on the four basic "measurements" statisticians use when gleaning meaning from data: mean, media, mode, and range. Also, see these concepts at work in everyday scenarios in which statistics plays a key role.
11.
Percent Problems
Use the skills you developed in the last lecture to better approach and solve different kinds of percentage problems you'd most likely encounter in your everyday life. Among these everyday scenarios: calculating the tip at a restaurant and determining how much money you're saving on a store's discount.
23.
Introduction to Probability
Learn more about probability, a cousin of statistics and another mathematical field that helps us make sense of the seemingly unexplainable nature of the world. You'll consider basic questions and concepts from probability, drawing on the knowledge and skills of the fundamentals of mathematics you acquired in earlier lectures.
12.
Ratios and Proportions
How do ratios and proportions work? How can you figure out if a particular problem is merely just a ratio or proportion problem in disguise? What are some pitfalls to watch out for? And how can a better understanding of these subjects help save you money? Find out here.
24.
Introduction to Algebra
Professor Sellers reviews the importance of math in daily life and previews the next logical step in your studies: Algebra I (which involves variables). Whether you're planning to take more Great Courses in mathematics or simply looking to sharpen your mind, you'll be sent off with new levels of confidence. |
Beginning Algebra - With Cd - 4th edition
Summary: For college-level courses in beginning or elementary algebra.
Elayn Martin-Gay's success as a developmental math author and teacher starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions provide new pedagogy and resources to build student confidence, help students develop basic skills and understand concepts, and provide the highest ...show morelevel of instructor and adjunct support.
Martin-Gay's series is well known and widely praised for an unparalleled ability to:
Relate to students through real-life applications that are interesting, relevant, and practical.
Martin-Gay believes that every student can:
Test better: The new Chapter Test Prep Video shows Martin-Gay working step-by-step video solutions to every problem in each Chapter Test to enhance mastery of key chapter content.
Study better: New, integrated Study Skills Reminders reinforce the skills introduced in section 1.1, "Tips for Success in Mathematics" to promote an increased focus on the development of all-important study skills.
Learn better: The enhanced exercise sets and new pedagogy, like the Concept Checks, mean that students have the tools they need to learn successfully.
Martin-Gay believes that every student can succeed, and with each successive edition enhances her pedagogy and learning resources to provide evermore relevant and useful tools to help students and instructors achieve success. ...show lessFLORIDA BOOKSTORE Gainesville, FL
2004 Hardcover Good
$6.00 +$3.99 s/h
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BookSleuth Danville, CA
Fast Shipping ! Used books may not include access codes, CDs or other supplements.
$7.20 +$3.99 s/h
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Millennial Technologies OK Oklahoma City, OK
2005 Good
$7 |
Secondary menu
Math and Media
In this class students will learn to apply math towards the creation of time based media. They will learn to author their own programs that analyze, convert, effect, and manipulate real time video and audio streams towards their own ends. Music is made, video is sequenced and stories are told Through the use of algorithms, conditionals, and operators. Media production is now firmly located in the digital domain and math has become an essential and flexible creative tool. Whereas packaged digital programs are designed around preconceived tasks, in this class artists pick up the equivalent of a stick, cram it in the digital morass and turn history on it's ear. The proof of this mathematics is in the making of media. This class will use Max/MSP/Jitter, a graphically based authoring program that allows one to program in a visual environment. In addition to real time video and audio processing students will learn to create 2D and 3D graphics and imbue them with interactive behaviors. |
Integral Calculus: An Introduction to the Anti-Derivative
If a function has an integral, it is said to be integrable. The function for which the integral is calculated is called the integrand. The region over which a function is being integrated is called the domain of integration.
In this class, the presenter will introduce the concept of Integration. We will describe it as simply, the reverse process of differentiation, hence, also called Anti-Differentiation.
The integral may be found without a definite specification or for a particular region leading to the development of indefinite & definite integrals. In case of the definite integrals, the domain of integration is defined by specifying the upper & lower limits of the enclosed region. Also, definite integrals may not be referred to as anti-derivatives which is a term used only for indefinite integrals in accordance with the fundamental theorem of calculus. Besides, the indefinite integral may be a constant or a function of the independent variable however, the definite integral is always constant.
We will also discuss about the geometrical & physical representation & significance of the integral. When we look into the practical applications of integrals, they appear in a number of practical situations.
Consider a swimming pool. If it is rectangular, then from its length, width, and depth we can easily determine the volume of water it can contain (to fill it), the area of its surface (to cover it), and the length of its edge (to rope it). But if it is oval with a rounded bottom, all of these quantities call for integrals. The best of problems in Physics too involve the integral.
About Rishabh Dev (Teacher)
Rishabh Dev is a teacher in Calculus & other mathematics disciplines. Dev has a remarkable style of delivering the very advanced math concepts useful for the various competitive exams in a very basic manner understandable to all.
He has developed innovative ways of teaching mathematics to his students. Rishabh teaches online and also takes face-to-face math classes for students in Bangalore / Bengaluru Area, Karnataka |
Scotch College
VCE: Mathematics
Rationale
Mathematics is the study of structure and pattern in number, logic and space. It provides both a framework for thinking and a means of symbolic communication that is powerful, logical, concise and unambiguous and a means by which people can understand and manage their environment. Essential mathematical activities include abstracting, investigating, modeling and problem solving. Each Mathematics study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the needs and aspirations of a wide range of students. It is also designed to promote students' awareness of the importance of Mathematics in everyday life in an increasingly technological society and their confidence in making effective use of mathematical ideas, techniques and processes. All students in all the mathematical units offered will apply knowledge and skills, model, investigate and solve problems. They will use technology to support learning Mathematics and its application in different contexts. Note that all VCE Mathematics students are expected to be familiar with the TI-nspire (CAS) calculator.
See Appendix 1 for an outline of the most common pathways in Mathematics from Year 10 to Year 12.
Structure
Units 1 and 2: General Mathematics (SM)
General Mathematics (SM) is an advanced mathematics course designed both to supplement students' mathematical learning in Mathematical Methods (CAS) and to provide an appropriate foundation for students who wish to undertake Specialist Mathematics in Year 12.
Topics to be covered may vary from year to year, and will include Algebra, Functions and Graphs, Trigonometry, Vectors, Analytical Geometry and Calculus. Any student undertaking this course must also be taking Mathematical Methods (CAS) and should have achieved high grades in Mathematics in Year 10.
Assessment
Examination
Common Tests
Application Task
Units 1 and 2: General Mathematics (FM)
General Mathematics (FM) is a course designed both to extend students' mathematical knowledge and skills beyond Year 10 level and to provide an appropriate foundation for students who wish to undertake Further Mathematics in Year 12.
Topics covered are almost entirely areas of Mathematics with significant applications in a wide range of careers, and will include Algebra, Functions, Graphs, Financial Arithmetic, Trigonometry, Geometry and Statistics.
Assessment
Examination
Common Tests
Application Task
Units 1 and 2: Mathematical Methods (CAS)
Mathematical Mathematics (CAS) is a demanding mathematics course which significantly extends students' knowledge in key areas of Algebra, Functions, Graphs, Combinatorics and Probability and also introduces them to the fundamental ideas of Transformational Geometry (including Matrix Methods) and Calculus. Extensive use will be made of the TI-89 Titanium or TI-nspire CAS calculator. Note that when taken alone, this course is allocated six periods per cycle, but when taken with General Mathematics (SM) it is allocated five periods per cycle. Any student undertaking Mathematical Methods (CAS) should have a strong background, particularly in Algebra, and should ideally have achieved at least a grade of B for his Semester 2 Mathematics examinations in Year 10.
Assessment
Examination
Common Tests
Application Task
Units 3 and 4: Further Mathematics
Further Mathematics covers a range of mathematical topics and techniques which are used in many day-to-day applications in a wide variety of careers. The course consists of a compulsory (core) area of study, (Data Analysis), and a selection of three from six Modules:
Number Patterns and Applications
Geometry and Trigonometry
Graphs and Relations
Business-related Mathematics
Networks and Decision Mathematics
MatricesFurther Mathematics: Examination 1 33 per cent
Examination 2 33 per cent
Units 3 and 4: Mathematical Methods (CAS)
This course both consolidates and extends the material covered in Mathematics Methods (CAS) Units 1 and 2. The main areas of study are Algebra, Functions and Graphs, Calculus and Probability. Any student attempting this course must be familiar with the content of Mathematical Methods (CAS) Units 1 and 2. Extensive use will be made of the TI89 Titanium or TI-nspire (CAS) calculator. |
Formats
Book Description
Publication Date: Oct 1 2006Product Description
Review
"Have you ever looked at your child's homework and been stumped by mathematical terms you haven't seen in years? This book will help alleviate hours of frustration for students. Math Dictionary includes a large variety of mathematical terms that often come up in student. Students will easily be able to locate the term and identify its meaning through definitions, examples, diagrams, and some photos. This book clearly explains how to find greatest common factor, differences in bar graphs, how to write in expanded form, and other often-confusing terms." --Library Media Connection
About the Author
Eula Ewing Monroe is a former classroom teacher. She lives in Provo, Utah, where she teaches mathematics education at Brigham Young5.0 out of 5 starsEnthusiastically recommended for junior high and high school libraries.Nov 4 2006
By Midwest Book Review - Published on Amazon.com
Format:Paperback
Math Dictionary: The Easy, Simple, Fun Guide To Help Math Phobics Become Math Lovers by Eula Ewing Monroe (teaches mathematics education at Brigham Young University) is a straightforward reference to basic mathematical terms for readers of all ages and backgrounds, from junior high and high school students to adults in need of a quick refresher. From "average" (including mean, median and mode) to "partial products algorithm" to "zero-dimensional" and much more, the terms cover general arithmetic, geometry, algebra, graphing, probability, statistics, and much more. Advanced mathematical terms such as those used in calculus are not covered. Each definition is spelled out in plain terms, often with simple diagrams to illustrate, eliminating any confusion. Amusing "Did You Know?" quips spice up Math Dictionary with amusing anecdotes such as how the number "googol" (ten to the hundredth power) got its name. Enthusiastically recommended for junior high and high school libraries.
12 of 13 people found the following review helpful
5.0 out of 5 starsCourtesy of Teens Read TooNov 8 2006
By TeensReadToo - Published on Amazon.com
Format:PaperbackReviewed by: Jennifer Wardrip, aka "The Genius"
1 of 1 people found the following review helpful
5.0 out of 5 starsWonderful ToolSep 26 2009
By L. Rentz - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
This math dictionary is an excellent resource for my development as an Elementary Teacher. This tool is user and kid friendly. My household use this referecnce source faithfully. My daughter is a Business Management Major and my son is in Middle School. We love the clear definitions and examples showing what the operation(s)look like. |
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Our Editors also recommend:Test Your Logic by George J. Summers Fifty logic puzzles range in difficulty from the simple to the more complex. Mostly set in story form, some problems involve establishing identities from clues, while others are based on cryptarithmetic.
Amusements in Mathematics by Henry E. Dudeney One of the largest puzzle collections — 430 brainteasers based on algebra, arithmetic, permutations, probability, plane figure dissection, properties of numbers, etc. More than 450 illustrations.
Sam Loyd's Book of Tangrams by Sam Loyd This classic by a famed puzzle expert features 700 tangrams and solutions, plus a charming satirical commentary on the puzzle's origins, its religious significance, and its relationship to mathematics.
Product Description:
160 math teasers and 40 alphametics will provide hours of mind-stretching entertainment. Accessible to high school students. Solutions. Four Appendices |
97801389412 Mathematics: A Source Book for AIDS, Activities, & Strategies
The art of teaching math lies in the ability of the instructor to motivate and inspire individuals to look beyond the numbers and understand the concepts. This book is designed to revive this art, focusing more on the aspects of learning the ideas behind the math rather than the sheer mechanics of mathematical operation. This text addresses the art of teaching mathematics while also providing specific aids and activities in arithmetic, geometry, algebra and probability and statistics for use in the classroom. The authors pay close attention to the role, importance, methods and techniques of motivation. They present ideas that will generate attention, interest, and surprise among students, and will thus foster creative thinking. The material in the text is based on talks given by the authors at professional meetings, as well as the actual application of their ideas in undergraduate and graduate classes they taught. Additionally, many laboratory and discovery activities have been used by authors in teaching junior and senior high school math classes. Instructors of mathematics, school administrators, math specialists, and parents |
Robert Molina
Faculty Profile: Robert Molina
the study of discrete (and usually finite) objects. In other
words, it deals with arrangement of items such as books on a shelf or
numbers in a defined set.
His interest in mathematics began at an early age, but his math
preparation in high school was so bad that he had to take a remedial
math class in college.
After leaving community college for a job, he chose mathematics as a
major when he went back for his bachelor's degree because he wanted to
finish in two years. He planned on teaching high school, but his
class was so unruly during student teaching that he jumped on his
professor's suggestion that he go to graduate school.
"I never realized I was that good at math," he says.
He came to Alma in 1993 and loves working with a wide variety of students.
"I like teaching mathematics in a liberal arts setting," he says. "I have the opportunity to teach students who might not like math, but
end up having fun and learning in the class."
In his spare time, he likes to hike, collect guitars and stay physically active |
Algebra Applicatons: Variables and Equations Using TI_Nspire Graphing Calculator In this episode of two real-world explorations are developed. Simulations of a river are used to bring real-world, relevant applications of algebra to students. The episode also
integrates technology through the use of the Texas Instruments
TI-Nspire graphing calculator. All keystrokes on the calculator are clearly shown. Dynamic river footage and animations bring the variables and equations in algebra math concepts to life.
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Cashill Variables in Algebra (A1-1.1) Evaluating algebraic expressions using variables. Definitions of variable, variable expression, and what evaluate a variable expression means are reviewed. Students are given problems to solve and then the answers are shown. this is a PowerPoint video with no sound.
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How to Multiply Monomials In algebra, two-X is one term because the two and the X are being
multiplied by each other. In this video a math teacher explains how to multiply the coefficients and the variables when multiplying monomials with examples on a whiteboard. Narrators speech is shown on bottom of screen.
(1924-1932)This episode discusses Zefferino Poli who is an emigrant who accepted the dollar religion, he grasped at once the American system. He was a frugal man and soon owns many theaters. Video also discusses other emigrants who influenced the Italians that were living in the United States. Despite the racism and economic difficulties the Italian passion for politics reemerges in the emigrant Author(s): No creator set
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Capitalization of Languages and Nationalities In this video, a teacher gives a brief overview of rules surrounding the capitalization of languages and nationalities, then gives examples of sentences written incorrectly that must be fixed.
Numbers from 1 to one million and ordinal numbers This video slide show presents numbers. The number is shown and read out. Then the spelling is shown and read out again. After number 20 only the next 2 are listed. There are examples with hundreds and thousands. Ordinal numbers are listed at the end. Author(s): No creator set
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Greed Does Not Pay This animated tale tells the story of a man who died and became a swam with golden feathers. He tries to help his family but his wife was too greedy and she is left with nothing. Author(s): No creator set
Battle Of Midway - WWII in colour This is part from WWII in colour series. This one deals with the Battle Of Midway. All footage is in color and in good quality. Author(s): No creator set
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I Made a Valentine Song This song uses hands and body movements to show why they made a valentine. Song is sung and then repeated. (Teacher-made video)
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Children of the Holocaust A montage of pictures showing the effects of the Holocaust on the children. Due to the graphic nature of some images, this would be appropriate for older students. Music is included, but not needed. 3:11 min. Author(s): No creator set
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Concentration Camp Liberation This two minute video shows the horror of thousands
of Jewish prisoners in Nazi camps at the time of their liberation by allied troops. This video has actually footage and some of it is grime so view it first. A great lesson for students on what happened if a nation uses hatred to attack a minority.
Interviews with survivors of the Holocaust This is a series of videos that include Testimony Excerpts from a bystander and two survivors. Very moving and insightful. Some videos about two minutes and others close of 30. This would be a great video series to show for International Holocaust Remembrance January 27.
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Astrology Planetary Associations Astrology twelve signs - Each of the twelve signs associates to planet and they are explained in this four minute video. A fun activity for students, but this is not a science. Author(s): No creator set |
rational functions take two
Two weeks ago in my Algebra 2 Trig Honors class we were finishing up our unit on rational expressions, equations, and functions. In past years, students at this level had focused on graphing only simple rational functions – transformations of y=1/x. (In Precalculus, students are exposed to general rational functions.) I was feeling frustrated, though, at how limited this approach felt – I didn't want students to be misled into ignoring the big vast ocean full of rational functions after looking at a goldfish bowl-sized sample. (Questions like: "so it will always look like this?" were driving me crazy.) But at the same time, I didn't want to bog them down with a tedious approach to graphing general cases by hand. I just wanted my students to get a feel for all of the different crazy shapes these graphs can make, notice patterns, and begin the process of generalizing.
Last year I had included an investigation of general rational functions using Wolfram Alpha on a homework assignment. In hindsight, leaving this activity for homework wasn't a good call – there wasn't enough time for thoughtful follow-up, and by having students work alone they missed out on the magic of discussing their findings with others and building understanding together. So this year, I took an extra class day to allow students time to play around with more complicated rational functions on the Desmos calculator. (Which I am a little bit in love with.)
In my 2nd period class, I didn't do a great job of setting up and explaining what I had envisioned for the hour. I showed them the Desmos calculator, told them they should be graphing a variety of rational functions, and gave them a sheet with 4 specific examples with bullet points for guided questions underneath to use as a framework for their investigation. On the back board, I had written "What do you notice/what are you wondering about…" with different categories for them to record some of their findings throughout the hour. The idea was that throughout class, I would circulate and peek in on their conversations, help answer some questions or poke at their thinking a bit, they would record their observations and questions on the back board, and at the end of class we'd save 10 minutes to discuss our findings on the board.
As I turned students loose to begin working, some problems became evident pretty quickly. While students were comfortable recognizing the one vertical and one horizontal asymptote for simple rational functions, they couldn't "see" the asymptotes for the more complicated graphs. This to me indicated that they didn't have a good enough understanding of what an asymptote truly was, but instead had mastered an algorithm for graphing the simple rational functions. I tried to chat with groups of students to see where the disconnect was, and I encouraged students to graph the lines that they visually predicted were asymptotes – then connect that to the algebra of each function. I also realized I had not done a good job explaining or modeling the way they should record what they noticed/wondered on the back board – I ended up with lots of random pictures and little interpretation or generalizations. I also did a horrible job keeping track of the timing of the class. It became clear we weren't going to have the 10 minutes I wanted at the end of class to pull together our big findings – instead, I had to take pictures of the back board and wait until the next day to summarize their investigation.
There were more nuanced conversations than the sloppy work on the board indicated, but overall I wasn't happy with the way things had gone. I didn't feel like we had arrived at enough clarity or closure for the big ideas I wanted them to be tackling.
Lucky for me, I learned a bit from my mistakes and in my 4th period class I did a MUCH better job of setting up the activity. I graphed the first specific example on Desmos, talked through how I could visually "see" the 2 vertical asymptotes and 1 horizontal asymptote, showed them to graph those lines to confirm the asymptotic behavior, returned to the algebra of the example function to make connections between the algebra and the graph, then added a generalization to the board of noticing/wondering.
During this hour, the students did a better job of working together, asked me fewer questions, and were more able to generalize their findings. They even surprised me with some observations I was *not* expecting them to make (see the last one under "V.A.") and a few students figured out how to use sliders with Desmos to more efficiently explore how changing different bits of the function they graphed would impact its shape. You can tell by looking at their noticings/wonderings how much more successful my second shot at this lesson was. During the follow-up conversation at the end of class, I addressed all of the points on the board, asked for students to help respond to some of the questions, and felt that the majority of students left with a better understanding of both the important features of these graphs and how the algebra of the functions controls their shape.
Since I first started this post a week ago (sorry, February is the worst), I have now given the test for this unit. General rational functions were not tested (only transformations of y=1/x), but I did decide to include a question that had students explain the shape of the parent function y=1/x. It was a great way for me to see if all of the investigation and conversation about the shapes of the graphs had paid off… were my students more "mathematically fluent" in the vocabulary and ideas associated with rational functions? I did have some very strong responses, and I've included my favorite below.
I'm sure there are ways for me to tweak and improve upon this lesson for future classes, but I was happy with the chance it afforded students to talk, play, investigate, and generalize.
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Responses
Some comments and questions here
* Love the guided questions along the way. Do you intend to move away from the more specific clues? Is the unit long enough for that?
* Love the writing on the second set of board snapshots. Why is it that students are so determined to misspell the word vertical even when it is in the question that they are answering?
* In addition to division for slant asymptotes, do you suggest division as a way to get at horizontal asymptotes as well?
* How comfortable are your kids with 'washing away the remainder' in these processes?
* I am intrigued by DESMOS – haven't used it. I'm partial to GeoGebra myself.
I like how you have students put their observations on the board – I'm not sure my algebra students are persistent enough in their investigations, but I would like to try something similar to this in Geometry. Have you ever done it with a class that is not honors?
No, that was actually my first time to have students record observations on the board like this. You can see how much better I modeled for students the types of things they should be recording in the 2nd class. I think I would be comfortable doing something like this in a non-honors class, but the investigation activity would have to be much more structured – I was asking a lot, conceptually, of my students here. |
7th Grade Curriculum Guide
Seventh grade English students will build upon their ... capitalization, and punctuation rules learned in elementary. ... Life Science for Christian Schools, Third Edition 2007 ...
Filetype:
Submitter: naseri
Number Properties and Operations
Other key words that signify a Level 1 ... that has more than one possible answer and ... of Primary3rd Grade 4th Grade 5th Grade MA-EP-5.3.1. Students will model real-world and ...
2007-2008 NEW Chemical Engineering Titles
... EN GI NEER ING THERMODYNAMICS Seventh Edition by ... NEW TO THIS EDITION 20% new and revised homework problems The ... International Edition NEW STATISTICS FOR ENGINEERS AND ...
Filetype:
Submitter: debi1562
Activities and Accomplishments
... Back-to-Class event, AddRan- Exploring a World of ... one of 70% (2007-8, from Digest of Education Statistics as ... Some students did not offer an answer and others gave ...
Curriculum Objective
Elementary and Middle School Mathematics by John Van deWalle ... units; decimals are used to express baseball statistics and ... The prism definitions used in the 5th Grade SOL are ...
Filetype:
Submitter: elongnt
DEKLARATV PROGRAMMANA
Verbal answer to questions in accordance with course ... Methods for solving elementary first order equations. ... relations among the world, camera and image coordinates. |
Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. M-Th 10.00-12.10 pm
Calculus I
Brief review of high school calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem. Use of symbolic manipulation and graphics software in calculus. M-Th 10.00-12.10 pm
Calculus II
Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and analytic geometry, first and second order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. M-Th 1.00-3.10 pm
Calculus, Part II with Probability and Matrices
Functions of several variables, partial derivatives, multiple integrals, differential equations; introduction to linear algebra and matrices with applications to linear programming and Markov processes. Elements of probability and statistics. Applications to social and biological sciences. Use of symbolic manipulation and graphics software in calculus. M-Th 1.00-3.10 pm
Ideas in Mathematics
Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. M-Th |
Welcome to the ClassJump site for all of my courses! I will use this site to post all assignments, class notes, solutions, and items of interest for each of my classes.
AP Physics C Electricity & Magnetism
A rigorous calculus-based physics course is an essential requirement for every student in the field of engineering or the physical sciences. This course will provide you with the opportunity to apply calculus to the physical principles underlying the laws of nature. Major emphasis is on problem solving with laboratory work and class demonstrations to provide data for developing analytical models that can be understood and manipulated mathematically.
For students desiring to study mathematics, engineering, physics, or chemistry at the university level, linear algebra/matrix theory is an absolute requirement. Linear Algebra is the mathematical study of vectors and vector spaces (also called linear spaces). Matrices are widely used to represent the linear transformations that input one vector and output another. Currently, you have received a solid foundation in Calculus. The only REAL prerequisite for this material is a good knowledge of high school algebra. We have designated AB Calculus as a requirement because everyone will need strong algebra skills and good analytical ability. Linear Algebra has many practical applications, not limited to math/physics/engineering. It shows up in economics, logistics, finance, computer science, operations research, and lots of other disciplines.
For students desiring to study mathematics, engineering, physics, or chemistry at the university level, advanced calculus is an absolute requirement. Currently, you have received a solid foundation in Advanced Placement Calculus AB & BC. The material in these courses however, has generally been limited to one independent variable expressed in the form of y = f(x). Multivariable/vector calculus is used to describe phenomena that result from the simultaneous effects of many variables. For example, in the case of the ideal gas law from chemistry, the pressure of an ideal gas is a result of the number of moles of the gas, the volume of the container, and the temperature. We could express this as P = f(n,V,T). If all three are changed simultaneously, how is the pressure changed?
Pre-AP PreCalculus provides opportunities to study real numbers, functions and their graphs, trigonometric relationships, parametric representations, sequences, and series. This course provides the necessary foundation for advanced placement or college calculus. Extends and builds on the foundation for the Advanced Placement program. Includes all of the regular Precalculus course with extensions, both guided and independent, in the areas of symbolic logic, linear programming, applications of polar coordinates, and topics from discrete mathematics. Typically, after taking Pre-AP PreCalculus a student would take AP Statistics and/or AP Calculus AB. |
Curriculum: Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding. Successful IGCSE candidates gain lifelong skills, including: the development of their mathematical knowledge, confidence by developing a feel for numbers, patterns and relationships, an ability to consider and solve problems and present and interpret results, communication and reason using mathematical concepts and a solid foundation for further study. Pre-AICE 1 focuses on the Algebra I skills and the beginning of Geometry.
Class rules:
Be on time to class (in your seat and quiet when the last bell rings) following "beginning of class procedures".
1st tardy results in a warning,
2nd tardy results in a phone call home.
3rd tardy (and all that follow) results in a referral to student management.
Materials: These need to be replaced if they are lost or used up during the year.
Scientificcalculator (save the directions)
Optional– graphing calculator (TI-83or TI-84 any edition) If you choose to buy another type of graphing calculator you are on your own to learn how to use it.
1½ in. 3-ring binder (to be used for math class only)
Pencil, notebook paper, graph paper
Highlighter
Dry erase markers (blue or black) to donate to the class
Box of tissue to donate to the class
Grading Procedure grading scale
Test/quizzes/projects 65% A 90 – 100
Daily work/ homework 30% B 80 – 89
(Assignments are collected each Wednesday or the day of quiz or test) C 70 – 79
(Bell-work is collected each Friday) 20 pts will be deducted for each day late ---unacceptable---
FCA 5% D 60 – 69
Discipline Procedure
Warning
Timeout in class or other classroom
Parent contact
Referral to dean
Administrative Referral
Make-up work
You are responsible for missed work and tests.
You have the number of days absent to make up assignments i.e. 1 day absent = 1 day to make up work. For foreseen extended absences, arrangements will need to be make IN ADVANCE.
Quizzes will NOT be made up. The test grade earned on the test covering the material missed will count for the quiz grade.
If you miss the day of a test, you must make up the examination the day you return to school. You may receive an alternate test in place of the original (this may or may not be the same format.)
If you are on a field trip you are responsible for all work. If an assignment is due the day you are out it must be turned in before leaving on the field trip. Not after you return. Send it with a friend or bring it to the main office to be put in my box.
A "0" will be entered in the grade book and remain there until the work is turned in.
Extra Help
I am available before school every day EXCET Thursdays and the 1st Wednesday of the month between 8 and 9:15 AM. You may call me at home at 591-2272 any time before 8:30 PM for help or questions. (DO NOT CALL ASKING FOR THE ASSIGNMENT.)
Returned work
You will find graded work in the baskets labeled with each period. It is up to you to get your work between classes or before school. Bell-works are graded but not returned. You may see and go over your graded tests before school, they are not returned because of test security.
.
Cooperative Class Expectations
Ask for and offer help.
Listen carefully and praise my classmates.
Share my ideas and work.
Give my best effort.
Be a good follower and a good leader.
Work hard. I'm here to help you and together we will succeed. We are going to have a great year. God Bless you. |
More About
This Textbook
Overview
With an emphasis on problem solving, this book introduces the basic principles and fundamental concepts of computational modeling. It emphasizes reasoning and conceptualizing problems, the elementary mathematical modeling, and the implementation using computing concepts and principles. Examples are included that demonstrate the computation and visualization of the implemented models.
The author provides case studies, along with an overview of computational models and their development. The first part of the text presents the basic concepts of models and techniques for designing and implementing problem solutions. It applies standard pseudo-code constructs and flowcharts for designing models. The second part covers model implementation with basic programming constructs using MATLAB®, Octave, and FreeMat.
Aimed at beginning students in computer science, mathematics, statistics, and engineering, Introduction to Elementary Computational Modeling: Essential Concepts, Principles, and Problem Solving focuses on fundamentals, helping the next generation of scientists and engineers hone their problem solving skills.
What People Are Saying
From the Publisher
… offers a solid first step into scientific and technical computing for those just getting started. … Through simple examples that are both easy to conceptualize and straightforward to express mathematically (something that isn't trivial to achieve), Garrido methodically guides readers from problem statement and abstraction through algorithm design and basic programming. His approach offers those beginning in a scientific or technical discipline something unique; a simultaneous introduction to programming and computational thinking that is very relevant to the practical application of computing many readers will experience later in their academic training, or early in their professional career.
—John West, SIGHPC Connect Newsletter, Vol. 1, June 2012
Related Subjects
Meet the Author
Jose M. Garrido is Professor of Computer Science in the Department of Computer Science, Kennesaw State University, Georgia. He holds a Ph.D. from George Mason University in Fairfax, Virginia, an M.S.C.S also from George Mason University, an M.Sc. from University of London, and a B.S. in Electrical Engineering from Universidad de Oriente, Venezuela.
Dr. Garrido's research interest is on: object-oriented modeling and simulation, multi-disciplinary computational modeling, formal specification of real-time systems, language design and processors, modeling systems performance, and software security. Dr. Garrido developed the Psim3, PsimJ, and PsimJ2 simulation packages for C++ and Java. He has recently developed the OOSimL, the Object Oriented Simulation Language (with partial support from NSF).
Dr. Garrido has published several papers in modeling and simulation, and on programming methods. He has also published six textbooks on objectoriented simulation and operating systems.
Computational Models and Simulation Introduction Categories of Computational Models Development of Computational Models Simulation: Basic Concepts Modular Decomposition Average and Instantaneous Rate of Change Area under a Curve The Free-Falling Object
Mathematical Models: Basic Concepts Introduction From the Real-World to the Abstract World Discrete and Continuous Models Difference Equations and Data Lists Functional Equations Validating a Model Models with Arithmetic Growth Using MATLAB and Octave to Implement the Model Producing the Charts of the Model |
While I do think that many pop-sci explanations of theoretical physics are fairly worthless and often actively misleading, I do not think that it is impossible to gain real insight into (say) the general theory of relativity without mastering differential geometry. Geroch's book presupposes only high school mathematics, but it provides a genuinely deep insight into relativity.
I described the requirements as algebra, analytic geometry, and basic calculus, which is more or less within advanced high-school math. (Without calculus, I don't see how you could explain integrals along the world line, which are the very heart of the matter.)
However, note that just high-school algebra is already worlds apart from purely prose-based, general-audience pop-science. I would guess that for an average reader (let alone owner) of pop-science books, following a text using algebra would be far harder than it would be to figure out tensors for a reasonably math-savvy twelfth grade student. |
Webinars
Upcoming Webinars
If you are interested in learning new teaching strategies, learning about current educational trends or hearing from experts in the math field, please join us for one of our FREE math webinars. Our webinars are designed to connect educators and administrators to their peers and experts in the field of mathematics to learn how we can better engage students in learning math.
Join us for a free webinar to learn more about the Carnegie Learning Math Series – written for the Common Core State Standards. Carnegie Learning is focused exclusively on mathematics and dedicated to helping raise student achievement in mathematics. Our Common Core Math Series for middle school and high school can be used as a comprehensive core mathematics curriculum or to complement your current math program. Carnegie Learning offers write-in textbooks, Cognitive Tutor® and MATHia® Software, and professional development developed specifically for the CCSS. Select the date and time that works best for you!
We are excited to announce the brand new Carnegie learning Common Core Programs for Geometry and Integrated Math II will begin shipping this summer. Carnegie Learning Common Core Geometry and Integrated Math II curricula were developed to align to the Common Core State Standards and promote the Standards of Mathematical Practice throughout each lesson.
We are excited to announce the brand new Carnegie learning Common Core Programs for Algebra II will begin shipping this summer. Carnegie Learning Common Core Algebra II and Integrated Math III curricula were developed to align to the Common Core State Standards and promote the Standards of Mathematical Practice throughout each lesson. |
DK: Teaching Pro Advanced Math - XS125808
Kids Age 13 and up will be Exposed to the Complete High School Math Curriculum in these Interaction Strategic Math Lessons Product Information
Dorling Kindersley Teaching Pro: Advanced Math delivers comprehensive coverage of the complete high school math curriculum with tips, tricks, and secrets that will help you make sense of teachers and textbooks! Each interactive strategic lesson supports state standards and follows grade-based curriculum using self-paced learning and stress-free quizzes to build your math knowledge and test-taking skills.
An ultimate skill-building resource with full subject comprehensive learning.
Comprehensive study aid for mandatory state tests and college entrance exams
Helpful hints through the program so you can avoid common mistakes
Strengthen your understanding of math by practicing world problems
Master topics with colorful presentations of key concepts and learn how to apply it step-by-step
Windows Requirements
Windows 200 XP Vista
850 MHz or faster processor
512 MB of RAM or higher
300-500 MB of free Hard Drive space
800 x 600 SVGA with 16-bit colors
24X CD-ROM drive
Keyboard
Mouse
Speakers
Internet Connection |
Web Site Webmath.com This is a dynamic math website where students enter problems and where the site's math engine solves the problem. Students in most cases are given a step-by-... Curriculum: Mathematics Grades: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
12.
Web Site Prentice Hall Math Textbook Resources This site has middle school and high school lesson quizzes, vocabulary, chapter tests and projects for most chapters in each textbook. In some sections, ther... Curriculum: Mathematics Grades: 6, 7, 8, 9, 10, 11, 12
Web Site Tutorials for the Calculus Phobe Explore a collection of animated calculus tutorials in Flash format. The tutorials that follow explain calculus audio-visually, and are the equivalent of a p... Curriculum: Mathematics Grades: 11, 12, Junior/Community College, University
Web Site Calculus Applets Discover the new way of learning Calculus. All manipula applets are visual and animation-oriented. Moving figures on the screen will help students to grasp ... Curriculum: Mathematics Grades: 9, 10, 11, 12, Junior/Community College, University
Web Site Online Calculus Tutorials From Algebra Review to Multi-Variable Calculus, this website provides step-by-step tutorials for high school and university students. Curriculum: Mathematics Grades: 10, 11, 12, Junior/Community College, University
By Resource Type:
Web Site Document or Handout Image Template Book Video |
IGCSE Mathematics for Edexcel Student's Book 2nd Edition
Alan Smith
IGCSE Mathematics for Edexcel, 2nd edition has been updated to ensure that this second edition fully supports Edexcel's International GCSE Specification A and the Edexcel Certificate in Mathematics.
Written by an experienced examiner, teacher and author, this is the perfect resource for Higher Tier students.
Each chapter starts with key objectives and a starter activity to introduce students to the content, and the straightforward explanations, worked examples and practice questions which follow cover every type of problem students are likely to face in their final exam. 'Internet challenges' also ensure regular and integrated use of ICT.
The book is accompanied by an interactive CD-ROM, which includes a digital version of the book, asnwers to all the questions and Personal Tutors to accompany every topic. Personal Tutors are interactive audio-visual presentations of worked examples which help students consolidate their learning.
This Student's Book is accompanied by IGCSE Mathematics Practice for Edexcel, 2nd edition, which contains a wealth of exam-style questions, and IGCSE Mathematics Teacher's Resource for Edexcel, which provides teaching and learning support.
This second edition has been revised to ensure it fully supports the requirements of Edexcel's International GCSE Specification A and the Edexcel Certificate in Mathematics
Clear learning objectives and summaries, worked examples and plenty of practice questions throughout the book provide students with the support they need to succeed at Higher Tier.
The accompanying CD-ROM contains Personal Tutors - interactive audio-visual presentations of worked examples - for every topic to help students consolidate their learning.
This Student's Book is part of a suite of resources, which also includes IGCSE Mathematics Practice for Edexcel, 2nd edition and IGCSE Mathematics Teacher's Resource for Edexcel, to ensure that both students and teachers have everything they need to succeed.
About the Author(s):
Alan Smith has run the Mathematics Department at Christ's Hospital School in Horsham for 15 years and was responsible for introducing Edexcel's IGCSE onto the curriclum in 2005. He has published extensively and is an experienced examiner with a number of awarding bodies. |
Physics Equations, Physical Quantities and Maths
A series of word documents that lists all of the equations and physical quantities encountered in the Standard Grade Physics curriculum and also a worksheet designed to help pupils cope with the maths used in Physics. |
Elementary
Mathematics Courses. In order to accommodate diverse
backgrounds and interests, several course options are available
to beginning mathematics students. All courses require three years
of high school mathematics; four years are strongly recommended
and more information is given for some individual courses below.
Students with College Board Advanced Placement credit and anyone
planning to enroll in an upper-level class should consider one
of the Honors
sequences and discuss the options with a mathematics advisor.
Students who need additional preparation for calculus are tentatively
identified by a combination of the math placement test (given
during orientation), college admission test scores (SAT or ACT), and high school grade point average. Academic advisors will discuss
this placement information with each student and refer students
to a special mathematics advisor when necessary.
Two courses preparatory to the calculus, MATH 105 and 110, are offered. MATH 105 is a course on data analysis, functions
and graphs with an emphasis on problem solving. MATH 110 is a
condensed half-term version of the same material offered as a
self-study course taught through the Math Lab and is only open
to students in MATH 115 who find that they need additional preparation
to successfully complete the course. A maximum total of 4 credits
may be earned in courses numbered 103, 105, and 110. MATH 103
is offered exclusively in the Summer half-term for students in
the Summer Bridge Program.
MATH 127 and 128 are courses containing selected topics from
geometry and number theory, respectively. They are intended for
students who want exposure to mathematical culture and thinking
through a single course. They are neither prerequisite nor preparation
for any further course. No credit will be received for the election
of MATH 127 or 128 if a student already has credit for a 200-(or
higher) level MATH course.
Each of MATH 115, 185, and 295 is a first course in calculus.
Generally credit can be received for only one of 115 or 185. The
sequence MATH 115-116-215 is appropriate for must students who
want a complete introduction to calculus. One of 215, 285, or
395 is prerequisite to most more advanced courses in Mathematics.
The sequences MATH 156-255-256, 175-186-285-286, 185-186-285-286, and 295-296-395-396 are Honors sequences. Students need not be
enrolled in the LS&A Honors Program to enroll in any of these
courses but must have the permission of an Honors advisor. Students
with strong preparation and interest in mathematics are encouraged
to consider these courses.
MATH 185-285 covers much of the material of MATH 115-215 with
more attention to the theory in addition to applications. Most
students who take MATH 185 have taken a high school calculus course, but it is not required. MATH 175-186 assumes a knowledge of calculus
roughly equivalent to MATH 115 and covers a substantial amount
of so-called combinatorial mathematics as well as calculus-related
topics not usually part of the calculus sequence. MATH 175 is
taught by the discovery method: students are presented with a
great variety of problems and encouraged to experiment in groups
using computers. The sequence MATH 295-396 provides a rigorous
introduction to theoretical mathematics. Proofs are stressed over
applications and these courses require a high level of interest
and commitment. Most students electing MATH 295 have completed
a thorough high school calculus course. MATH 295-396 is excellent
preparation for mathematics at the advanced undergraduate and
beginning graduate level.
Students with strong scores on either the AB or BC version
of the College Board Advanced Placement exam may be granted credit
and advanced placement in one of the sequences described above;
a table explaining the possibilities is available from advisors
and the Department. In addition, there is one course expressly
designed and recommended for students with one or two semesters
of AP credit, MATH 156. MATH 156 is an Honors course intended
primarily for science and engineering concentrators and will emphasize
both applications and theory. Interested students should consult
a mathematics advisor for more details.
In rare circumstances and with permission of a Mathematics
advisor, reduced credit may be granted for MATH 185 after MATH
115. A list of these and other cases of reduced credit for courses
with overlapping material is available from the Department. To
avoid unexpected reduction in credit, a student should always consult
an advisor before switching from one sequence to another. In all
cases a maximum total of 16 credits may be earned for calculus
courses MATH 115 through 396, and no credit can be earned for
a prerequisite to a course taken after the course itself.
Students completing MATH 116 who are principally interested
in the application of mathematics to other fields may continue
either to MATH 215 (Analytic Geometry and Calculus III) or to
MATH 216 (Introduction to Differential Equations); these two courses
may be taken in either order. Students who have greater interest
in theory or who intend to take more advanced courses in mathematics
should continue with MATH 215 followed by the sequence MATH 217-316
(Linear Algebra-Differential Equations). MATH 217 (or the Honors
version, MATH 513) is required for a concentration in Mathematics;
it both serves as a transition to the more theoretical material
of advanced courses and provides the background required to optimal
treatment of differential equations in MATH 316. MATH 216 is not
intended for mathematics concentrators.
A maximum total of 4 credits may be earned in MATH 103, 105, and 110. A maximum total of 16 credits may be earned for calculus courses MATH 112 through MATH 396, and no credit can be earned for a prerequisite to a course taken after the course itself.
MATH 103. Intermediate Algebra.
Instructor(s):
Prerequisites & Distribution: Only open to designated summer half-term Bridge students. (Excl). May not be repeated for credit. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.
MATH 105. Data, Functions, and Graphs.
THERE ARE JOINT EVENING EXAMS FOR ALL SECTIONS of MATH 105: WED, OCT 1 & MON, NOV 3, 6-8PM. ALSO A JOINT FINAL. CAUTION! AVOID SCHEDULING ANOTHER CLASS THAT CONFLICTS WITH THESE EVENING EXAMS.
Instructor(s):
Prerequisites & Distribution: (4). (MSA). (QR/1). May not be repeated for credit.Credits: (4).
Course Homepage: No homepage submitted.
MATH 105 serves both as a preparatory course to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who complete MATH 105 are fully prepared for MATH 115.MATH 110. Pre-Calculus (Self-Study).Instructor(s):
Prerequisites & Distribution: See Elementary Courses above. Enrollment in MATH 110 is by recommendation of MATH 115 instructor and override only. (2). (Excl). May not be repeated for credit. No credit granted to those who already have 4 credits for pre-calculus mathematics courses. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.
Credits: (2).
Course Homepage: No homepage submitted.
The course covers data analysis by means of functions and graphs. MATH 110 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. The course is a condensed, half-term version of MATH 105 (MATH 105 covers the same material in a traditional classroom setting) designed for students who appear to be prepared to handle calculus but are not able to successfully complete MATH 115. Students who complete MATH 110 are fully prepared for MATH 115. Students may enroll in MATH 110 only on the recommendation of a mathematics instructor after the third week of classes.MATH 115. Calculus I.
Instructor(s):
Prerequisites & Distribution: Four years of high school mathematics. See Elementary Courses above. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit usually is granted for only one course from among 115, 185, and 295. No credit granted to those who have completed MATH 175 uniform midterm and final exam. The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing, and questioning skills.
Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. MATH 185 is a somewhat more theoretical course which covers some of the same material. MATH 175 includes some of the material of MATH 115 together with some combinatorial mathematics. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions, and Graphs). MATH 116 is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186. The cost for this course is over $100 since the student will need a text (to be used for MATH 115 and 116) and a graphing calculator (the Texas Instruments TI-83 is recommended).
Instructor(s):
Prerequisites & Distribution: MATH 115. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit is granted for only one course from among MATH 116, 156, 176, and 186.
Credits: (4).
Course Homepage: No homepage submitted.MATH 147. Introduction to Interest Theory.
Instructor(s):
Prerequisites & Distribution: MATH 115. (3). (MSA). (BS). May not be repeated for credit. No credit granted to those who have completed a 200- (or higher) level mathematics course.
Credits: (3).
Course Homepage: No homepage submitted.
This course is designed for students who seek an introduction to the mathematical concepts and techniques employed by financial institutions such as banks, insurance companies, and pension funds. Actuarial students, and other mathematics concentrators should elect MATH 424, which covers the same topics but on a more rigorous basis requiring considerable use of calculus. Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds, and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values. This course is not part of a sequence. Students should possess financial calculators.
MATH 156. Applied Honors Calculus II.
Prerequisites & Distribution: Score of 4 or 5 on the AB or BC Advanced Placement calculus exam. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit is granted for only one course among MATH 116, 156, 176, 186, and 296.
Math 156 is a 2nd term Honors calculus course for engineering and science students. The course emphasizes applications of calculus, computational skills, and conceptual understanding. The
prerequisite is a score of 4 or 5 on the Advanced Placement calculus AB or BC exam. Math 156 provides students with the calculus background they need for subsequent courses in engineering, math, and
science.
The aim of Math 156 is to provide students with the math background they need for
subsequent courses. Math 156 strikes a balance between theory and application. Theorems
are stated carefully and several are proven, but technical details are omitted (though
reference is made to higher-level math courses where such issues are discussed). The
proofs are presented in easily understood steps, based on the course coordinator's prior
experience. Examples are given to illustrate the theory.
The course starts by reviewing the definition of the integral as a limit of Riemann sums.
The students presumably have seen this topic in their AP class, but many comment that
the Math 156 treatment is different. The class moves quickly to topics that most students
haven't seen before, including improper integrals, and applications such as work, center of
mass, arclength, surface area, hydrostatic force, and probability density functions. Math
156 avoids the traditional segment on "methods of integration for their own sake"; instead
the methods are discussed as they arise in concrete problems. Taylor approximation is
discussed in some depth with emphasis on applications the students will likely encounter
in later courses (e.g., far-field expansion for the electrostatic potential of a pair of charged particles).
Part I. Integration
sigma notation
area
definite integral
fundamental theorem of calculus
indefinite integrals
work
improper integrals
arclength
surface area
hydrostatic force, center of mass
probability density functions
Part II. Differential Equations
modeling with differential equations
exponential growth and decay
logistic equation
Part III. Series
sequences
series
integral test
comparison test
alternating series
absolute convergence, ratio test
power series
Taylor series
binomial series
applications of Taylor polynomials
Additional Topics (time permitting)
parametric curves
area defined by parametric curves
polar coordinates
complex numbers
Review (as needed)
substitution
inverse trigonometric functions
hyperbolic functions
L'Hopital's rule
integration by parts
trigonometric integrals
trigonometric substitution
partial fractions
The enrollment is roughly 1/2 engineering majors and 1/2 science majors. The class meets 4 times per week and each
class is 50 minutes long. There are uniform weekly homework assignments and uniform
exams (two 90 minute midterms and one 2 hour final exam). The homework assignments
include problems from the assigned text and customized problems. The students are introduced to MAPLE in a computer lab. There is brief exposure
to special topics such as Bessel function, Gamma function, error function, fractal sets, Laplace transform, polar coordinates, complex numbers.
Text: "Calculus" by James Stewart, 5th edition, Brooks/Cole Publishing Company
MATH 185. Honors Calculus I.
Section 001, 002The sequence MATH 185-186-285-286 is the Honors introduction to calculus. It is taken by students intending to concentrate in mathematics, science, or engineering as well as students heading 185. Honors Calculus I.
Section 003, 004Credits: (4).
Course Homepage: No homepage submitted.
The sequence MATH 185-186-285-286 is the Honors introduction to calculus. It is taken by students intending to concentrate 214. Linear Algebra and Differential Equations.
Prerequisites & Distribution: MATH 115 and 116This course is intended for second-year students who might otherwise take MATH 216 (Introduction to Differential Equations) but who have a greater need or desire to study Linear Algebra. This may include some Engineering students, particularly from Industrial and Operations engineering (IOE), as well as students of Economics and other quantitative social sciences. Students intending to concentrate in Mathematics must continue to elect MATH 217.
While MATH 216 includes 3-4 weeks of Linear Algebra as a tool in the study of Differential Equations, MATH 214 will include roughly three weeks of Differential Equations as an application of Linear Algebra.
MATH 215. Calculus III.
Instructor(s):
Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296 midterm and final exam. Maple software. MATH 285 is a somewhat more theoretical course which covers the same material. For students intending to concentrate in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is MATH 217. Students who intend to take only one further mathematics course and need differential equations should take MATH 216.
MATH 216. Introduction to Differential Equations.
Instructor(s):
Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. Not intended for Mathematics concentrators. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit can be earned for only one of MATH 216, 256, 286, or 316 engineering and the sciences. Math concentrators and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. After an introduction to ordinary differential equations, the first half of the course is devoted to topics in linear algebra, including systems of linear algebraic equations, vector spaces, linear dependence, bases, dimension, matrix algebra, determinants, eigenvalues, and eigenvectors. In the second half these tools are applied to the solution of linear systems of ordinary differential equations. Topics include: oscillating systems, the Laplace transform, initial value problems, resonance, phase portraits, and an introduction to numerical methods. There is a weekly computer lab using MATLAB software. This course is not intended for mathematics concentrators, who should elect the sequence MATH 217-316. MATH 286 covers much of the same material in the honors sequence. The sequence MATH 217-316 covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 404 covers further material on differential equations. MATH 217 and 417 cover further material on linear algebra. MATH 371 and 471 cover additional material on numerical methods.
MATH 217. Linear Algebra.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285 concentrators Therefore the student entering MATH 217 should come with a sincere interest in learning about proofs. The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; eigenvalues and eigenvectors; diagonalization; and inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics. MATH 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way. The intended course to follow MATH 217 is 316. MATH 217 is also prerequisite for MATH 412 and all more advanced courses in mathematics.
MATH 285. Honors Calculus III.
Instructor(s):
Prerequisites & Distribution: MATH 176 or 186, or permission of the Honors advisorSee MATH 185 for a general description of the sequence MATH 185-186-285-286.
Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; maximum-minimum problems; line, surface, and volume integrals and applications; vector fields and integration; curl, divergence, and gradient; Green's Theorem and Stokes' Theorem. Additional topics may be added at the discretion of the instructor. MATH 215 is a less theoretical course which covers the same material.
MATH 289. Problem Seminar.
Instructor(s):
One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. The student has an opportunity to participate more actively in his/her education and development. This course is intended for superior students who have exhibited both ability and interest in doing mathematics, but it is not restricted to honors students. This course is excellent preparation for the Putnam exam. Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students.
MATH 295. Honors Mathematics I.
Instructor(s):
Prerequisites & Distribution: Prior knowledge of first year calculus and permission of the Honors advisor. (4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 185.
Credits: (4).
Course Homepage: No homepage submitted.
MATH 295-296-395-396 is the main Honors calculus sequence. It is aimed at talented students who intend to major in mathematics, science, or engineering. The emphasis is on concepts and problem solving, as well as the underlying theory and proofs of important results. Students interested in taking advanced mathematical courses later should seriously consider starting with this sequence. The expected background is high school trigonometry and algebra (previous calculus not required). This sequence is not restricted to students enrolled in the LS&A Honors Program. Real functions, limits, continuous functions, limits of sequences, complex numbers, derivatives, indefinite integrals and applications, and some linear algebra. MATH 175 and MATH 185 are less intensive Honors courses. MATH 296 is the intended sequel.
MATH 316. Differential Equations.
Instructor(s):
Prerequisites & Distribution: MATH 215 and 217. (3). (Excl). (BS). May not be repeated for credit. Credit can be earned for only one of MATH 216, 256, 286, or 316.
Credits: (3).
Course Homepage: No homepage submitted.
This is an introduction to differential equations for students who have studied linear algebra (MATH 217). It treats techniques of solution (exact and approximate), existence and uniqueness theorems, some qualitative theory, and many applications. Proofs are given in class; homework problems include both computational and more conceptually oriented problems. First-order equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvector-eigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higher-order equations, reduction of order, variation of parameters, series solutions; qualitative behavior of systems, equilibrium points, stability. Applications to physical problems are considered throughout. MATH 216 covers somewhat less material without the use of linear algebra and with less emphasis on theory. MATH 286 is the Honors version of MATH 316. MATH 471 and/or MATH 572 are natural sequels in the area of differential equations, but MATH 316 is also preparation for more theoretical courses such as MATH 451.
MATH 333. Directed Tutoring.
Instructor(s):
Prerequisites & Distribution: Enrollment in the secondary teaching certificate program with concentration in mathematics. Permission of instructor required. (1-3). (Excl). (EXPERIENTIAL). May be repeated for credit for a maximum of 3 credits. Offered mandatory credit/no credit.
Credits: (1-3).
Course Homepage: No homepage submitted.
An experiential mathematics course for elementary teachers. Students tutor pre-calculus (Math. 105) or calculus (Math. 115) in the Math. Lab. They also participate in a bi-weekly seminar to discuss mathematical and methodological questions. Mandatory Credit/No Credit grading.
MATH 371 / ENGR 371. Numerical Methods for Engineers and Scientists.
Instructor(s):
Prerequisites & Distribution: ENGR 101; one of MATH 216, 256, 286, or 316. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in Math 471This is a survey course of the basic numerical methods which are used to solve practical scientific problems.
Important concepts such as accuracy, stability, and efficiency are discussed. The course provides an introduction
to MATLAB, an interactive program for numerical linear algebra. Convergence theorems are discussed and
applied, but the proofs are not emphasized.
Objectives of the course
Develop numerical methods for approximately solving problems from continuous mathematics on the
computer
Implement these methods in a computer language (MATLAB)
Apply these methods to application problems
Computer language:
In this course, we will make extensive use of Matlab, a technical computing environment for numerical
computation and visualization produced by The MathWorks, Inc. A Matlab manual is available in the MSCC Lab.
Also available is a MATLAB tutorial written by Peter Blossey.
MATH 385. Mathematics for Elementary School Teachers.
Instructor(s):
Carolyn A Dean
Prerequisites & Distribution: One year each of high school algebra and geometry. (3). (Excl). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 485.
Credits: (3).
Course Homepage: No homepage submitted.
All elementary teaching certificate candidates are required to take two
math courses, MATH 385 and MATH 489, either before or after admission to
the School of Education. MATH 385 is offered in the Fall Term, MATH 489
in the Winter Term. Enrollment is limited to 30 students per section; class-size limits will be STRICTLY enforced. Anyone who can elect MATH 385 in the Spring Term is urged to do so. It is the surest way to guarantee yourself a place in the course.
This course, together with its sequel MATH 489, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable. Topics covered include problem solving, sets and functions, numeration systems, whole numbers (including some number theory), and integers. Each number system is examined in terms of its algorithms, its applications, and its mathematical structure. There is no alternative course. MATH 489 is the required sequel.
MATH 395. Honors Analysis I.
Section 001.
Instructor(s):
Mario Bonk
Prerequisites & Distribution: MATH 296 or permission of the Honors advisor. (4). (Excl). (BS). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
This course is a continuation of the sequence MATH 295-296 and has the same theoretical emphasis. Students are expected to understand and construct proofs. This course studies functions of several real variables. Topics are chosen from elementary linear algebra (vector spaces, subspaces, bases, dimension, and solutions of linear systems by Gaussian elimination); elementary topology (open, closed, compact, and connected sets, and continuous and uniformly continuous functions); differential and integral calculus of vector-valued functions of a scalar; differential and integral calculus of scalar-valued functions on Euclidean spaces; linear transformations (null space, range, matrices, calculations, linear systems, and norms); and differential calculus of vector-valued mappings on Euclidean spaces (derivative, chain rule, and implicit and inverse function theorems).
MATH 404. Intermediate Differential Equations and Dynamics.
Instructor(s):
Prerequisites & Distribution: MATH 216, 256 or 286, or 316. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This is a course oriented to the solutions and applications of differential equations. Numerical methods and computer graphics are incorporated to varying degrees depending on the instructor. There are relatively few proofs. Some background in linear algebra is strongly recommended. First-order equations, second and higher-order linear equations, Wronskians, variation of parameters, mechanical vibrations, power series solutions, regular singular points, Laplace transform methods, eigenvalues and eigenvectors, nonlinear autonomous systems, critical points, stability, qualitative behavior, application to competing-species and predator-prey models, numerical methods. MATH 454 is a natural sequel.
MATH 412. Introduction to Modern Algebra.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285; and 217. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 512. Students with credit for MATH 312 should take MATH 512 rather than 412. One credit granted to those who have completed MATH 312.
Credits: (3).
Course Homepage: No homepage submitted.
This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions or the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. MATH 217 or equivalent required as background. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, and complex numbers). These are then applied to the study of particular types of mathematical structures such as groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied.
MATH 312 is a somewhat less abstract course which substitutes material on finite automata and other topics for some of the material on rings and fields of MATH 412. MATH 512 is an Honors version of MATH 412 which treats more material in a deeper way. A student who successfully completes this course will be prepared to take a number of other courses in abstract mathematics: MATH 416, 451, 475, 575, 481, 513, and 582. All of these courses will extend and deepen the student's grasp of modern abstract mathematics.
MATH 416. Theory of Algorithms.
Instructor(s):
Prerequisites & Distribution: MATH 312 or 412 or EECS 203, and EECS 281. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
Many common problems from mathematics and computer science may be solved by applying one or more algorithms — well-defined procedures that accept input data specifying a particular instance of the problem and produce a solution. Students entering MATH 416 typically have encountered some of these problems and their algorithmic solutions in a programming course. The goal here is to develop the mathematical tools necessary to analyze such algorithms with respect to their efficiency (running time) and correctness. Different instructors will put varying degrees of emphasis on mathematical proofs and computer implementation of these ideas. Typical problems considered are: sorting, searching, matrix multiplication, graph problems (flows, travelling salesman), and primality and pseudo-primality testing (in connection with coding questions). Algorithm types such as divide-and-conquer, backtracking, greedy, and dynamic programming are analyzed using mathematical tools such as generating functions, recurrence relations, induction and recursion, graphs and trees, and permutations. The course often includes a section on abstract complexity theory including NP completeness. This course has substantial overlap with EECS 586 — more or less depending on the instructors. In general, MATH 416 will put more emphasis on the analysis aspect in contrast to design of algorithms. MATH 516 (given infrequently) and EECS 574 and 575 (Theoretical Computer Science I and II) include some topics which follow those of this course.
MATH 417. Matrix Algebra I.
Instructor(s):
Prerequisites & Distribution: Three courses MATH 513.
Credits: (3).
Course Homepage: No homepage submitted.
Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.
MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.
MATH 419. Linear Spaces and Matrix Theory.
Instructor(s):
Prerequisites & Distribution: Four terms of college mathematics in MATH 513.
Credits: (3).
Course Homepage: No homepage submitted.
MATH 419 covers much of the same ground as MATH 417 but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. A previous proof-oriented course is helpful but by no means necessary. Basic notions of vector spaces and linear transformations: spanning, linear independence, bases, dimension, matrix representation of linear transformations; determinants; eigenvalues, eigenvectors, Jordan canonical form, inner-product spaces; unitary, self-adjoint, and orthogonal operators and matrices, and applications to differential and difference equations.
MATH 417 is less rigorous and theoretical and more oriented to applications. MATH 217 is similar to MATH 419 but slightly more proof-oriented. MATH 513 is much more abstract and sophisticated. Math 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.
Instructor(s):
This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing derivative instruments such as options and futures. The goal is to understand how the models reflect observed market features, and to provide the necessary mathematical tools for their analysis and implementation. The course will introduce the stochastic processes used for modeling particular financial instruments. However, the students are expected to have a solid background in basic probability theory.
Instructor(s):
This course explores the concepts underlying the theory of interest and then applies them to concrete problems. The course also includes applications of spreadsheet software. The course is a prerequisite to advanced actuarial courses. It also helps students prepare for the Part 4A examination of the Casualty Actuarial Society and the Course 140 examination of the Society of Actuaries. The course covers compound interest (growth) theory and its application to valuation of monetary deposits, annuities, and bonds. Problems are approached both analytically (using algebra) and geometrically (using pictorial representations). Techniques are applied to real-life situations: bank accounts, bond prices, etc. The text is used as a guide because it is prescribed for the Society of Actuaries exam; the material covered will depend somewhat on the instructor. MATH 424 is required for students concentrating in actuarial mathematics; others may take MATH 147, which deals with the same techniques but with less emphasis on continuous growth situations. MATH 520 applies the concepts of MATH 424 together with probability theory to the valuation of life contingencies (death benefits and pensions).
MATH 425 / STATS 425. Introduction to Probability.
Instructor(s):
Mathematics faculty 425 / STATS 425. Introduction to Probability.
Section 001.
Instructor(s): Math 116 and 215. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis. Math 525 is a similar course for students with stronger mathematical background and ability. Stat 426 is a natural sequel for students interested in statistics. Math 523 includes many applications of probability theory.Instructor(s):
Kausch 427 / HB 603. Retirement Plans and Other Employee Benefit Plans.
Section 001.
Prerequisites & Distribution: Junior standing. (3). (Excl). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
An overview of the range of employee benefit plans, the considerations (actuarial and others) which influence plan design and implementation practices, and the role of actuaries and other benefit plan professionals and their relation to decision makers in management and unions. Particular attention will be given to government programs which provide the framework, and establish requirements, for privately operated benefit plans. Relevant mathematical techniques will be reviewed, but are not the exclusive focus of the course. MATH 521 and/or MATH 522 (which can be taken independently of each other) provide more in-depth examination of the actuarial techniques used in employee benefit plans. No textbook
MATH 429. Internship.
Instructor(s):
Prerequisites & Distribution: Concentration in Mathematics. (1). (Excl). (EXPERIENTIAL). May be elected up to three times for credit. Internship credit is not retroactive and must be prearranged. May not apply toward a Mathematics concentration. May be used to satisfy the Curriculum Practical Training (CPT) required of foreign students. Offered mandatory credit/no credit.
Credits: (1).
Course Homepage: No homepage submitted.
Credits is granted for a full-time internship of at least eight weeks that is used to enrich a student's academic experience and/or allows the student to explore careers related to his/her academic studies.
This course is a study of the axiomatic foundations of Euclidean and non-Euclidean geometry. Concepts and proofs are emphasized; students must be able to follow as well as construct clear logical arguments. For most students this is an introduction to proofs. A subsidiary goal is the development of enrichment and problem materials suitable for secondary geometry classes. Topics selected depend heavily on the instructor but may include classification of isometries of the Euclidean plane; similarities; rosette, frieze, and wallpaper symmetry groups; tessellations; triangle groups; and finite, hyperbolic, and taxicab non-Euclidean geometries. Alternative geometry courses at this level are MATH 432 and 433. Although it is not strictly a prerequisite, MATH 431 is good preparation for MATH 531.
MATH 433. Introduction to Differential Geometry.
Section 001.
Prerequisites & Distribution: MATH 215 (or 255 or 285), and 217. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This course is about the analysis of curves and surfaces in 2- and 3-space using the tools of calculus and linear algebra. There will be many examples discussed, including some which arise in engineering and physics applications. Emphasis will be placed on developing intuitions and learning to use calculations to verify and prove theorems. Students need a good background in multivariable calculus (MATH 215) and linear algebra (preferably MATH 217). Some exposure to differential equations (MATH 216 or 316) is helpful but not absolutely necessary. Topics covered include (1) curves: curvature, torsion, rigid motions, existence and uniqueness theorems; (2) global properties of curves: rotation index, global index theorem, convex curves, 4-vertex theorem; and (3) local theory of surfaces: local parameters, metric coefficients, curves on surfaces, geodesic and normal curvature, second fundamental form, Christoffel symbols, Gaussian and mean curvature, minimal surfaces, and classification of minimal surfaces of revolution. MATH 537 is a substantially more advanced course which requires a strong background in topology (MATH 590), linear algebra (MATH 513), and advanced multivariable calculus (MATH 551). It treats some of the same material from a more abstract and topological perspective and introduces more general notions of curvature and covariant derivative for spaces of any dimension. MATH 635 and MATH 636 (Topics in Differential Geometry) further study Riemannian manifolds and their topological and analytic properties. Physics courses in general relativity and gauge theory will use some of the material of this course.
MATH 450. Advanced Mathematics for Engineers I.
Section 001.
Prerequisites & Distribution: MATH 215, 255, or 285. (4). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 354 or 454.
Credits: (4).
Course Homepage: No homepage submittedMATH 451. Advanced Calculus I.
Instructor(s): extends 451. Advanced Calculus I.
Section 001.
Instructor(s):
Peter L Duren extends 454. Boundary Value Problems for Partial Differential Equations.
Section 001.MATH 454. Boundary Value Problems for Partial Differential Equations.
Section 002.
Instructor(s):This course will concentrate on the applications of ordinary differential
equations to physiological systems. Partial differential equations will
not be covered in detail. Thus, a course in ODEs such as 216 or 316 will
be sufficient preparation for this course.
Who could take the course? Basically anybody who is interested
in applying mathematical methods to the biological sciences. For instance, students from Biology, Chemistry, Physics, Complex Systems, Biophysics, Biomedical Engineering, Mathematics, Chemical Engineering, Physiology, Microbiology, and Epidemiology.
What kind of background will you need? Basically a course in differential
equations, such as 216 or 316. If you have never seen a differential equation
before, you may have trouble with the course. You will also need to be familiar
and comfortable with computers, as a lot of the work in the course will
have to be done on a computer. You will not need to be an expert in biology, as we will learn most of what we need to know as we go.
MATH 471. Introduction to Numerical Methods.
Section 001.
Instructor(s):Credits: (3).
Course Homepage: No homepage submitted 471. Introduction to Numerical Methods.
Section 002. 481. Introduction to Mathematical Logic.
Instructor(s):
Prerequisites & Distribution: MATH 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
All of modern mathematics involves logical relationships among mathematical concepts. In this course we focus on these relationships themselves rather than the ideas they relate. Inevitably this leads to a study of the (formal) languages suitable for expressing mathematical ideas. The explicit goal of the course is the study of propositional and first-order logic; the implicit goal is an improved understanding of the logical structure of mathematics. Students should have some previous experience with abstract mathematics and proofs, both because the course is largely concerned with theorems and proofs and because the formal logical concepts will be much more meaningful to a student who has already encountered these concepts informally. No previous course in logic is prerequisite. In the first third of the course the notion of a formal language is introduced and propositional connectives (and, or, not, implies), tautologies, and tautological consequence are studied. The heart of the course is the study of first-order predicate languages and their models. The new elements here are quantifiers ('there exists' and 'for all'). The study of the notions of truth, logical consequence, and provability lead to the completeness and compactness theorems. The final topics include some applications of these theorems, usually including non-standard analysis. MATH 681, the graduate introductory logic course, also has no specific logic prerequisite but does presuppose a much higher general level of mathematical sophistication. PHIL 414 may cover much of the same material with a less mathematical orientation. MATH 481 is not explicitly prerequisite for any later course, but the ideas developed have application to every branch of mathematics.
MATH 485. Mathematics for Elementary School Teachers and Supervisors.
Instructor(s):
Prerequisites & Distribution: One year of high school algebra. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 385. May not be included in a concentration plan in mathematics.
Credits: (3).
Course Homepage: No homepage submittedThis is an elective course for elementary teaching certificate
candidates that extends and deepens the coverage of mathematics begun in the
required two-course sequence MATH 385-489. Topics are chosen from geometry and
algebra.
MATH 501. Applied & Interdisciplinary Mathematics Student Seminar.
Instructor(s):
Prerequisites & Distribution: At least two 300 or above level math courses, and graduate standing; Qualified undergraduates with permission of instructor only. (1). (Excl). (BS). May be repeated for credit for a maximum of 6 credits. Offered mandatory credit/no credit.
Credits: (1).
Course Homepage: No homepage submitted.
The Applied and Interdisciplinary Mathematics (AIM) student seminar is an introductory and survey course in the methods and applications of modern mathematics in the natural, social, and engineering sciences. Students will attend the weekly AIM Research Seminar where topics of current interest are presented by active researchers (both from U-M and from elsewhere). The other central aspect of the course will be a seminar to prepare students with appropriate introductory background material. The seminar will also focus on effective communication methods for interdisciplinary research. MATH 501 is primarily intended for graduate students in the Applied & Interdisciplinary Mathematics M.S. and Ph.D. programs. It is also intended for mathematically curious graduate students from other areas. Qualified undergraduates are welcome to elect the course with the instructor's permission.
Student attendance and participation at all seminar sessions is required. Students will develop and make a short presentation on some aspect of applied and interdisciplinary mathematics.
MATH 513. Introduction to Linear Algebra.
Section 001.
Prerequisites & Distribution: MATH 412. (3). (Excl). (BS). May not be repeated for credit. Two credits granted to those who have completed MATH 214, 217, 417, or 419.
Credits: (3).
Course Homepage: No homepage submitted.
This is an introduction to the theory of abstract vector spaces and linear transformations. The emphasis is on concepts and proofs with some calculations to illustrate the theory. For students with only the minimal prerequisite, this is a demanding course; at least one additional proof-oriented course e.g., MATH 451 or 512) is recommended. Topics are selected from: vector spaces over arbitrary fields (including finite fields); linear transformations, bases, and matrices; eigenvalues and eigenvectors; applications to linear and linear differential equations; bilinear and quadratic forms; spectral theorem; Jordan Canonical Form. MATH 419 covers much of the same material using the same text, but there is more stress on computation and applications. MATH 217 is similarly proof-oriented but significantly less demanding than MATH 513. MATH 417 is much less abstract and more concerned with applications. The natural sequel to MATH 513 is MATH 593. MATH 513 is also prerequisite to several other courses (MATH 537, 551, 571, and 575) and may always be substituted for MATH 417 or 419.
Student Body: a mix of math and computer science undergrads and non-math majors
Background and Goals: This is an introduction to the theory of abstract vector spaces and linear
transformations. The emphasis is on concepts and proofs with some calculations to illustrate the theory.
Alternatives: MATH 419 (Lin. Spaces and Matrix Thy) covers much of the same material using the same text, but there is more stress on computation and applications. MATH 217 (Linear Algebra) is similarly
proof-oriented but significantly less demanding than MATH 513. MATH 417 (Matrix Algebra I) is much less
abstract and more concerned with applications.
Subsequent Courses: The natural sequel to MATH 513 is MATH 593 (Algebra I). MATH 513 is also prerequisite
to several other courses: MATH 537, 551, 571, and 575, and may always be substituted for MATH 417 or
419.
MATH 520. Life Contingencies I.
Section 001.
Prerequisites & Distribution: MATH 424 and 425. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
The goal of this course is to teach the basic actuarial theory of mathematical models for financial uncertainties, mainly the time of death. In addition to actuarial students, this course is appropriate for anyone interested in mathematical modeling outside of the physical sciences. Concepts and calculation are emphasized over proof. The main topics are the development of (1) probability distributions for the future lifetime random variable, (2) probabilistic methods for financial payments depending on death or survival, and (3) mathematical models of actuarial reserving. MATH 523 is a complementary course covering the application of stochastic process models. MATH 520 is prerequisite to all succeeding actuarial courses. MATH 521 extends the single decrement and single life ideas of 520 to multi-decrement and multiple-life applications directly related to life insurance and pensions. The sequence MATH 520-521 covers the Part 4A examination of the Casualty Actuarial Society and covers the syllabus of the Course 150 examination of the Society of Actuaries. MATH 522 applies the models of MATH 520 to funding concepts of retirement benefits such as social insurance, private pensions, retiree medical costs, etc.
MATH 523. Risk Theory.
Instructor(s):
Risk management is of major concern to all financial institutions and is an active area of modern finance. This course is relevant for students with interests in finance, risk management, or insurance and provides background for the professional examinations in Risk Theory offered by the Society of Actuaries and the Casualty Actuary Society. Students should have a basic knowledge of common probability distributions (Poisson, exponential, gamma, binomial, etc.) and have at least junior standing. Two major problems will be considered: (1) modeling of payouts of a financial intermediary when the amount and timing vary stochastically over time; and (2) modeling of the ongoing solvency of a financial intermediary subject to stochastically varying capital flow. These topics will be treated historically beginning with classical approaches and proceeding to more dynamic models. Connections with ordinary and partial differential equations will be emphasized. Classical approaches to risk including the insurance principle and the risk-reward tradeoff. Review of probability. Bachelier and Lundberg models of investment and loss aggregation. Fallacy of time diversification and its generalizations. Geometric Brownian motion and the compound Poisson process. Modeling of individual losses which arise in a loss aggregation process. Distributions for modeling size loss, statistical techniques for fitting data, and credibility. Economic rationale for insurance, problems of adverse selection and moral hazard, and utility theory. The three most significant results of modern finance: the Markowitz portfolio selection model, the capital asset pricing model of Sharpe, Lintner and Moissin, and (time permitting) the Black-Scholes option pricing model.
MATH 525 / STATS 525. Probability Theory.
Section 001.
Instructor(s):
Charles R Doering
Prerequisites & Distribution: MATH 451 (strongly recommended) or 450. MATH 425 would be helpful. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This course is a thorough and fairly rigorous study of the mathematical theory of probability. There is substantial overlap with MATH 425, but here more sophisticated mathematical tools are used and there is greater emphasis on proofs of major results. MATH 451 is preferable to MATH 450 as preparation, but either is acceptable. Topics include the basic results and methods of both discrete and continuous probability theory. Different instructors will vary the emphasis between these two theories. EECS 501 also covers some of the same material at a lower level of mathematical rigor. MATH 425 is a course for students with substantially weaker background and ability. MATH 526, STATS 426, and the sequence STATS 510-511 are natural sequels.
Background and Goals: This course in intended for students with a strong background in topology, linear algebra, and multivariable advanced calculus equivalent to the courses MATH 513 and MATH 590. Its goal is to introduce the basic concepts and results of differential topology and differential geometry.
Content: Manifolds, vector fields and flows, differential forms, Stokes' theorem, Lie group basics, Riemannian metrics, Levi-Civita connection, geodesics
Alternatives: MATH 433 (Intro to Differential Geometry) is an undergraduate version which covers less material in a less sophisticated way.
Subsequent Courses: MATH 635 (Differential Geometry)
This course is an introduction to the theory of complex valued functions of a complex variable with substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical problems are emphasized over proofs, but arguments are rigorous. The prerequisite of a course in advanced calculus is essential. Differentiation and integration of complex valued functions of a complex variable, series, mappings, residues, and applications. Evaluation of improper real integrals and fluid dynamics. MATH 596 covers all of the theoretical material of MATH 555 and usually more at a higher level and with emphasis on proofs rather than applications. MATH 555 is prerequisite to many advanced courses in science and engineering fields.
MATH 556. Methods of Applied Mathematics I.
Section 001.
Prerequisites & Distribution: MATH 217, 419, or 513; 451 and 555. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This is an introduction to analytical methods for initial value problems and boundary value problems. This course should be useful
to students in mathematics, physics, and engineering. We will begin with systems of ordinary differential equations. Next, we will
study Fourier Series, Sturm-Liouville problems, and eigenfunction expansions. We will then move on to the Fourier Transform, Riemann-Lebesgue Lemma, inversion formula, the uncertainty principle and the sampling theorem. Next we will cover distributions, weak convergence, Fourier transforms of tempered distributions, weak solution of differential equations and Green's functions. We
will study these topics within the context of the heat equation, wave equation, Schrödinger's equation, and Laplace's equation.
The syllabus will describe this more thoroughly, but this course is designed primarily for students in math, computer science, and related fields.
The first half of the course is on graph theory and some complexity theory, while the second half deals with some major topics from algebraic and geometric
combinatorics: partially ordered sets, simplicial complexes as they arise in combinatorics, and matroids. In the course of examining these topics, we also will briefly discuss and use a few of the major techniques from enumerative combinatorics, namely bijective proofs, generating functions and inclusion-exclusion via
Möbius functions. The second half of the course will not follow the textbook quite as closely as the first half.
MATH 575. Introduction to Theory of Numbers I.
Section 001 — [3 credits].
Instructor(s):
Kannan Soundararajan
Prerequisites & Distribution: MATH 451 and 513. (1, 3). (Excl). (BS). May not be repeated for credit. Students with credit for MATH 475 can elect MATH 575 for 1 credit.
Credits: (1, 3).
Course Homepage: No homepage submitted.
Many of the results of algebra and analysis were invented to solve problems in number theory. This field has long been admired for its beauty and elegance and recently has turned out to be extremely applicable to coding problems. This course is a survey of the basic techniques and results of elementary number theory. Students should have significant experience in writing proofs at the level of MATH 451 and should have a basic understanding of groups, rings, and fields, at least at the level of MATH 412 and preferably MATH 512. Proofs are emphasized, but they are often pleasantly short. A computational laboratory (MATH 476, 1 credit) will usually be offered as a supplement to this course. Standard topics which are usually covered include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic reciprocity and quadratic fields, application of these ideas to the solution of classical problems such as Fermat's last 'theorem'. Other topics will depend on the instructor and may include continued fractions, p-adic numbers, elliptic curves, Diophantine approximation, fast multiplication and factorization, Public Key Cryptography, and transcendence. MATH 475 is a non-Honors version of MATH 575 which puts much more emphasis on computation and less on proof. Only the standard topics above are covered, the pace is slower, and the exercises are easier. All of the advanced number theory courses (MATH 675, 676, 677, 678, and 679) presuppose the material of MATH 575. Each of these is devoted to a special subarea of number theory.
MATH 590. Introduction to Topology.
Section 001.
Instructor(s):
Arthur G Wasserman
Background and Goals: Math 590 is an introduction to point set topology. It is quite theoretical and requires extensive construction of proofs.
Content: Topological and metric spaces, continuous functions, homeomorphism, compactness and connectedness, covering spaces and other topics.
Text: Topology, Second Edition, by Munkres, Prentice Hall
The course will cover (most of) chapters 2 through 6 of the text.
Grades will be based on weekly individual homework assignments, class participation, two tests and the final exam.
MATH 591. General and Differential Topology.
Section 001.
Prerequisites: Math 451 or the equivalent is a prerequisite. In addition, we will assume a knowledge of Chapter 1 of Munkres' book. Students may wish to go over this chapter before the course.
This course will be a introduction to general topology and differential topology. We will spend roughly half of the semester on each of these topics.
Math 591 is the first part of a two-semester sequence in topology, the sequel being Math 592. The course will be a preparation for part of the topology QR exams. Students who already have a good background in general and differential topology should consider taking Math 537 instead.
We'll cover:
Topological Spaces and Continuous Functions
Quotient Topologies
Connectedness and Local Connectedness
Compactness and Local Compactness
Countability and Separation Axioms
Urysohn's Lemma
Tychonoff's Theorem
Complete Metric Spaces
Manifolds and Smooth Maps
Derivatives and Tangents
Immersions and Submersions
Transversality
Homework assignments will be given periodically. There will also be a midterm exam and a final exam.
Text :
Topology, a First Course by James Munkres, Prentice-Hall and Differential Topology by Victor Guillemin and Alan Pollack, Prentice-Hall.
We will cover roughly Chapters 2-4 of Munkres' book, parts of Chapters 5 and 7, and Chapter 1 of Guillemin and Pollack. |
Disciplinary network of data processing The Network includes disciplinary data processing exercises addressed to students of the Basic Education and Secondary schools: lessons, games, software, vocabulary and symbols. It also includes activities of teachers in the regions as well as the history of idata procesing, methods to help students in their exercises..
Disciplinary network of mathematics The Network includes disciplinary mathematics exercises addressed the students of the Basic Education and Secondary: lessons, games, software, vocabulary and symbols. It also includes activities of teachers in the regions as well as the history of mathematics, page methods to help students in their exercises and the modern in the field of mathematics.
Area of collaboration network of mathematics CM@TIC (Community Mathematics of Information Technology and Communication) is a collaborative web portal devoted to disciplinary network of mathematics. Here you will find extensive information on various topics sorted resources by type, by levels ...
Its goal is to build relationships between teachers on the one hand and teachers / students on the other. Teachers can register, write articles, submit and download files and communicate via the forum or messaging. Students can view all articles, download files and communicate deposited from the Forum. |
7.5 Anti-differentiation with a boundary condition to determine the constant term Definite integrals Area between a curve and the x-axis or y-axis in a given interval, areas between curves Volumes of revolution(136)
7.7 Graphical behaviour of functions: tangents and normals, behaviour for large |x|; asymptotes The significance of the second derivative; distinction between maximum and minimum points Points of inflexion with zero and non-zero gradients
A3 Distribution of the sample mean The distribution of linear combinations of independent normal random variables The central limit theorem The approximate normality of the proportion of successes in a large sample
A4 Finding confidence intervals for the mean of a population Finding confidence intervals for the proportion of successes in a population
B6 The identity element e The inverse a^(−1) of an element a Proof that left-cancellation and right-cancellation by an element a hold, provided that a has an inverse Proofs of the uniqueness of the identity and inverse elements
B7 The axioms of a group {G, *} Abelian groups
B8 R, Q, Z, C under addition; matrices of the same order under addition; invertible matrices under multiplication; symmetries of a triangle, rectangle; invertible functions under composition of functions; permutations under composition of permutations
B9 Finite and infinite groups The order of a group element and the order of a group
B10 Cyclic groups Proof that all cyclic groups are Abelian
B11 Subgroups, proper subgroups Use and proof of subgroup tests Lagrange's theorem Use and proof of the result that the order of a finite group is divisible by the order of any element (Corollary to Lagrange's theorem)
B12 Isomorphism of groups Proof of isomorphism properties for identities and inverses
C3 Series that converge absolutely Series that converge conditionally Alternating series
C4 Power series: radius of convergence and interval of convergence Determination of the radius of convergence by the ratio test
C5 Taylor polynomials and series, including the error term Maclaurin series for e^x, sinx, cosx, arctanx, ln(1 + x), (1 + x)^p Use of substitution to obtain other series The evaluation of limits using l'Hôpital's Rule and/or the Taylor series
D1 Division and Euclidean algorithms The greatest common divisor, gcd(a, b), and the least common multiple, lcm(a, b), of integers a and b Relatively prime numbers; prime numbers and the fundamental theorem of arithmetic |
Specification
Aims
To introduce students to the basic notions of affine and
projective algebraic geometry.
Brief Description of the unit
Algebraic geometry studies objects called varieties defined by polynomial equations.
A very simple example is the hyperbola defined by the equation xy = 1 in the plane.
There is a way of associating rings to varieties, and then the geometric properties can be studied
using algebra, for example points correspond to maximal ideals, or the geometry of the variety can
give information about certain algebraic properties of the ring.
Algebraic geometry originated in nineteenth century Italy, but it is still a very active area of
research. It has close connections with algebra, number theory, topology, differential geometry and
complex analysis.
Learning Outcomes
Successful students will
understand the correspondences between algebraic
varieties, ideals and co-ordinate rings both in the affine and
projective cases,
be able to calculate the singular points and the dimension of algebraic varieties,
be able to carry out calculations on elliptic curves.
Future topics requiring this course unit
Syllabus
Affine and projective spaces.
Affine and projective varieties.
Co-ordinate rings.
Function fields.
Morphisms and rational maps.
Hilbert's Nullstellensatz.
The classification of curves.
The group law on the points of an elliptic curve.
Textbooks
Miles Reid, Undergraduate Algebraic Geometry, CUP.
Teaching and learning methods
Two lectures per week plus one weekly examples class. In addition students should expect to do at least four hours private study each week for this course unit. |
Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more. |
Calculus Problem Solver (REA) (Problem Solvers)
Each undergraduate and graduate studies.
Here in this highly useful reference is the finest overview of calculus currently available, with hundreds of calculus problems that cover everything from inequalities and absolute values to parametric equations and differentials. Each problem is clearly solved with step-by-step detailed solutions.
Customer Reviews:
Excellent
By Robert T Carroll - September 16, 2003
I was recently offered a high school teaching job, so I needed to brush up on my calc, and this book did the trick. Unlike other books, this one "teaches by example". I always found that too many college professors & textbooks spend too much time trying to "explain" the concept. My experience has been to skip the lecture part, do the problems, and in doing so, the concept will come to you. The fact that the problems are all solved in detail is also a plus. A lot of texts simply list the answer to the problem, so you're often left wondering how they got it. This won't be an issue with this text.
This is exactly what the title says
By ophelia99 - January 3, 2005
Even if you understand the principles, the handful of problems in the average textbook are too few to really drill you on the procedures. It's a little like the difference between understanding some music theory and being able to play an instrument. Practice, for those of us who are not math prodigies, is essential. If you are willing to put in the hours and hours, this hugh collection of solved problems is well worth the price.
Step by Step
By Ivan J. Villescas "randomivan" - January 8, 2004
I have been out of college for 7 years. I began Grad school last quarter. This book gave me the basic steps to relearn and remember Calculus. It takes you through each kind of problem without skipping steps or assuming you already know what you are doing. A big crutch for understanding single and multivariable calculus. -I passed the placement exam and then used the book to assist in other engineering classes.
Written by an elementary teacher especially for teachers in the elementary grades (K 5) to help implement problem solving in the classroom, this book includes questions and answers designed to help ... |
Bart Algebra world applications for discrete math. Linear algebra is a branch of math that deals with vector spaces and linear mappings. For less complicated problems, systems of equations can be used
...Over Based on America's issues with mathematics (as detailed in the book... |
"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics. [via]
More editions of 102 Combinatorial Problems: From the Training of the USA Imo TeamThis book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics.
From the table of contents: * Proof Machines * Tightening the Target * The Hypergeometric Database * The Five Basic Algorithms: Sister Celine's Method, Gosper&'s Algorithm, Zeilberger's Algorithm, The WZ Phenomenon, Algorithm Hyper * Epilogue: An Operator Algebra Viewpoint * The WWW Sites and the Software (Maple and Mathematica) Each chapter contains an introduction to the subject and ends with a set of exercises. [via]
The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by a further 250 problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order, and in a thought-provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds, mathematics, computer science or engineering will appreciate this appealing introduction. [via]
As linear orders, as elements of the symmetric group, modeled by matrices, modeled by graphs&permutations are omnipresent in modern combinatorics. They are omnipresent but also multifaceted, and while several excellent books explore particular aspects of the subject, no one book has covered them all. Even the classic results are scattered in various resources.
Combinatorics of Permutations offers the first comprehensive, up to date treatment of both enumerative and extremal combinatorics and looks at permutation as linear orders and as elements of the symmetric group. The author devotes two full chapters to the young but active area of pattern avoidance. He explores the quest for the Stanley-Wilf conjecture and includes the recent and spectacular Marcus-Tardos proof of this problem. He examines random permutations and Standard Young Tableaux and provides an overview of the very rich algebraic combinatorics of permutations. The final chapter takes an in-depth look at combinatorial sorting algorithms.
The author's style is relaxed, entertaining, and clearly reflects his enthusiasm for the "serious fun" the subject holds. Filled with applications from a variety of fields and exercises that draw upon recent research results, this book serves equally well as a graduate-level text and a reference for combinatorics researchersThe book presents the solutions to two problems: the first is the construction of expanding graphs graphs which are of fundamental importance for communication networks and computer science; the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres. Both problems were partially solved using the Kazhdan property (T) from representation theory of semi-simple Lie groups. Later, complete soultions were obtained for both problems using the Ramanujan conjecture from analytic number theory. The author, who played an important role in these developments, explains the two problems and their solutions from a perspective which reveals why all these seemingly unrelated topics are so interconnected. The unified approach shows interrelations between different branches of mathematics such as graph theory, measure theory, Riemannian geometry, discrete subgroups of Lie groups, representation theory and analytic number theory.
Special efforts were made to make the book accessible to graduate students in mathematics and computer science. A number of problems and suggestions for further research are presented.
Reviews:
"This exciting book marks the genesis of a new field. It is a field in which one passes back and forth at will through the looking glass dividing the discrete from the continuous. (...) The book is a charming combination of topics from group theory (finite and infinite), combinatorics, number theory, harmonic analysis." - Zentralblatt MATH
"The Appendix, written by J. Rogawski, explains the Jacquet-Langlands theory and indicates Delignes proof of the Petersson-Ramanujan conjecture. It would merit its own review. (...) In conclusion, this is a wonderful way of transmitting recent mathematical research directly "from the producer to the consumer." - MathSciNet
"The book is accessible to mature graduate students in mathematics and theoretical computer science. It is a nice presentation of a gem at the border of analysis, geometry, algebra and combinatorics. Those who take the effort to glance what happens behind the scene wont regret it." - Acta Scientiarum Mathematicarum
[via]
This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch or problem posers". It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, Erdosos in a comprehensive and well-documented volume, the authors hope to continue the work of an unusual and special man who fundamentally influenced the field of mathematics. [via]
This book is a tribute to Paul Erd\H{o}s, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, Erd\H{o}s\H{o}s in a comprehensive and well-documented volume, the authors hope to continue the work of an unusual and special man who fundamentally influenced the field of mathematics. [via]
This book is a concise, yet carefully written, introduction to modern graph theory, covering all its major recent developments. It This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymour theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for both individual study and classroom use andThe importance of discrete mathematics has increased dramatically within the last few years but until now, it has been difficult-if not impossible-to find a single reference book that effectively covers the subject. To fill that void, The Handbook of Discrete and Combinatorial Mathematics presents a comprehensive collection of ready reference material for all of the important areas of discrete mathematics, including those essential to its applications in computer science and engineering. Its topics include:
Logic and foundations
Counting
Number theory
Abstract and linear algebra
Probability
Graph theory
Networks and optimization
Cryptography and coding
Combinatorial designs The author presents the material in a simple, uniform way, and emphasizes what is useful and practical. For easy reference, he incorporates into the text:
Many glossaries of important terms
Lists of important theorems and formulas
Numerous examples that illustrate terms and concepts
Helpful descriptions of algorithms
Summary tables
Citations of Web pages that supplement the text If you have ever had to find information from discrete mathematics in your work-or just out of curiosity-you probably had to search through a variety of books to find it. Never again. The Handbook of Discrete Mathematics is now available and has virtually everything you need-everything important to both theory and practice.
Jacob E. Goodman, co-founder and editor of Discrete & Computational Geometry, the preeminent journal on this area in the international mathematics and computer science community, joins forces with the distinguished computer scientist Joseph O'Rourke and other well-known authorities to produce the definitive handbook on these two interrelated fields.
Over the past decade or so, researchers and professionals in discrete geometry and the newer field of computational geometry have developed a highly productive collaborative relationship, where each area benefits from the methods and insights of the other. At the same time that discrete and computational geometry are becoming more closely identified, applications of the results of this work are being used in an increasing number of widely differing areas, from computer graphics and linear programming to manufacturing and robotics. The authors have answered the need for a comprehensive handbook for workers in these and related fields, and for other users of the body of results.
While much information can be found on discrete and computational geometry, it is scattered among many sources, and individual books and articles are often narrowly focused. Handbook of Discrete and Computational Geometry brings together, for the first time, all of the major results in both these fields into one volume. Thousands of results - theorems, algorithms, and tables - throughout the volume definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is presented clearly enough to assist the novice, but in enough depth to appeal to the specialist. Every technical term is clearly defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples. Information on current geometric software - what it does, how efficiently it does it, and where to find it - is also included. [via]
The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups. [via]
Flexibly designed for CS students needing math review. Also covers some advanced, cutting edge topics (running 120 pages and intended for grad students) in the last chapter (8). This text fits senior year or intro. grad course for CS and math majors. [via]
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.
Introductory Combinatorics emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs). Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents. The third edition of Introductory Combinatorics has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. A valuable book for any reader interested in learning more about combinatorics. [via]
The algorithms in this text have been rewritten in a language-neutral pseudocode making the book useful to computer science students. Each chapter begins with a "motivating problem" which occurs later as an exercise. Tables and bullet notes have been added througout, with examples. [via]
Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science. This Sixth Edition of Mathematical Structures for Computer Science covers all the topics in the CC2001 suggested curriculum for a one-semester intensive discrete structures course, and virtually everything suggested for a two-semester version of a discrete structures course. Gersting's text binds together what otherwise appears to be a collection of disjointed topics by emphasizing the following themes: Importance of logical thinking Power of mathematical notation Usefulness of abstractions [via]
More editions of Mathematical Structures for Computer Science: A Modern Approach to Discrete Mathematics:An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader. [via]
The it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader. [via] [via]
The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erd/s, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added. According to the great mathematician Paul Erd/s, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, sis, com binatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics. [via]
"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999
"... the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999
This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals".
The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.
The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included. The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms.
Donald E. Knuth is one of the most prominent figures of modern computer science. His works in The Art of Computer Programming are classic. He is also renowned for his development of TeX and METAFONT. In 1996, Knuth won the prestigious Kyoto Prize, considered to be the nearest equivalent to a Nobel Prize in computer science. [via]
More editions of Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms: |
Course Description: This course is designed for students planning to attend college that require additional background in Algebra concepts. This course will build on the concepts and skills learned in Algebra 1.
Teacher's Goals, Expectations, and Student Participation: Students are expected to be on time to class and prepared for the class activities. Class will usually start with a "Do Now" problem which is to be completed at the start of class. I expect classroom rules, as well as school wide rules to be followed in class. There will be homework almost every night, and you should expect a quiz every 2 to 3 sections. A test will be given at the end of each Chapter.
Course Materials:You will need a notebook with 3 sections; one for classwork and "Do Now " problems, one for notes, and one for homework. You should bring this notebook to class every day along with a writing utensil and any homework due that day. You should also have your own scientific calculator as it is difficult to provide a full class set and I cannot guarantee that I will have enough to go around.
Assessment Procedures and Policies:
Tests – 40%
Quizzes – 30%
Homework/Class work/Class Participation – 30%
Each Marking Period is 22% of your Y1 grade, the other 12% is the Final Exam.
Contact Information:
Email Address: [email protected]
Extra Help is available by appointment before and after school as well as during the day if arranged ahead of time. See me if you need help!!! |
Algebrahelp.com: Algebrahelp.com is a collection of tools created to assist students and teachers of algebra.
Cut-the-Knot: A web site devoted to the deductive science of Mathematics. Learning to appreciate Mathematics, as well as tutorials, is a feature of this siteMathematical Atlas: This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and is a pointer to more information, as well as answers to some common questionsCalculus on the Web:a system for learning, practicing and experimenting with the ideas and techniques of calculus - is ongoing work of Gerardo Mendoza and Dan Reich of the Mathematics Department at Temple University.
Calculus Page: This site is calculus done the old-fashioned way — one problem at a time, one easy-to-follow step at a time, with problems ranging in difficulty from easy to challengingGeometry
Computational Geometry Algorithms Library:The goal is to make the most important of the solutions and methods developed in computational geometry available to users in industry and academia. The goal is to provide easy access to useful, reliable geometric algorithmsGeometry in Action: Ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications on this site. It contains brief descriptions of those applications and the geometric questions arising from them, as well as pointers to web pages on the applications themselves and on their geometric connections. It is organized by application but some major general techniques are also listed as topics
Manipula Math with Java: This is a collection of 279 Math Applets. Interactive programs and animation illustrate the meaning of mathematical ideasTrigonometry and Forum: This site helps students learn mathematics through the use of the Internet and innovative technologies. It also gives advanced students an opportunity to pursue their interests as well as use their skills to help othersGames & Fun
Against All Odds: A video program for high school and college students emphasizing "doing statistics". The series goes on location to help uncover statistical solutions to everyday problems. Requires logging in.
Cut-the-Knot: A web site devoted to the deductive science of Mathematics. Learning to appreciate Mathematics, as well as tutorials, is a feature of this siteIBM's Ponder This: This portion of the official IBM web site is for the person who can't see a problem without wanting to take a crack at solving it. If you are that kind of person, then IBM is looking for you. The people at IBM cordially invite you to match wits with them. Each month they post a mathematical problem. Then, in the next month, they offer the solution. Forge ahead and ponder this month's problem |
Program Navigation
Lial, Hornsby, Schneider, Trigonometry, 9th Edition
Lial, Hornsby, Schneider, Trigonometry, 9th Edition
Authors
Bob Blitzer
Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Pearson Prentice Hall.
Marge Lial
Marge Lial's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
John Hornsby
When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum.
David Schneider
David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. |
MATH 222 – MATHEMATICS FOR ELEMENTARY EDUCATION
Theory and application of arithmetic, algebra, geometry, and probability at the primary school level. This course is exclusively for students pursuing a certification in elementary school education; it is a co-requisite of EDUC 322 (3 credits).
MATH 261 –SYMBOLIC COMPUTING Concepts and practical use of a Computer Algebra System such as Maple: Data types and control structures. Two- and three dimensional plotting. Symbolic computing of solutions to selected problems in algebra and analysis. Contrasting exact and numerical solutions (3 credits).
MATH 262 –NUMERICAL COMPUTING
Programming constructs and data structures for a programming language suitable for compute intensive applications, such as C++. Development, implementation, and debugging of algorithms for selected computational problems on workstations and clusters (3 credits).
Prerequisite: Symbolic Computing or permission of the Department chairperson.
MATH 341 –ABSTRACT ALGEBRA I
The first part of a two semester sequence. An introduction to algebraic structures with an emphasis on groups, normal subgroups, cosets, Lagrange's Theorem, and the fundamental homomorphism theorems (3 credits).
Prerequisites: Linear Algebra I.
MATH 342 – ABSTRACT ALGEBRA II
The second part of a two semester sequence. Further study of algebraic structures, such as rings, integral domains, fields. The homomorphism theorem and its applications (3 credits).
Prerequisites: Abstract Algebra I. |
Combinatorial Problems and Exercises
9780821842621
ISBN:
0821842625
Pub Date: 2007 Publisher: American Mathematical Society
Summary: The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems.
Ships From:Boonsboro, MDShipping:Standard, ExpeditedComments:Brand new. We distribute directly for the publisher. The main purpose of this book is to provide... [more] [[ allows the reader to practice the techniques by completing the proof. In the third part, a full solution is provided for each problem. This book will be useful to those students who intend to start research in graph theory, combinatorics or their applications, and for those researchers who feel that combinatorial techniques might help them with their work in other branches of mathematics, computer science, management science, electrical engineering and so on. For background, only the elements of linear algebra, group theory, probability and calculus are needed.[less] |
This set can be started with any child who can add and subtract well and knows how to do long multiplication and division. Check out the information on our "Where to Start" page for more detailed information about where and when to start your student. This set would be considered a middle school math program, for students in 5th through 9th grades. When they are finished these books, they are ready to begin the High School Set. Many high school aged students would benefit by going quickly through these books to lay foundations that they might have missed.
This set can be started with any student who has completed Life of Fred Fractions, Decimals and Percents, PreAlgebra 1 with Biology, and PreAlgebra 2 with Economics or has completed a Pre-Algebra program in another curriculum.
This set can be started with any student who has completed Life of Fred Beginning and Advanced Algebra or has completed Algebra 2 in another curriculum. This set could also be considered a College Prep set as it prepares the student for college level maths. After completing this set, the student is ready to go into the College Set.
Want to purchase all of the upper level Life of Fred Math Books at once? Purchase this kit and you will have the books to take your student from Pre-Algebra Fractions straight through College/University Level math. |
This course is designed to assist students whose high school mathematics background is insufficient for the standard first-year mathematics courses. It is primarily intended as a preparation for MATH-035. Topics include: algebraic operations, factoring, exponents and logarithms, polynomials, rational functions, trigonometric functions, and the logarithmic and exponential functions. Graphing and word problems will be stressed. This course is not intended to complete the math/science requirement in the College. Fall.
Credits: 3
Prerequisites: None
Other academic years There is information about this course number in other academic years: |
Algebra (elementary mathematics)
The elementary algebra east is a branch of the Mathématiques whose object is the study of the laws which govern the numerical quantities. The qualifier of elementary appears at the same time as the modern algebra in order to differentiate it from this one. Today, it is the first approach of the algebra in the school course.
The algebra is different from the arithmetic by the introduction of letters (a, b, c,…, x, y, z,…, \ alpha, \ beta, \ gamma,…) indifferently representing all the numbers and to which are applied same the rules of calculations that if it were about numbers.
It is thus possible to establish laws depending only on the nature of the operations, independently of the numbers.
The resolutions of equations and inequations, the study of the polynomials are applications of the algebra.
Algebraical expressions
An algebraical expression consists of numbers, letters and operational signs: |
Self-Check
Quizzes randomly generates a self-grading quiz
correlated to each lesson in your textbook. Hints are available
if you need extra help. Immediate feedback that includes specific
page references allows you to review lesson skills. Choose
a lesson from the list below.
The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices and balancing a checkbook.
The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations, such as tiling, fabric design, art, and scaling.
The student will make comparisons, predictions, and inferences, using information displayed in frequency distributions; box-and-whisker plots; scattergrams; line, bar, circle, and picture graphs; and histograms. |
Pre-Algebra
9780078651083
ISBN:
0078651085
Pub Date: 2005 Publisher: Glencoe/McGraw-Hill School Pub Co
Summary: "Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.78651085 Student Edition. Missing up to 3 pages. Heavy wrinkling from liquid damage. Does not affect the text. Light wear, fading or curling of cover or spine. May have use [more]
0078651085 |
About Me
Wednesday, August 31, 2011
Most math text books have examples that are completely worked out with the solution given. Take a piece of paper and hide the textbook answer and work, but show the question. Redo the problem and then check your work with their work and solution.
2. Study for Tests and Quizzes.
It is easy to just do the review homework and feel like you are ready for the test. You need to do this and more. Study for the test or quiz by going back through problems that have been given and solved in class. Actually redo them and check your work. Studying for math is DOING the MATH.
3. Make sure your homework is correct.
Check your answers with those that are in the back of the book while you are doing your assignment.
4. Do math EVERYDAY.
Do your homework every day. Try not to skip any days of homework. If you are cramming all your work into a short single session you will find this usually ends up in frustration as well as poor long term memory with the topic.
5. Attempt the most difficult questions.
The most difficult questions will usually teach you the most about the material. Never skip them. Try to get the most exposure to these problems as you can. Try to solve them on your own. Revisit them. Go in for help. Ask a question on the problems in class.
6. Take a break.
Give yourself a break when working with math. If you are being efficient, then three fifteen minute sessions in a day are better than one 45 minute session. Stand up. Stretch. Go for a walk. Move your work to a new place. A break is needed when working with math.
7. Have a good attitude.
Never think "I'm terrible at math". You usually meet your own expectations. Believe that you can do it!
8. Go in for help with your teacher and bring a specific question.
When you bring in a specific question to your math teacher they can help you with where you are struggling. The teacher then can typically give you more examples that are similar to what you are struggling with.
9. 5 minutes.
Once your homework is done, then take an extra 5 minutes to look at these possible things: vocabulary, formulas, notes, projects, and book examples.
Wednesday, August 24, 2011
Yesterday I made a math problem so that it took up one whole page of typing paper. I cut it up into 6 equal pieces that were approximately 3 by 3 inches. I put it a random order and put a paper clip on it. I did this for 5 problems in all and 2 sets of each for a total of 10 questions. I have 20 students in my class. So I had my students work in pairs. It is real easy to cut these problems up with a paper cutter. See the above cut out lines that I took with the problem.
Then I put the 5 stations with 2 sets of the same problem around the room. Four people, or two pairs of partners would be at each station. I would then have them start on the problem and set the timer for ONE MINUTE. The partners together would have to unscramble the pieces and then solve the problem. They would write their answer down on their paper. Once they were done, they could check the answer that is provided at each station. After the minute was over and students had checked their answers, I told them to rotate. They went to the next station and we did the process all over again.
I was happy with the outcome because they seemed to enjoy trying to figure out the puzzle and do the math. It also helps the students to MOVE and LEARN. They are moving after each problem. |
Algebra: A Complete Course
by VideoText Interactive
Is VideoText a Pre-Algebra course, an Algebra 1 course, an Algebra 2 course, or all of these courses?
The reason that we named our program "Algebra: A Complete Course," is that we believe the best way to learn Algebra is to start at the beginning and end at the end! In this program you will find a complete study of the essential material covered in a traditional Algebra 1 and Algebra 2 course.
However, we need to continue a little further with this answer because Algebra 1 and Algebra 2 are terms that refer mostly to the traditional way that Algebra has been taught. Traditional Algebra 1 classes attempt to cover most of Algebra in the first year, but the methods that are used, and the speed with which the material is covered, hinders student understanding of the material. Instead, the student is just exposed to memorizing rules, formulas, tricks, and shortcuts. By the time they get to what is called an Algebra 2 course, (sometimes after they take a Geometry course), they have forgotten almost all of the Algebra that they memorized. So, that Algebra 2 course (which is by definition, a rehash of whatever has been called "Algebra 1"), must repeat practically all of the Algebra 1 course. In fact, it usually repeats a lot of the Pre-Algebra material as well. This is usually referred to as the "spiral method" of learning, and it is not very effective in helping students to excel, especially at this level of mathematics.
We think that this huge overlap is generally unproductive, and largely unnecessary if the concepts are taught analytically. Therefore we call our program "Algebra: A Complete Course," because we employ a mastery-learning approach, sometimes moving at a slower pace, but without the overlap. As a result, students often complete the course even more quickly.
VideoText's Algebra: A Complete Course program contains 176 video lessons contained in 10 unit directories. The program covers Pre-Algebra, Algebra I and Algebra II, and is a firm foundation for students advancing to VideoText's Geometry: A Complete Course, covering Geometry and Trigonometry.
Materials in the complete course include:
176 Video Lessons - Each of the 5-10 minute lessons explore Algebra concepts in a detailed logical order. Because no shortcuts or tricks are used, the methods are easy to follow and promote clear understanding.
360 pages of Course Notes - These notes allow students to review the logical development of a concept. Each page chronologically follows the video lesson, repeating exactly what was shown on the screen.
590 pages of Student WorkText - These pages review the concept developed in each lesson. More examples are given and exercises are provided for students. The explanations are virtually free of complicated language, making it easy for students to follow the logic of each concept.
Solutions Manuals - These manuals provide detailed, step-by-step solutions for every problem in the student WorkText. This resource is a powerful tool when used by students to complete an error-analysis of their work, and to check their thought processes.
Progress Tests - These tests, with the answer keys included, are designed to have students demonstrate understanding, lesson-by-lesson, and unit-by-unit. There are two versions of each test, allowing for retesting or review, to make sure students have mastered concepts.
The quality of mathematics is extremely important to me, as math and science go hand-in-hand. There are many students who cannot handle my chemistry course, for example, because they have not had a good algebra course. That is why I strongly encourage you to look at Videotext Interactive's algebra course. It is, truly, the best that I have seen.
The course teaches real mathematics. It does not use tricks or shortcuts. Instead, it teaches the student to think mathematically. That's what is missing from many algebra courses! The use of animation and graphics is excellent. They do not detract from the learning, as is the case with some video courses I have seen. Instead, they enhance the student's ability to understand what is happening in each and every step along the way.
If you want your student to really learn algebra, then you should use this course. In short, this course is a scientist's dream come true! Every science-oriented student should use it |
Welcome to
Math 152. If you are looking for the main course
website, then please go HERE.
If you are looking for the Lab homepage, then you
have come to the right place.
UPDATES:
Hey guys, reading week is over, and hopefully you all had fun and adventures.
Several people have been asking how reading week interacts with the whole "take a lab every two weeks" rule.
If you are in the first batch of labs (refered to as EVEN on the timetable on this website) you will have a lab this week.
If you had a lab just before reading break, then you will not have one this week.
Cheers,
Alastair.
The Basics During your time in Math 152,
you will be required to take part in 6 "Lab
sessions" designed to help you get familiar with
MATLAB- a software package designed to solve large
Matrix equations. You will attend lab sessions every
second week, and with each lab session you will be
expected to hand in a short assignment. A TA will be
at the lab to collect homework and provide
assistance.
Lab times: There are 24 lab
sessions, labeled L2A to L2Z. It is very important
that you attend your own lab session- if everyone
turned up at the time that best suited them, then
some labs would be empty while others ran out of
computers. Also your tutors will not accept homework
handed in during the wrong lab session. Click
here to find out when and where your lab is.
Lab Assignments: Each fortnight you will be expected to hand in
an assignment along with your lab. You must hand in
your assignment before the end
of the lab session you are assigned to.
These assignments will sometimes take time and
experimentation, thus it is recommended that you
start them before your one hour lab session (except
for your first assignment). All Lab assignments will
be made available early in the term, on this
webpage, so you may approach them at whatever pace
you wish, as long as they are finished before their
hand in date. Lab 1 Lab 2 Lab 3 Lab 4 Lab 5 Lab 6
Your
Lab Password: To access a computer in the lab, you
will need a login ID and password. Your login ID
is the first 8 characters of your first name,
middle name and last name written together without
any spaces and all lowercase.
Example: Your Name: John Xavier Woo Your Login: johnxavi
Your password is the character S (
uppercase required ) followed by the first seven
digits of your student number.
Example: Student Number: 31415926 Password: S3141592
If your login does not work, it may
be because another student's name generates the
same login as yours. If this happens, talk to your
TA to get your correct login details.
Your TA's Your lab TA is there to help you
explore the Matlab software, and help with both
technical and conceptual issues (IE, if either you
or the computer is confused, your tutor is there
to help.)
A List of TA emails will soon be avaliable on this
site, possibly with a brief description.
Name: Alastair Jamieson-Lane Email: [email protected] Description: Hey Team- I'm the head Lab T.A.
for this course. That's a fancy title which means I
end up doing more paperwork, and odd jobs around
here (such as scratching together this webpage). I'm
from New Zealand and have just arrived at UBC to
start my Masters in evolutionary game theory. If you
have any questions which you can't take to your Lab
TA for any reason, feel free to email me (or Ozgur
Yilmaz if it is very serious)
Name: Bernhard Konrad Email: [email protected] Description: Hi, I am a third year PhD
student in Mathematical Biology at UBC. I use MatLab
to study HIV dynamics within an infected individual,
and how treatment could be improved. I look forward
to seeing you in the labs.
Name: Nabil Fadai Email: [email protected] Description: Hi! My name's Nabil, and I'm a
4th year student in Honours Mathematics. I focus
mainly on applied Mathematics, especially relating
to Differential Equations. As many Differential
equations are impossible to solve (exactly) by hand,
it is important to use numerical approximations and
computer software, such as Matlab, to make sense of
these equations. I wish you all the best of luck as
you begin your journey into the fascinating world of
MatLab
Name: Mengdi Hua Email: [email protected] Description: Hi, I am a master student
entering the 2nd semester and will be your TA for
sessions L2C and L2D. Feel free to contact me if you
have questions about our exciting labs. |
This is an entirely online basic mathematics course that will cover the fundamentals of arithmetic and beginning algebra. This online course is fitting for a diverse set of individuals seeking to fill in the gaps of their mathematical knowledge.
Individuals that would find this course extremely useful include
students who need to review for a future college course they will be taking
teachers who desire a better a foundation in order to enhance their classroom teaching
community members needing review for state tests.
The course material will coincide with K-12 standards. Along with the content to be covered, additional tools provided throughout the course include: strategies for success, skills in computation, critical thinking and problem solving. |
The main purpose of Linear Algebra and Linear Models is to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms are developed along the way. The book is aimed at advanced undergraduate... more...
This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational... more...
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the... more...
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be... more... |
Peltier, Doug
Calculus is a college level class, and as such, most of the emphasis will be placed on how well students do on assessments (tests and quizzes). As a result, student grades are calculated in the following manner: 10% for daily work, and 90% for assessments.
Daily work is collected at the end of every chapter on the day of the chapter test. The students are well aware of this fact, and will probably be scrambling the night before the test to finish any work that remains undone (unless they are not procrastinators, then it will already be done!).
At the bottom of the page you will find the PowerPoint lessons for this class, available usually after the day the material was presented in class, but occasionally the same day. This is the exact same presentation as was given in class, minus any bad jokes and commentary on my part. |
Math Strategies
Course Description
Math Strategies is designed to help students who struggle in math. We will concentrate on the following: Basic Skill Review – This includes computation and vocabulary Problem Solving Strategies – We will work on these both collaboratively and individually. Math Homework Help – This is to ensure students understand the concept beign taught in order to complete the assignment. Working on Individual Math Deficits – through Odyssey Compass Learning.
Enduring Understandings
Mathematics can help us make more informed decisions, work efficiently, solve problems, and appreciate its relevance in the world.
Geometric methods can help us to make connections and draw conclusions from the world in which we live.
Functions and number operations play fundamental roles in helping us to make sense of various situations.
Using prior knowledge, appropriate technology, and logical thinking, we can analyze data and effectively communicate the reasonableness of solutions.
Multiple mathematical approaches and strategies can be used to reach a desired outcome.
Algebraic models, patterns, and graphical representations are tools that can help us make meaningful connections to real-world situations.
Essential Questions:
What are the essential elements of Algebra that have grown out of the study of Pre Algebra?
How can numbers be used to make comparisons? How can mathematics help us make more informed decisions, work efficiently, and understand the world around us? |
Personal tools
Sections
Mathematica
Mathematica is a powerful, general-purpose numeric and symbolic computation tool.
Mathematica is a computer algebra system that is widely used in science, engineering, mathematics, finance, and other fields. MATLAB also has a symbolic algebra package, but Mathematica's symbolic computation facilities are more sophisticated and integrated with the rest of its features.
Mathematica has the ability to analytically and numerically solve differential equations using the DSolve and NDSolve commands. As a result, it can an indispensable tool for an instructor wanting to check or generate examples or problems.
Mathematica is not designed primarily for educational purposes, and its LISP-inspired syntax creates a steep learning curve for students and instructors alike. However, since it is widely used in academia and industry it may be beneficial for students to become familiar with its capabilities.
Instructors may find the Manipulate command in Mathematica an especially helpful tool for creating interactive tools for exploring differential equations. The Wolfram Demonstrations Project contains a large number of interactive tools built with the Manipulate (and related) commands. |
Courses
Enter search criteria above, or choose a subject below…
Ma 101: Basic College Mathematics
3 cr.
A survey course. Topics include real number system expressions and equations emphasizing practical elementary mathematics. Required of students with math ACT below 18. Not applicable toward a major or minor.
Ma 109: Essential Mathematics for Teachers
3 cr.
A study of mathematics properties, processes and symbols for prospective teachers on the elementary level. Sets, relations, number theory, the real number system and problem solving. Not applicable toward a major or minor.
Ma 110: Foundations of Mathematics for Teachers
3 cr.
A study of mathematics properties, processes and symbols for prospective teachers on the elementary level. Measurement, the metric system, geometry, congruence, coordinate geometry, probability and statistics. Not applicable toward a major or minor.
Ma 150: Introduction to Mathematical Reasoning
3 cr.
A bridge or transition course between the lower level mathematics courses to more abstract and theoretical upper level courses in which mathematical proof is essential. Development of mathematical maturity is the ultimate goal of this class. This will be accomplished by developing the ability to interpret and use mathematical language and notation, understand elementary logic, learn how to read and understand mathematical definitions and proofs, construct and write mathematical proofs. Not applicable toward a math major or minor. Required of all before taking first 300 level math class unless waived by passing Mathematics Reasoning placement test.
Ma 180: Introduction to Calculus
3 cr.
A calculator-based applied calculus class in one variable. Derivatives, integrals and their applications will be studied. Required calculator: TI 83, 84 or Nspire. Not applicable toward a major or minor.
Ma 201: Calculus II
3 cr.
A continuation of Ma 200. Topics include definite integration, differentiation and integration of transcendental functions and other algebraic curves, and applications. Required calculator: TI 89 or Nspire CAS.
Ma 210: Elementary Statistics
3 cr.
Descriptive statistics, elementary probability, the study of the binomial, uniform, and normal probability distributions, point and interval estimations, and elementary hypothesis testing. Required calculator: TI 83, 84 or Nspire. TI 89 or Nspire CAS may be used with permission. Not applicable toward a major or minor.
Ma 211: Theory of Geometry
3 cr.
Structure of proof, deductive reasoning, a survey of the theory of Euclidean geometry with an emphasis on proofs involving lines, angles, triangles, polygons and circles, theory of transformational geometry, analytical geometry and conics. Experience with Geometer's Sketchpad. Not applicable toward a mathematics or actuarial science major or minor.
Ma 380: Actuarial Science I 381: Actuarial Science II 388: Actuarial Exam FM Preparation
1 cr.
This course is a self-study course designed to prep the student for the SOA exam FM.
Prerequisite: Ma 308.
This course is not offered this academic year.
Ma 390: Linear Optimization
3 cr.
A study of linear programming methods employed in operations research. Topics include an introduction to modeling, the theory and application of the simplex method, duality and sensitivity analysis with applications directed toward business.
Prerequisite: Ma 300.
This course is not offered this academic year.
Ma 391: Topics in Optimization
3 cr.
A study of deterministic methods employed in operations research. Topics include specific cases of linear programming problems as well as integer and nonlinear programming.
Ma 402: Abstract Algebra
3 cr.
The theory of mathematical structures with an emphasis on group theory. Examples are taken from the real number system, linear algebra and calculus. Elements of number and set theory are used extensively. The study of homomorphisms, isomorphisms and related theory is included. Required calculator: TI 89 or Nspire CAS.
Ma 403: Intermediate Analysis
3 cr.
The real and complex number systems, point-set theory, concepts of limits and continuity, differentiation of functions of one and more variables, functions of bounded variation, rectifiable curves and connected sets. Required calculator: TI 89 or Nspire CAS.
Ma 479: Mathematics Seminar
1 cr.
Required of all students majoring in Mathematics. Gives senior math majors an opportunity to examine difference facets of a career in Mathematics. These facets include independent study of an advanced topic and presenting that study to a group of his peers. Not applicable toward a major or minor. |
Description
This accessible text is designed to help readers help themselves to excel. The content is organized into two parts: (1) A Library of Elementary Functions (Chapters 1—2) and (2) Finite Mathematics (Chapters 3—Features
Examples are annotated and the problem-solving steps are clearly identified. This gives students extra assistance in understanding the solution.
Selected examples include steps that are usually performed mentally to provide a "basics refresher" for students who need it. (These steps are set off with dashed lines; see page 109, example 4.)
A Matched Problem follows each example, providing students with an opportunity to reinforce and test understanding before moving on.
More than 5,600 carefully selected and graded exercises are designed to help you craft the right assignments for students.
A, B, and C levels of exercises make it easy to appropriately challenge your students.
Paired exercises of the same type and difficulty level (consecutive odd and even) allow you control over student use of answers (odd answers at the back of the text).
Ample and up-to-date applications illustrate the relevance of mathematics and give students opportunities to create and interpret mathematical models.
Optional graphing-utility and spreadsheet examples and exercises are clearly identified by an icon. These provide a deeper understanding of mathematical concepts and allow students to solve problems that are not feasible to solve by hand.
Explore & Discuss problems in every section encourage students to think about a relationship or process before a result is stated or to investigate additional consequences of a development in the text. These problems can help students of all levels gain better insight into the mathematical concepts and are effective in both small and large classroom settings.
Conceptual Insight boxes, appearing in nearly every section, make explicit connections to previously learned concepts, helping students place this new information in context.
An Algebra Diagnostic Test prior to Chapter 1 helps students assess their prerequisite skills, while the Basic Algebra Review in Appendix A (referenced in the answers to the Algebra Diagnostic Test) provides students with the content they need to remediate those skills.
Chapter Reviews include exercises at the A, B, and C levels as well as thorough end-of-chapter summaries keyed by page number to worked examples within the chapter.
Topic selection, coverage, and organization reflect the course outlines and catalogs of many major colleges and universities. This text takes into account the way the course is typically taught and gives students the essential mathematical skills needed to effectively pursue courses of study in business and economics.
A Library of Elementary Functions (Chapters 1 & 2) provides optional material that can be covered in its entirety or referred to as needed. These chapters encourage students to view mathematical ideas and processes graphically, numerically, and algebraically.
Emphasis on the construction of mathematical models, especially in linear systems and linear programming, gives students critical tools for solving application problems.
Technology coverage is optional, but brief discussions on using graphing calculators and spreadsheets are included where appropriate.
Mini-Lectures are included for most sections from the text and provide additional classroom examples, a summary of suggested learning objectives to cover, and teaching notes for the material. These mini-lectures are ideal for instructors who do not teach this course frequently, or just need some additional guidance or resources. Mini-lectures are available for download from the Instructor Resource Center as well as within MyMathLab®.
Worksheets for Classroom or Lab Practice offer a convenient, ready-to-use format, with ample space for students to show their work. The worksheets are written specifically for this text, are organized by Learning Objective, and highlight key Vocabulary Terms and Vocabulary Exercises for student reference as a study guide.
MyMathLab features an ample selection of homework exercises plus instructional videos for every example in the text.
Author |
Mathematica Basics (Spanish)
This screencast helps you get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions Chinese translation.
This is part 8 of an 8-part screencast series giving an overview of the benefits of Mathematica 8 for education, with a focus on building an example presentation complete with calculations, graphics, and data. Includes Japanese audio.
This is part 2 of an 8-part screencast series giving an overview of the benefits of Mathematica 8 for education, with a focus on different methods for getting started with Mathematica Spanish audio Includes Japanese audio.
This screencast helps you to get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions.
This screencast helps you get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions. Includes Spanish audio. |
Founded by two Harvard educated brothers—Greg and Shawn Sabouri—Teaching Textbooks is designed to make learning math in a homeschool setting the best possible experience. Since it was designed specifically for homeschoolers, the text is self-explanatory for independent learners, and the hundreds of hours of CD-ROM teaching allow students to work through problems with a tutor in the comfort of their own homes! Plain language, friendly fonts, highlighted phrases, constant review and flexibility make Teaching Textbooks one of the most popular math programs available.
Early primary-grade math lays the framework for all later mathematical skills, and is also vitally important for everyday life. Ensure that your students understand adding and subtracting multiple numbers, writing fractions, carrying, multiplication, money, telling time, and more.
All the fantastic features that have made other Teaching Textbooks are
so popular are included in the new Math 5. Fifth grade topics covered include operations with whole numbers,
adding & subtracting, multiplication, rounding & estimation, fractions, decimals, and more.
Directions written to the student, answer booklet and CD-ROM
collection with step-by-step audiovisual solutions to every one of the
thousands of homework and test problems are included to start your
students on the right track to upper-level math.
Looking for a math curriculum with enough instruction for the
independent, homeschooling student? Search no more! This applauded Math
7 curriculum was written by two Harvard-associated brothers specifically
for homeschooled students.
Teaching Textbooks' Algebra 1 2.0 includes automated grading, a digital gradebook with multiple student accounts which may be edited by a parent, over a dozen more lessons and hundreds of new problems and solutions, interactive lectures, hints and second chance options for many problems, and more.
Lessons that require a teacher, horrifically dull examples, and
forbidding language are all hurdles that homeschoolers must survive
when looking at math curriculum...or do we? This applauded geometry
curriculum features clear instructions and employs a conversational style of
writing.
Each chapter features a conversational lesson and
features multiple illustrations before moving on to practice exercises
and a problem set-both of which include questions based on problems
found in the CLEP and SAT II math tests. |
ne... read more
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Two-Person Game Theory by Anatol Rapoport Clear, accessible treatment of mathematical models for resolving conflicts in politics, economics, war, business, and social relationships. Topics include strategy, game tree and game matrix, and much more. Minimal math background required. 1970The Green Book of Mathematical Problems by Kenneth Hardy, Kenneth S. Williams Popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. Includes questions drawn from geometry, group theory, linear algebra, and other fields never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics. Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.
Bonus Editorial Feature:
Frederick Mosteller (1916–2006) founded Harvard University's Department of Statistics and served as its first chairman from 1957 until 1969 and again for several years in the 1970s. He was the author or co-author of more than 350 scholarly papers and more than 50 books, including one of the most popular books in his field, first published in 1965 and reprinted by Dover in 1987, Fifty Challenging Problems in Probability with Solutions.
Mosteller's work was wide-ranging: He used statistical analysis of written works to prove that James Madison was the author of several of the Federalist papers whose authorship was in dispute. With then–Harvard professor and later Senator Daniel P. Moynihan, he studied what would be the most effective way of helping students from impoverished families do better in school — their answer: to improve income levels rather than to simply spend on schools. Later, his analysis of the importance to learning of smaller class sizes buttressed the Clinton Administration's initiative to hire 100,000 teachers. And, as far back as the 1940s, Mosteller composed an early statistical analysis of baseball: After his team, the Boston Red Sox, lost the 1946 World Series, he demonstrated that luck plays an enhanced role in a short series, even for a strong team. In the Author's Own Words: "Though we often hear that data can speak for themselves, their voices can be soft and sly." — Frederick Mosteller |
What Kind of Problems Might I Work On?
While they may differ widely by discipline and job title, one thing remains constant among careers in mathematics—problem solving. Some potential problems that someone with mathematical training might encounter are briefly discussed below. It may be useful to note which of them you find most intriguing, and why.
How can an airline use smarter scheduling to reduce costs of aircraft parking and engine maintenance?
How can one design a detailed plan for a clinical trial? Building such a plan requires advanced statistical skills and sophisticated knowledge of the design of experiments.
Is ethanol a viable solution for the world's dependence on fossil fuels? Can biofuel production be optimized to combat negative implications on the world's economy and environment?
How can automotive systems become more efficient and reduce emissions as mandated by U.S. public policy?
How do we use major advances in computing power to incorporate knowledge about interactions between the oceans, the atmosphere and living ecosystems into models used to predict long-term change?
How can automotive and aircraft companies test performance, safety, and ergonomics, while at the same time lowering the cost of construction and testing prototypes?
A pharmaceutical company wants to
search a very large database of proteins to find one that is similar in shape or activity to one they have discovered. What's the most efficient way to do so?
How might disease spread in populated areas in the event of
a bioterrorism incident, and how would it be contained?
How do you design a robotic hand to grip a coin and drop it in
a slot?
How can you mathematically model the spread of a forest fire depending on weather, ground cover and type of trees?
How can you allocate an investment among various financial instruments to meet a risk/reward trade-off?
Since a chemical company cannot test potential new products by releasing them into the atmosphere, it must develop models of atmospheric chemistry that simulate the complex chemical reactions in the atmosphere. Can computational simulations show sufficient detail to capture the effects of the chemicals, but still be fast enough to permit studies of many different chemicals?
How can genome sequencing analysis help in making clinical decisions based on a personalized medicine approach?
Recommendation algorithms provide users of e-commerce systems with unique ratings and recommendations of items and products based on their past purchases, behavior and interests. How can mathematics improve rating prediction performance and help enhance the consumer experience?
Part of the preparation for your future is obtaining a solid foundation in mathematical and computational knowledge—tools like differential equations, probability, combinatorics, applied algebra, and matrices, as well as the art of abstraction and advanced computing and programming skills. Preparation for a career in applied mathematics and computational science also involves being able to apply these skills to real-life problems, and achieving practical results. Mathematical and computational skills are a huge career asset that can set you apart and open doors. |
Mathematics Programs
K-8 Mathematics Programs:
Connected Math Project 2 (CMP2) and
Gomath and Glencoe Math
High School Mathematics Text Books:
Foerster Algebra I & II and Jurgenson Geometry
Read below for detailed information about these district programs, district mathematics partnerships, and curriculum maps.
Holyoke Public Schools Math Programs
Connected Math Project 2 (CMP2) is a researched based program that is being used for middle school mathematics instruction. The overarching goal of the program is that all students be able to reason and communicate proficiently in mathematics. CMP helps students develop an understanding of important concepts, skills, procedures, and ways of thinking and reasoning in number sense, measurement, geometry, algebra, probability and statistics. The concepts are embedded in engaging problems that students explore individually, in a small group, or with a whole class. The problems presented over time give student practice with important concepts, related skills, and algorithms. A three-phased workshop model that support s problem centered instruction is used to deliver the curriculum in these classes. Teachers have had opportunities for training in CMP2 made available to them through district initiatives, America's Choice On-Grade Level Training, and CMP Training from Lesley University and Pearson Learning. The District Math Coaches and Lesley University will continue to provide teachers with training in the mathematical content and implementation of lessons.
The Math programs are implemented using the Workshop Model. This three-phase instructional workshop model used to deliver instruction in all math classrooms in grades K - 8. In the initial phase, Launch or Opening – the teacher sets the problem, introduces new ideas, clarifies definitions reviews, old concepts, and connects to past experiences without lowering the challenge of the task. During the second phase, Explore or Work Time – students work independently or in small groups to gather data, share ideas, look for patterns, and make conjectures. In the final phase Summary or Closing – the students present and discuss their solutions as well as the strategies they used as the teacher guides them to reach the mathematical goal of the class and connect their new understanding to prior knowledge. Teachers have had opportunities for training on the workshop model made available to them through district initiatives, America's Choice On-Grade Level Training, CMP Training from Lesley University and Pearson Learning, and Math Investigations Training from Hampshire Educational Collaborative. District Math Coaches will continue to work with teachers to enhance the implementation of the program and help to deepen the understanding and connection of the mathematical strands.
Curriculum Maps for K – 8 have been designed to ensure that students are exposed to a rigorous curriculum in every school and every grade, and to have consistent instruction and assessment district wide. The district's expectation is for students to successfully meet the Massachusetts Mathematics Standards and to score at the proficient range on the MCAS test in mathematics. In order to facilitate this, teachers are required to follow the curriculum maps. The successful implementation of these maps requires teachers to work through the project and problems prior to planning their lessons. The math coaches and other district personnel were trained in curriculum mapping by America's Choice, became the principle architects of the documents, and are now providing professional development to the grade level teachers as the first of these maps are available. |
Problem Solving and Word Problem Smarts!
Are you having trouble with math word problems or problem solving? Do you wish someone could explain how to approach word problems in a clear, simple way? From the different types of word problems to effective problem solving strategies, this book takes a step-by-step approach to teaching problem solving.
This book is designed for students to use alone or with a tutor or parent, provides clear lessons with easy-to-learn techniques and plenty of examples. Whether you are looking to learn this information for the first time, on your own or with a tutor, or you would like to review some math skills, this book will be a great choice.
show more show less
Edition:
2012
Publisher:
Enslow Publishers, Incorporated
Binding:
Trade Cloth
Pages:
64
Size:
6.75" wide x 9 |
The joint Entrance Examination (JEE) for admission to the Indian Institutes of Technology (IITs) and the Banaras Hindu University of Technology (IIT-BHU) is one of the most competitive examinations in India and only the best survive. HOW WILL THIS BOOK HELP YOU' From january 2000, IIT has been read more...
This fourth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses: discrete mathematics, graph theory, modern algebra, and/or combinatorics. More elementary read more...
This colourful mini hardback is an invaluable reference guide for children at the Maths Key Stage 1 level. Easily understandable text and bright illustrations teach the child the basics of maths such as measuring units, quantities and the vocabulary of maths. Its small size makes it ideal for read more...
An essential resource that will enable all parents – whatever their ability – to help their child with homework and general numeracy questions Does the sight of your child's maths homework fill you with dread? Do you look for any excuse when they ask you to explain fractions or multiplication? read more...
As technology progresses, we are able to handle larger and larger datasets. At the same time, monitoring devices such as electronic equipment and sensors (for registering images, temperature, etc.) have become more and more sophisticated. This high-tech revolution offers the opportunity to observe read more...
David Acheson's extraordinary little book makes mathematics accessible to everyone. From very simple beginnings he takes us on a thrilling journey to some deep mathematical ideas. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes read more... |
Discrete Mathematics
9780130890085
ISBN:
0130890081
Edition: 5 Pub Date: 2000 Publisher: Prentice Hall PTR
Summary: For one or two term introductory courses in discrete mathematics. This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has woven techniques of proofs into the text as a running theme. Each chapter has a problem-solving corner that shows students how to attack and solve problems |
The global spatial data model (GSDM) preserves the integrity of three-dimensional spatial data. Combining horizontal and vertical data into a single, three-dimensional database, this text provides a logical development of theoretical concepts and practical tools that can be used to handle spatial data efficiently. more...
This book is designed for grades K–2 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-10 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data... more...
This book is designed for grades 3–5 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-15 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data... more...
Maths is enjoying a resurgence in popularity. So how can you avoid being the only dinner guest who has no idea who Fermat was or what he proved, and what Fibonacci?s sequence or Pascal?s triangle are? The more you know about Maths, the less of a science it becomes. 30 Second Maths takes the top 50 most engaging mathematical theories, and explains... more... Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results... more... |
Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd
9780077460396
ISBN:
0077460391
Edition: 8 Pub Date: 2011 Publisher: McGraw-Hill Higher Education
Summary: Be guided through every step of the fundamentals of statistics. It is a great introduction to statistics for college students who have a basic grasp of algebra. It covers all the main concepts effectively and provides a lot of opportunity for practical application. Students are taught problem solving using detailed instructions and examples. It also focuses on the different digital applications used in statistics suc...h as Excel, graphing calculators and MINITAB. It also complements an online course so students can receive more from their course and excellent feedback from the online platform. We offer many top quality used statistics textbooks for college students |
Formal Definition of the Derivative. The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials. Product Rule and Quotient Rule. The Chain Rule and Higher Derivatives. Derivatives of Trigonometric Functions. Derivatives of Exponential Functions. Derivatives of Inverse and Logarithmic Functions. Approximation and Local Linearity. Review Problems.
Functions of Two or More Independent Variables. Limits and Continuity. Partial Derivatives. Tangent Planes, Differentiability, and Linearization. More About Derivatives. Applications. Systems of Difference Equations. Review |
CME Project
Funded by the National Science Foundation, the Center for Mathematics Education (CME) project is a four-year comprehensive high school mathematics program.
This problem-based, student-centered project emphasizes the development of students' mathematical habits of mind. The curriculum is organized around the familiar themes of Algebra 1, geometry, Algebra 2, and precalculus and is published by Pearson. |
INTRODUCTION TO HIGH SCHOOL ALGEBRA
Grade Level: 9-10
Prerequisite: None
Introduction to High School Algebra is a course designed to develop the skills required to be successful in Algebra I. Mathematical content includes number sense, patterns and functions, and problem solving. This course will meet High School graduation requirements.
ALGEBRA 1-2
Grade Level: 9-12
Prerequisite: None
Meets the UC/CSU "C" requirement
This course is the first year of algebra. Students learn about operations with algebraic expression, solutions to first and second degree equations, factoring, graphing linear equations, inequalities, irrational numbers, the quadratic formula, and other similar topics. The typical student spends at least one-half hour on homework daily. This course has been aligned to the PUSD and State Standards for Mathematics, and meets the PUSD math requirements.
GEOMETRY 1-2
Grade Level: 9-12
Prerequisite: C or better in Algebra 1-2 or C or better in Algebra 2A-2B
Meets the UC/CSU "C" requirement
This course teaches deductive reasoning and organized thinking. Students study postulates, definitions, and theorems to use in formal proofs. Both semesters emphasize using algebraic skills to solve problems. Plane geometry and solid geometry are taught. Students also learn straightedge and compass constructions and transformations.
HONORS GEOMETRY 1-2
Grade Level: 9-10
Prerequisite: B or better in Algebra 1-2 Teacher recommendation
Meets the UC/CSU "C" requirement
This course is a faster-paced version of Geometry 1-2, allowing time for extensive review of algebra topics to prepare students for Honors Algebra 3-4.
ALGEBRA 3-4
Grade Level: 10-12
Prerequisite: Geometry 1-2
Meets the UC/CSU "C" requirement
This course is a review and extension of first year algebra. New topics include conic sections, probability, logarithms, matrices and properties of functions. It is intended for college bound students who are not math or science majors.
TRIGONOMETRY (Fall semester only)
Grade Level: 11-12
Prerequisite: C or higher in Algebra 3-4 or Honors Algebra 3-4
Meets the UC/CSU "C" or "G" requirement
This is a one semester course in trigonometry. Topics covered include special triangles, the unit circle, using the graphing calculator, proving trigonometric identities, solving equations, solving triangles, angular velocity, and the laws of sines and cosines. It is intended for college bound students who are not math or science majors.
STATISTICS (Spring semester only)
Grade Level: 11-12
Prerequisite: Algebra 1-2 and Geometry 1-2
Meets the UC/CSU "C" or "G" requirement
Statistics is a college preparatory course that will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Probability and counting methods are included. Students will apply descriptive statistics to a wide range of disciplines.
ADVANCED PLACEMENT STATISTICS 1-2
The multidisciplinary aspects and applications of statistics make it one of the most rewarding classes to take. The study blends the rigor, calculations, and deductive thinking of mathematics, the real-world examples and problems of social science, the decision-making needs of business and medicine, and the laboratory methods and experimental procedures of the natural sciences. This course is designed to prepare students to take the Advanced Placement Exam for Statistics.
HONORS PRE-CALCULUS 1-2
Grade Level: 11-12
Prerequisite: C or higher in Honors Algebra 3-4 B or higher in both Algebra 3-4 and Trig/Stats
Meets the UC/CSU "C" or "G" requirement
This course is for advanced college prep students. It provides the foundation for students to proceed to Calculus. Reviews Trigonometry, Geometry, and Algebra. It introduces the study of polynomials including synthetic division, graphing theory, limits, and derivatives.
COLLEGE ALGEBRA/TRIGONOMETRY 1-2
This course is designed for the advanced math student who is preparing to take Honors Pre-Calculus or college mathematics. Non-algebra based topics (such as network theory and number theory) will be studied, along with some pre-calculus concepts, in order to bring diversity and interest to the curriculum. Students will leave the course prepared to take a pre-calculus, statistics, or discrete math course in either high school or college mathematics.
ADVANCED PLACEMENT CALCULUS AB 1-2
This course is a college-level class for students who have completed the equivalent of 4 years of college preparatory mathematics. Students will receive little or no review. Topics include derivatives, differentials, integrations, and applications. Many problems are atypical and require students to synthesize new solutions. A graphing calculator is required. The course is designed to prepare students to take the Advanced Placement Exam for Calculus AB.
ADVANCED PLACEMENT CALCULUS BC 1-2
Grade Level: 11-12
Prerequisite: B or better in Calculus AB 1-2 Teacher Recommendation
Meets the UC/CSU "C" or "G" requirement
This course is for students who have completed four years of college preparatory math including Calculus AB. New topics covered include parametric equations, vector functions, indeterminate forms of limits, polar curves, advanced integration techniques, infinite series, and Taylor polynomials. This course prepares the student to take the Advanced Placement Exam for Calculus BC. |
EMMentor_Light 3.0
Review
Interactive multilingual mathematics software for training problem-solving skills offers more than 500 of math problems, a variety of appropriate techniques to solve problems and a unique system of performance analysis with methodical feedback. The software allows students at all skill levels to practice at their own pace, learn from both errors and solutions, review their work and get optimal exercises for building missing math knowledge and skills. A translation option offers a way to learn math lexicon in a foreign language. Test preparation options facilitate development of printable math tests and automate preparation of test variants. Covered subject areas are arithmetic, pre-algebra, algebra, trigonometry and hyperbolic trigonometry. Included are basic and advanced math topics |
This course is designed to assist in achievement on the PSSA (Pennsylvania State System of Assessment) for 8th Grade Mathematics. It includes lessons aligned with the state anchors that include interactive activities, videos, games, and images. Students are asked to write and explain work in a variety of situations that include blogs, open-ended assignments, journals, and Unit Projects. Quizzes are designed in a multiple-choice format, to mirror the questions on the state exam. Use of a scientific calculator is encouraged. |
Synopses & Reviews
Publisher Comments:
BEGINNING ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master algebraic concepts, problem solving, and communication skills. Students learn how to solve problems generated from realistic applications, instead of learning techniques without conceptual understanding. The authors have developed several key ideas to make concepts real and vivid for students. First, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Second, the authors integrate applications, drawing on realistic data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Third, the authors develop key concepts as students progress through the course. For example, the distributive property is introduced in real numbers, covered when students are learning how to multiply a polynomial by a constant, and finally when students learn how to multiply a polynomial by a monomial. These concepts are reinforced through applications in the text. Last, the authors' approach prepares students for intermediate algebra by including an introduction to material such as functions and interval notation as well as the last chapter that covers linear and quadratic modeling.
About the Author
Mark Clark graduated from California State University Long Beach with a Bachelor's and Master's in Mathematics in 1995. He is a full-time Associate Professor at Palomar College and has taught there for the past 9 years. He is a member of AMATYC and regularly attends the national AMATYC and ICTCM conferences. He has also done extensive reviewing and testing of various classroom technologies and materials. Through this work, he is committed to teaching his students through applications and using technology to help his students both understand the mathematics in context and communicate their results clearly. Intermediate algebra is one of his favorite courses to teach, and he continues to teach several sections of this course each year.
Table of Contents
"This book has just the right balance of skill and application problems.It does a good job of helping the students throughout the sectionswithout just giving all the answers away."Kate Bella, Instructor, Manchester Community College "It is easily readable for students, the explanations are clear, and themargin notes are a nice feature that makes the text more reader friendly."Daniel Lopez, Instructor, Brookdale Community College "I love how the text is centered on real-life situations. Students aregiven a great deal of assistance from the margin notes and well-workedexamples."Brianne Lodholtz, Instructor, Grand Rapids Community College "The approaches of Concept Investigations and Concept Connectionscaught my attention right away. I believe they will help studentsunderstand concepts better."Xiaomin Wang, Instructor, Rochester Community and Technical College |
Mathematics Department Handbook
Welcome to the Department of Mathematics at the University of Rochester.
We have compiled these notes in order to assist you, the first year
student, in making the transition from high school to university. This
is sometimes a difficult process for various reasons. As far as first
year mathematics courses go, there are two main difficulties:
First, the Department of Mathematics expects students who take courses
in mathematics to take the responsibility for mastering the course
material. There is lots of assistance offered, all detailed in these
notes, but it is your responsibility to use these resources. Second,
many talented students have been able to do well in their high school
math courses in spite of not having regular work habits, but now the
situation is very different. It is almost impossible to pass first
year university mathematics courses without developing these habits.
We hope this Guide will help you learn how.
We have also included in these notes some hints on study techniques and
writing examinations, expanded descriptions of first year courses, and a
reading list for students interested in expanding their knowledge of
mathematics in a general way.
Again, welcome, and we wish you every success in your academic
endeavors. |
Guides and instructs students on preparing for the SAT mathematics level 1 subject test, providing test-taking strategies and tips, and includes seven full-length practice exams with explanations of each answer.
In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day, using illustrative case studies drawn...
From ancient Babylon to the last great unsolved problems, Ian Stewart brings us his definitive history of mathematics. In his famous straightforward style, Professor Stewart explains each major development -... |
Graphing Calculator Tutorials & Lessons
A Selection of Guides and Manuals for Graphing Calculators A variety of resources selected by your guide to support the use of graphing calculators in a variety of topics for beginner and advanced users. Topics addressed include statistics, calculus, algebra, graphing, geometry and precalculus.
Graphing Calculator Guides in PDF Here you'll find guides for the HP 48G/GX, the TI-82/83, and the TI-85/86. Broken down by chapters, these guides are extremely handy for calculus problems.
Graphing Calculator Help An interactive graphing calculator to assist you with the basic to the very advance functions. Click on the model you use and use the right hand index to assist you with your problem.
Graphing Calculator Instructions Excellent step by step guides for all of your graphing calculator functions. Complete with easy to read instructions and screenshots. |
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