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Upon completion of this course you will effectively learn the most important factors to be considered when answering questions in a maths exam. You will be aware of the most common mistakes in maths exams. You will gain a good knowledge of first and second order differential equations and second derivatives. You will learn about kinematics including acceleration, distance and velocity. You will understand Newton's laws of motion, Newton's laws of cooling, and Euler's method for solution of differential equations. This course will teach you the resolution of forces and how to calculate vectors. | 677.169 | 1 |
--- calculations. The program comes on a 5.25 inch disk, with instructions on disk, on cassette, and in large type, and a summary of functions and commands in braille. COMPATIBILITY: Apple. SYSTEM REQUIREMENTS: Apple II with at least 128K or RAM. For complete speech accessibility, it requires an Echo or Slotbuster synthesizer | 677.169 | 1 |
Abstract Algebra
The three primary topics of this course are groups, rings, and fields. Groups will be studied, including homomorphisms, normal subgroups, and the symmetric and alternating groups. The theorems of Lagrange, Cauchy, and Sylow will be developed and proven. Rings, including subrings, ideals, quotient rings, homomorphisms, and integral domains will be covered. Lastly, finite and infinite fields will be discussed. Prerequisite: MATH295. | 677.169 | 1 |
What a great step-by-step explanations. As a father, sometimes it helps me explaining things to my children more clearly, and sometimes it shows me a better way to solve problems. Tara Fharreid, CA
I'm not much of a math wiz but the Algebra Buster helps me out with fractions and other stuff I need to know for my math appreciation class in college. Sarah Jones, CA
Be it Step by Step explanation for an equation or graphical representation, you get it all. I just love to use this due to the flexibility it provides while studying. C.B., Iowa
Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them? | 677.169 | 1 |
Appropriate for upper level undergraduate and graduate courses in Mathematical Modeling offered in math, engineering departments, and applied math departments. Prerequisite is some exposure to differential equations and to matrices. This accessible and practical text is designed to nurture a "m... | 677.169 | 1 |
Program Details
TI-84 Plus and TI-83 Plus graphing calculator program for calculating the area under a curve and the area between 2 curves.
Program Keywords:
TI Programs, TI-83 Plus, TI-84 Plus, Graphing Calculators, Calculus, Integrals: Area Under a Curve, Area Between 2 Curves
Program Description:
This program finds the area under a curve and the area between curves. The program uses numerous methods of finding the area including left, right and middle, trapezoidal, solids of revolution and standard integration. The program can also find definite integrals, even when the equation is unknown, as long as co-ordinates are given. This program is great for any type of integral problems that might appear on homework, tests or final exams in calculus. | 677.169 | 1 |
Books
Geometry & Topology
This edition includes the most recent Geometry Regents tests through August 2012. These ever popular guides contain study tips, test-taking strategies, score analysis charts, and other valuable features. They are an ideal source of practice and test preparation. The detailed answer explanations make each exam a practical learning experience. Topics reviewed include the language of geometry; parallel lines and quadrilaterals and coordinates; similarity; right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and an introduction to solid geometry.
This classroom text presents a detailed review of all topics prescribed as part of the high school curriculum. Separate chapters analyze and explain: the language of geometry; parallel lines and polygons; congruent triangles and inequalities; special quadrilaterals and coordinates; similarity (including ratio and proportion, and proving products equal); right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and working in space (an introduction to solid geometry). Each chapter includes practice exercises with answers provided at the back of the book
A bestselling math book author takes what appears to be a typical geometry workbook, full of solved problems, and makes notes in the margins adding missing steps and simplifying concepts so that otherwise baffling solutions are made perfectly clear. By learning how to interpret and solve problems as they are presented in courses, students become fully prepared to solve any obscure problem. No more solving by trial and error!
• Includes 1000 problems and solutions • Annotations throughout the text clarify each problem and fill in missing steps needed to reach the solution, making this book like no other geometry workbook on the market • The previous two books in the series on calculus and algebra sell very well
The new and improved Tutor in a Book's Geometry. Designed to replicate the services of a skilled private tutor, TIB's Geometry, presents a teen tested visual presentation of the course and includes more than 500 well illustrated, carefully worked out proofs and problems with step by step explanations. Throughout the book, time tested solution and test taking strategies are demonstrated and emphasized. The recurring patterns that make proofs doable are explained and illustrated. Dozens of graphic organizers that help students understand, remember and recognize the connection between concepts are included. With the intent to level the playing field between students who have tutors and those that don't, long time successful private mathematics tutor and teacher, Jo Greig, packed 294 pages with every explanation, every drawing, every hint, every memory tool, examples of the right proofs and problems, and every bit of enthusiasm that good tutors impart to their private tutoring students. Ms. Greig holds a bachelors' degree in mathematics. Dr. J. Shiletto, the book's mathematics editor, holds a Ph.D in mathematicsFor seven years, Paul Lockhart's A Mathematician's Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.
In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.
Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can "do the math" in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work. | 677.169 | 1 |
The study of differential equations is a wide field in both pure and applied mathematics. Pure mathematicians study the types and properties of differential equations, such as whether or not solutions exist, and should they exist, whether they are unique. Applied mathematicians, physicists and engineers are usually more interested in how to compute solutions to differential equations. These solutions are then used to simulate celestial motions, design bridges, automobiles, aircraft, sewers, etc. Often, these equations do not have closed form solutions and are solved using numerical methods. | 677.169 | 1 |
Saxon Geometry Homeschool Kit
A welcome addition to Saxon's curriculum line, Saxon Geometry is the
perfect solution for students and parents who prefer a dedicated
geometry course...yet want Saxon's proven methods!
Presented in the
familiar Saxon approach of incremental development and continual
review, topics are continually kept fresh in students' minds. Covering
triangle congruence, postulates and theorems, surface area and volume,
two-column proofs, vector addition, and slopes and equations of lines,
Saxon features all the topics covered in a standard high school
geometry course. Two-tone illustrations help students really "see" the
geometric concepts, while sidebars provide additional notes, hints, and
topics to think about. Parents will be able to easily help their
students with the solutions manual, which includes step-by-step
solutions to each problem in the student book; and quickly assess
performance with the test book (test answers included). Tests are
designed to be administered after every five lessons after the first
ten.
Key To Geometry Books 1-8
Key to Geometry offers a non-intimidating way to prepare students for
formal geometry as they do step-by-step constructions. Using only a
pencil, compass, and straightedge, students begin by drawing lines,
bisecting angles. Books are also sold separately.
Key To Geometry (KTG) Answers Notes, Books #1-3
The series of workbooks, Key to Geometry To Geometry (KTG) Answers Notes, Books #4-6
Key to
Geometry offers a non-intimidating way to prepare students for formal
geometry as they do step-by-step constructions. Using only a pencil,
compass, and straightedge, students begin by drawing lines, bisecting
angles
Book 4: Perpendiculars, Book 5: Squares and Rectangles, Book 6: Angles.
These are the answers and notes for Books 4-6 of the Key to Geometry
Series.
Key to Geometry (KTG) Answers Notes, Book #7
The series of workbooks, Key to Geometry, to Geometry (KTG) Answers Notes, Book #8
Key to Geometry
offers a non-intimidating way to prepare students for formal geometry
as they do step-by-step constructions. Using only a pencil, compass,
and straightedge, students begin by drawing lines, bisecting angles,
and reproducing segments. Later they do sophisticated constructions
involving over a dozen steps and are prompted to form their own
generalizations. When they finish, students have been introduced to 134
geometric terms and are ready to tackle formal proofs. Book 8:
Triangles, Parallel Lines, Similar Polygons This book contains the
answers and notes for Book 8 of the Key to Geometry Series.
The Complete Idiot's Guide to Geometry 2nd Ed.
See geometry from all the right angles.
Here is a
non-intimidating, easy-to-understand, and fun companion to the
textbooks required for high school and college geometry courses. Written
by a math professor who developed a geometry class for liberal arts
students, this book covers all standard curriculum concepts—from angles
and lines to tangents and topology.
Geometry, Level 2
Never waste a single minute, when you fill in down time with Daily
Warm-Ups. Give your students the skill to become confident at solving
problems, and helps prepare them for standardized tests. Contains 180
warm-ups, from converting distance to tesselations and everything in
between. Spice up your geometry class with this book and your kids will
thank you for it!
Geometry the Easy Way
This third edition of "Geometry the Easy Way" covers the "how" and
"why" of geometry with hundreds of examples and exercises with
solutions. More than 700 drawings, graphs, and tables help to
illustrate angles, parallel lines, proving triangles congruent, formal
and informal proofs, special quadrilaterals, inequalities, the right
triangle, ratio and proportion, circles, area and volume, locus,
coordinate geometry, and constructions.
Proofs Workbook
The concepts that are studied and applied in a geometry course fall
into two categories: theorems and postulates. This workbook will
provide an opportunity to develop specific skills used in proof
writing. Each strategy develops a particular technique that can be used
when writing a proof. Includes:
Informal presentations of theorems, postulates and definitions.
Perfect complement to any textbook.
Applications of ideas developed in clear explanations and practice exercises. | 677.169 | 1 |
Tensor analysis is an essential tool in any science (e.g. engineering,
physics, mathematical biology) that employs a continuum
description. This concise text offers a straightforward treatment of
the subject suitable for the student or practicing engineer. The final
chapter introduces the reader to differential geometry, including the
elementary theory of curves and surfaces. A well-organized formula
list, provided in an appendix, makes the book a very useful
reference. A second appendix contains full hints and solutions for the
exercises. | 677.169 | 1 |
Introduction to Calculus
The Collins College Outline for Introduion to Calculus tackles such topics as funions, limits, continuity, derivatives and their applications, and integrals and their applications. This guide is an indispensable aid to helping make the complex theories of calculus understandable. Completely revised and updated by Dr. Joan Van Glabek, this book includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, illustrations, and examples.
The Collins College Outlines are a completely revised, in-depth series of study guides for all areas of study, including the Humanities, Social Sciences, Mathematics, Science, Language, History, and Business. Featuring the most up-to-date information, each book is written by a seasoned professor in the field and focuses on a simplified and general overview of the subje for college students and, where appropriate, Advanced Placement students. Each Collins College Outline is fully integrated with the major curriculum for its subje and is a perfe supplement for any standard textbook.
Elementary Algebra... | 677.169 | 1 |
This manual includes resources designed to help both new and experienced instructors with course preparation and classroom management. This includes mini-lectures for each section of the text, chapter by chapter teaching tips, sample syllabi, support for media supplements, and more.
Using MyMathTest as a Student
You can use MyMathTest to practice for and take placement tests, or to do a refresher course to improve your maths skills. MyMathTest helps you build your skills by taking practice tests and working through a personalised Study Plan based on those results.
Whe... | 677.169 | 1 |
Congratulations to Folena DeGeus for winning a Certificate of Merit in the UVM Mathematics Prize Exam and for winning Best in School in the UVM Math Prize Exam.
Congratulations to Kevin Keene for winning a Certificate of Merit in the UVM Mathematics Prize Exam.
Mathematics
The Mathematics Department has developed a curriculum that is designed to meet the needs of every student. We offer courses at many different levels of difficulty, so that each student can take courses that are appropriate for his or her mathematical development. The courses are planned in a sequence that provides reinforcement of previously learned concepts and the sequential development of new material. Each course has prerequisites that are designed to ensure that every student will have a high probability of success.
The Mathematics Department also recognizes that appropriate study skills are important to academic success. Therefore, each student is required to maintain a comprehensive notebook. Regular attendance, participation in class, and completion of daily assignments are also considered minimum requirements. | 677.169 | 1 |
The curriculum in mathematics is designed to serve students of varying abilities and interests. Its purpose is to enable students to develop their thinking and problem-solving capacities, as well as to provide them with basic mathematical skills and positive attitudes about their use of mathematics. | 677.169 | 1 |
GCSE Maths: Simplifying logarithmic expressions
Activities to enable learners of secondary mathematics to develop their understanding, and practise using, the laws of logarithms to simplify numerical expressions involving logarithms. This standards unit is part of the 'Mostly algebra' set of materials. | 677.169 | 1 |
easy for the beginner to do and understand algebra. It also has a "Einstein" level that even algebra experts will find fun and challenging. You can choose from a ten problem, a time trial, or a two-player game. High scores are saved and you are given a rank according to your score. The ranks are Novice, Learner, Veteran, Calculator, Math Pro, Math Whiz, Math Genius, and Einstein.
The practice menu lets you practice each function individually. The game menu lets you choose one function, two functions, and so on up to 21 functions. You can choose from calculate value (1 x and 1y value and the equation to solve), choose formula (you figure out the equation using the given x, y, and z values), or figure formula and calculate (you figure out the equation and solve for the missing z value).
If you get stuck trying to figure out what the function (equation) is a hint will be displayed. If you choose the wrong answer it will help you figure out the right one. The calculate option combined with the practice game enables students to practice solving the problems in the area they are having trouble with.
Algebra - One On One | 677.169 | 1 |
Math Homework Answers
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Math Homework Answers GetMath answers Step by Step From Framing of Formulas to Expansions, Indices, Linear Equations to Factorization and Quadratic Equations you get all Math Homework Answers online using our well structured and wel thought out Math tutoring program. Students get not just the answer but answers step by step. Below is provided a demo example of getting math answers step by step from us: Example: Find out the area of a triangle, height 8 cm, base 6 cm. Answer: 242 cm Steps to follow: 1. Since, Area of a triangle formula = 1/2 x b x h (b = base, h = height) 2. Here, base = 6 cm and height = 8 cm 3. Therefore, the area of the given triangle = 1/2 x 6 cm x 8 cm 4. Math answer to the given problem = 242 cm This is a geometry example. Likewise get free answers to al your math problems. Now make your math easy with Tutorvista. | 677.169 | 1 |
College Mathematics
Credits: 3Catalog #10804107
This course is designed to review and develop fundamental concepts of mathematics pertinent to the areas of: 1) arithmetic and algebra; 2) geometry and trigonometry; and 3) probability and statistics. Special emphasis is placed on problem solving, critical thinking and logical reasoning, making connections, and using calculators. Topics include performing arithmetic operations and simplifying algebraic expressions, solving linear equations and inequalities in one variable, solving proportions and incorporating percent applications, manipulating formulas, solving and graphing systems of linear equations and inequalities in two variables, finding areas and volumes of geometric figures, applying similar and congruent triangles, converting measurements within and between U.S. and metric systems, applying Pythagorean Theorem, solving right and oblique triangles, calculating probabilities, organizing data and interpreting charts, calculating central and spread measures, and summarizing and analyzing data. Prerequisite: Basic Algebra, 74-854-793 with a "C" or better or appropriate placement score.
Course Offerings
last updated: 09:01:51 | 677.169 | 1 |
Understanding Mechanics has proved to be a popular text with students of A-level
Mathematics. Syllabuses are varied at this level. But the aim has been to cover
all topics that could appear on single Mathematics Papers, at the same time as
providing an extension into several Further Mathematics topics.
Recent changes to syllabuses have brought about the need for this new edition,
and there are two particular emphases in modern syllabuses that have been dealt
with. One of these is on the use of vectors, and for this reason we have
introduced vectors right at the beginning of the book. The other emphasis in of
the use of modeling. Students are required to understand the relationship
between real-life situations and mathematical models. They need to understand
the limitations of many common assumptions so that they can evaluate their own
assumptions when setting up mathematical models to solve problems. We have
provided some commentary to help with this.
In each chapter the theory sections are followed by a number of worked examples
which are typical of, and lead to the questions in the exercises. By reading the
theory sections and following the worked examples, the reader should be able to
make considerable progress with the exercise that follows. After the
introductory vector work, each chapter closes with a comprehensive selection of
recent examination questions, allowing the student to evaluate and apply the
skills learnt in the preparatory sections. These exercises are carefully graded,
progressing to some quite demanding questions at the end.
We are grateful to the following examination boards for permission to use their
questions specimen questions are denoted by spec. the answers provided for these
questions are the sole responsibility of the authors.
University of examinations and Assessment Council ULEAC.
University of Cambridge Local examinations syndicate UCLES.
University of Oxford delegacy of local examinations UODLE.
Oxford and Cambridge Schools examination Board OCSEB.
Midland examining Group MEG.
Associated examining board AEB.
Welsh Joint education committee WJEC.
Northern Ireland Council for his curriculum examinations and assessment NICCEA.
Southern Universities Joint Board SUJB.
Finally, we wish to acknowledge the help of four experienced teachers who helped
with the writing of the new text: Julian Berry Bloxham School , Dr Dominic
Jordan University of Keele. Robert Smedley Liverpool Hope University College.
And Garry Wiseman Radley College. Special thanks are due to Garry Wiseman, who
also played a central editorial role in melding the new and existing material
together. | 677.169 | 1 |
Nine PlanetsA Multimedia Tour of the Solar System: one star, eight planets, and more
Search for Benicia Geometry Tutors
Subject:
Zip:
...One good way to proofread is to read the paper aloud, especially if this is your final version. Reading aloud from a typed copy should allow you to spot typing errors, such as words left out or misspelled words (or words whose spelling you want to look up in the dictionary). If you are reworking...The concepts of Linear Algebra are at the heart of (1) numerical methods (used to develop and evaluate solution techniques that are used by computers to solve large numerical systems such as finite element analyses), (2) numerical solutions of overdetermined systems (i.e., "least squares" which a | 677.169 | 1 |
College Calculus Study Guide
This study guide can help you learn material quickly and succeed in your college Calculus classes.
Northstar Workforce Readiness covers the full College Calculus course series curriculum (usually three, sometimes four semesters). Our study guide is comprehensive and includes 57 units with in-depth lessons, and practice questions with an explanation for each correct answer. Our online study guide contains randomly-generated numbers, so you don't see the same questions over and over. Northstar Workforce Readiness covers several critical topics including Limits, Differentiation, Integration, Transcendental Functions and Differential Equations, Parametric and Polar Funcations, Vectors and the Geometry of Space, and much more.
Northstar Workforce Readiness is online, available 24/7, and is very affordable. There is no software to download or install. You can work through the study guide at your own pace and master the types of questions that give you the most trouble. With individualized instruction, feedback, and grading, you can master the material you need to be successful in your College Calculus courses. In addition to practice questions, Northstar Workforce Readiness includes diagrams, graphs, illustrations, and other images to help you understand the material. Northstar Workforce Readiness Study Guides provide the best way to quickly learn challenging material and get higher grades in your classes.
Lesson Example and Practice Exam Question
Topics
Click on an image above to see examples of what our program looks like and how it works.
What our users are saying:
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UCD School of Mathematical Sciences
Scoil na nEolaíochtaí
Matamaitice UCD
The following are guidelines on how to use the Mathematics Support Centre (MSC).
Drop in!You do not have to make an appointment with us as the MSC works on a drop-in basis
Come early, use often! If you are having difficulties with maths,come along as earlyin the year as you can and visit us as frequently as you like!
Bear in mind that we are an additional service to lectures and tutorials. Do not try to use the MSC as a substitute for these! MSC is a free service for UCD students
Important: Tutors in the MSC should not do problems for students.You will be expected to engage with the material either in the centre or elsewhere. We can provide loads of help as you need it but you will ultimately do the work!
If you have a particular maths problem:
Try to prepare for your visit as much as possible by reading your lecture notes
Bring along your attempts at the problem
Bring along your lecture notes or at least know where they are if they are published on the web
If you have a more general problem with some area of maths
Bear in mind that you may need to vist the Centre on a regular basis
If you have difficulty with lecture notes, read them up as far as you understand them before you visit the centre.
Again bring along your lecture notes or at least know where they are if they are published on the web
If you have no particular problem with maths and you just want a place to work on your maths, then the MSC is for you as well! Many students find the MSC to be a great place to study your maths notes,sample problem sheets etc. and having a tutor on hand if you want to check your work is a bonus! | 677.169 | 1 |
Outcome
Type
Tuition Fees
Sponsors
College: College of Physical and Engineering Science
Department: Department of Mathematics and Statistics
Instructors
Prof. Joe Cunsolo
Description
Getting Ready for Calculus is a non-credit course designed as a preparation for university-level mathematics.
This course is for you if you lack a solid mathematics background and/or skills and find that you need to take more mathematics to reach your educational and/or career goals. In designing this course, the Department of Mathematics recognizes the diverse mathematical backgrounds and concerns of students. The material in this course spans Grade 9 through to and including part of the OAC Calculus course. The course starts with a basic review of algebra from Grades 9 and 10, and then it focuses on the mathematical material from Grades 10, 11 and 12 that allows the introduction of material from the OAC Calculus course. This design allows you to develop a more solid grounding in the mathematics that is needed for university-level mathematics courses.
Call us (519-767-5010) if you have any questions regarding this unique preparatory course.
Note: This is a non-credit course | 677.169 | 1 |
WJEC Linear and Unitised GCSE Mathematics
From first award in 2014 (first teaching on two-year courses September 2012) all centres in England will be required to follow linear GCSE specifications, whichever awarding organisation they use. Linear specifications are those where all examinations are taken at the end of the course.
This means that centres in England using WJEC GCSE Mathematics specifications MUST follow this linear specification.
GCSE Mathematics
The GCSE Mathematics Linear and Unitised specifications for teaching from September 2010 are now available to download under Specifications.
New WJEC Level 2 Certificate in Additional Mathematics
This qualification, for first teaching from September 2010, will provide a course of study for the most able candidates for GCSE Mathematics to be stretched and challenged. It will also provide an appropriate course of study for candidates who acquire GCSE Mathematics early.
Specification and specimen assessment materials are now available for download: | 677.169 | 1 |
Lesson Plan
Factoring Polynomials
Grade Levels
Commencement
,
9th Grade
Description
In this lesson, students will review multiplying two binomials together (FOIL) in the "Do-Now". Students will then learn how to factor a quadratic equation in the form of x2 + bx + c, when a is equal to 1.
Support Materials
SMART Board
This instructional content was intended for use with a SMART Board. The .xbk file below can only be opened with SMART Notebook software. To download this free software from the SMART Technologies website, please click here. | 677.169 | 1 |
The practice book supplements the students class text book and provides thousands of graded practice questions. Not all are required to be completed. However, some students have trouble with certain concepts. The practice questions are designed to re-inforce existing knowledge and then by gradually increasing the level of difficulty, take students easily to the next level.
An activity kit is provided to each student. The kit consists of a number of shapes and activities that are done in the session, particularly to build a deep subject understanding that goes beyond being able to apply formulae.
Each student also has access to a number of online resources, provided through a dashboard. The online materials are not essential to the learning process, but can help enhance the learning experience.
Additional Assessments. A student can take additional assessments of chapters at their convenience. These assessments will also show up in their reports
Content used in class. All the materials used by the teacher in the class are available as a reference
Practice Exercises. Practice exercises are also available online. These are the same as those available in the Practice Book but can be accessed in multiple ways
Reports. There are a large variety of reports available online providing a detailed assessment of progress.
Additional Referral Materials. For each chapter, we provide links to a set of materials that we believe are useful in learning. These are typically video links or interesting stories or puzzles that engage children in the learning process | 677.169 | 1 |
FIRST COURSE IN PROBABILITY leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus.
A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more. | 677.169 | 1 |
This is the ultimate mathematics course. We will cover everything from Algebra I and work our way up to Calculus concepts with some great discussions along the way. Mathematics is a language and if you can become fluent in it (which if you complete this course, I promise you will be!), then that is simply one more step in your great knowledge bank. (Every student has the option to pick a certain semester or set of semesters to learn from, as I do know that this is a very long course. Thus, if there is simply a few things that you would like to work on, pick a semester and let me know. If you just want to get the whole feel of the course, I will be glad to start from the beginning.)
Please know that I am a bit more of a lecture type of teacher, and thus, you may hear me speak quite a lot. However, within mathematics, the main thing we try to accomplish is your knowledge of the basic priniciples, and thus, mathematics consists of repetition, repetition, repetition! Here is the basic outline of a daily lesson:
Get acquainted and review material from last lesson
Teach new material
Practice new material
Q/A Session
Assigned Work
Now, you will most likely learn a few new principles in one lesson, so steps 2 and 3 may be repeated a few times. Homework will be given daily, and you can usually just download the homework from clicking the links below. Tests will be at least once a week, and unit tests will be about every 3 - 4 weeks, unless changed by me. Attendance is crucial in this type of course! If you are not here for two to three days at a time, then we will not be able to effectively absorb the knowledge that is being presented to you, and thus, it will take longer to learn this. At the end of every semester, you will have a final exam which will cover all of what you have learned.
Below lists all semesters and lessons that will be involved with your course. Next to each lesson is a set number of problems. This is basically how much homework you will have for each lesson, and you will have until the end of the week to get all problems completed. Soon, each set of problems will have a hyperlink within them that goes to a page where the assignment is, and you can simply do the problems from there. These are listed so that potential students can examine how much work will be involved in each semester, and how you can estimate the approximate time that you will need to devote to this course. | 677.169 | 1 |
International Society for Bayesian Analysis (ISBA)
Promotes the development of Bayesian statistical theory and its application to problems in science, industry and government. News, history and minutes, archive of abstracts, information about the Reverend Thomas Bayes, and open positions in the field.Japanese Association of Mathematical Sciences (JAMS)
A scientific research organization whose main activity is to publish scientific journals in English, French or German, in particular Scientiae Mathematicae Japonicae. Journal and submission information, newsletter, and meetings. Also available in JapaneseMarc Chamberland
A mathematician at Grinnell College interested in differential equations and dynamical systems. Resources for the 3x + 1 problem and the Jacobian Conjecture include papers to download in PostScript format and information and proceedings for related conferences.
...more>>
Mathematics of Planet Earth
Mathematics of Planet Earth (MPE) "provides a platform to showcase the essential relevance of mathematics to planetary problems, coalesces activities currently dispersed among institutions, and creates a context for mathematical and interdisciplinary
...more>>
Minnesota Council of Teachers of Mathematics (MCTM)
An affiliate of the National Council of Teachers of Mathematics (NCTM). The site provides information about conferences, events, and programs; membership; listings of recommended math sites; MCTM highlights (Presidential Awardees, Shape of Space video,
...more>>
MOTIVATE - Univ. of Cambridge, UK
MOTIVATE is a project incorporating a series of videoconferences, run by the Millennium Mathematics Project at Cambridge. The objectives of MOTIVATE are: to enrich the mathematical experience of school students, to broaden their mathematical horizons,
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MSPnet: The Math and Science Partnership Network - TERC
The Math and Science Partnership (MSP) Program is a major research and development effort to understand and improve the performance of K-12 students in mathematics and science. MSPnet is their electronic community. Learn about individual partnership projects;
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National Council of Supervisors of Mathematics (NCSM)
A resource site for those interested in leadership in mathematics education. The site lists meetings and conferences, membership information and how to subscribe to the NCSM mailing list, publications, operations, information about the summer Leadership
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SyllabusWeb - Syllabus Press, Inc.
From the publishers of Syllabus Magazine, a technology magazine for high schools, colleges, and universities. Highlights of recent issues of the magazine and full text archives of all Press publications. The June 1995 issue covers telecommunications and
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Fundamental Theorem of Calculus
In this lesson, Professor John Zhu gives an introduction to the fundamental theorem of calculus. He goes over the properties for the fundamental theorem of calculus as well as the definition of integral. He reviews four rules/ properties for calculus and performs a few example problems.
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Fundamental Theorem of Calculus
Simply evaluating integral at 2
bounds
Area under a curve
Accumulated value of
anti-derivative function
Fundamental Theorem of Calculus
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. | 677.169 | 1 |
Appendix D. Exact Solutions of Polynomial Equations
Introduction
For thousands of years the solution of polynomial equations was one of the most important and productive problems in algebra, and indeed in all of mathematics. Apart from the question of solution methods, the study of quadratic, cubic, and quartic equations and their geometric equivalents led to great advances in the concept of number over a period of more than two millennia, including irrational, negative, and complex numbers, and the limitations of numbers constructible with ruler and compass. Later on, the problem of quintic and higher order equations led to what has been called higher algebra or abstract algebra, that is, to the study of structures such as groups, rings, fields, vector spaces, and algebras of many other kinds, further greatly expanding the concept of number, and many other concepts. All of these structures and many others were then gathered together into category theory, which studies all of the mappings within and between all such objects, providing insight not only into the algebraic structures themselves, but also into algebraic geometry, the study of geometric objects by means of algebraic structures defined on them.
Furthermore, the solution of quadratic equations turned out to be fundamental in elementary physics in the period from Galileo to Newton. (Going beyond the elementary level requires calculus, as explained, for example, in Ken Iverson's book Elementary Analysis, which can be used as a continuation from this study of algebra.) For example, in elastic collisions, where both momentum and energy are conserved, the conservation laws are respectively linear and quadratic in form, so that the solution which preserves both reduces to the two solutions of a quadratic equation. If m and v0 are two-element vectors of masses and initial velocities, we must find a vector v1 such that:
(+/m*v0)=(+/m*v1)
(+/m**:v0)=(+/m**:v1)
One solution, v0, represents the state before the collision, and the other solution represents the state after the collision.
The solution of polynomial equations is fundamental to computer graphics, computer-aided design, and robotics.
The original problem of solving polynomials was to find solutions that could be expressed exactly in terms of the five basic algebraic operations, + - * % %:, starting from integers. The body of this textbook has been concerned only with numeric solutions, but this Appendix reviews the classical results and methods for solving quadratic, cubic, and quartic equations.
General Considerations
We know that every polynomial is a product of linear terms, of the form */x-r possibly multiplied by a constant that has no effect on the roots. We can divide the coefficient vector c of a polynomial by its last element _1{c, giving a new coefficient vector for a polynomial with 1 for the coefficient of the highest power of x present. We call this a monic polynomial.
The monadic case of the polynomial verb p. allows us to convert between coefficient vectors and a representation of a polynomial with boxed multiplier and list of roots. For example:
Each linear polynomial of the form x-r has a root r, so the product polynomial has a root for each of the r values. That is, at each of those values, at least one term has the value 0, so the product also has the value 0. These are the only roots, because at any other value of x, the factors are all non-zero and therefore the product is non-zero.
Furthermore, we know that the constant term in a polynomial */x-r is the product of all of the roots, by construction. The second-highest order term is the sum of all of the roots, again by construction. In the case of a quadratic polynomial, we saw in Chapter 14 that the coefficients of the polynomial are (r0*r1),(-r0+r1),1, possibly multiplied by a constant. Thus the polynomial with roots 2 3 has coefficients 6 _5 1, as above. A cubic polynomial has a term composed of the sum of products of pairs of roots, that is, (r1*r2)+(r0*r2)+(r0*r1). A quartic polynomial has a term composed of sums of products of triples of roots, and so on.
These terms represent functions of the roots with the special property that interchanging roots does not change the value of the function, unlike, say r0-r1, which is negated by interchanging r0 and r1. Functions with this property are called symmetric. Their study was fundamental in the proof that quintic and higher-order polynomials do not have solutions using only the functions + - * % %:, known as solutions in radicals.
Quadratic Equations
Although many mathematicians in Babylonia, Egypt, Greece, India, and China developed partial methods for solving quadratic equations, the general method to be described here is due to Muhammad ibn Musa al-Khwarizmi of Persia in the 9th century. It was introduced into Europe in the 12th century, first appearing in a Hebrew work by Abraham bar Ḥiyya ha-Nasi, then in Latin translations of al-Khwarizmi and ha-Nasi. However, the full solution including negative and complex roots was not recognized until the 19th century.
Given a three-element coefficient vector c from which we can make the polynomial p=.c&p., where the last element of c is not 0, how can we go about solving the equation 0=p x for its two roots, r0 and r1? We can begin by dividing by the last element of c to give an equivalent monic polynomial.
We can graph p, and find approximate roots by inspection.
We can use the iterative rootfinder described in Chapter 12.
We can look for integer roots by factoring the constant term.
We can graph the sum and product terms r0+r1 (a straight line) and r0*r1 (a hyperbola) on r0 and r1 axes, and look for roots where the two curves meet, as in the following graph.
Graph
None of these methods is entirely satisfactory. What we would like is an expression for the roots in terms of the coefficients of the polynomial. There is a particular case where this is very easy, the case where the two roots are equal. We have
(x-r)*(x-r)
(x^2)+(-2*r*x)+(r^2)
Setting 0=.*:(x-r) and solving gives us
0=*:x-r
(%:0)=x-r
r+0=x
r=x
as desired. Graphically, we can see that this is the case where the curve just touches the x axis at the point (r,0), as in the following graph:
Graph
Usually the graph of a quadratic polynomial in real numbers intersects the x axis in two distinct points, or not at all. But in those cases, adding a constant to the polynomial would move the graph up (for a positive constant) or down (for a negative constant), so there must be an intermediate value that would move the graph to just touch the x axis. Let us call that number n. Then adding n,0 0 to c, or setting p1=.n+p, has this result in the graph.
Graph
We now know that p1 is the square of x-r for some still unknown r, but we also know that
(1{c)=2*r
((1{c)%2)=r
Using this r, we can proceed as follows:
0=p1 x
n=n+p x
(%:n)=x-r
(r+%:n)=x
Now in fact n has two square roots, one of which is returned by the %: function. We call this the principal square root, or the principal value of the square root function. For positive y, %:y is the positive square root, and there is also a negative root. For negative y, *:y is 0j1*%:-y. Its negation is also a square root of y. So to get both square roots of y, it suffices to write 1 _1*%:y. (For complex numbers in general other than real numbers, %:z is the square root with positive imaginary part. The other square root is the negation of this principal square root.) Inserting this into the solution above above gives:
(r+1 _1*%:n)=x
It now remains to find n. We know that the square of x-r is (x^2)+(_2*r*x)+r^2. So if we have (x^2)+(_2*r*x)+k we want to add s=.(r^2)-k, or equivalently, in terms of values we know (*:b%2)-k, which results in the square of the monomial. We then know how to take the square roots of (*:b%2)-k, and it is easy to arrange the results in a convenient form for calculation. This method of solution is called completing the square.
Given a polynomial in the form (a*x^2)+(b*x)+c, we therefore proceed as follows:
This result is correct within the limit of precision of computer arithmetic. Examining the formula for the solutions shows that these roots are of the form:
-b%a
1
(*:b)-4*a*c)
5
(1+1 _1*%:5)%2
1.61803 _0.618034
The first of these is known as the Golden Ratio. It plays an important role in art, mathematics, biology and other areas.
We can now use the expression derived above to create an explicit function definition for solving quadratic equations given the coefficient vector c, as follows:
qe=.3 : 0
('c';'b';'a')=.y
((-b)+(1 _1*%:(*:b)-4*a*c))%2*a
)
For example:
c=._12 1 1
qe c
3 _4
c p. 3 _4
0 0
For an equation with real coefficients, the character of the solution depends on the sign of the expression (*:b)-4*a*c, the argument of the square root function. If it is positive, there are two real roots. If it is 0, there are two equal real roots. If it is negative, there are two complex roots. This expression is therefore called the discriminant, because it discriminates among these cases. For example, if we first define disc as the discriminant function:
Cubic Equations
The cube of a positive real number is positive, and the cube of a negative real number is negative. It follows that any cubic polynomial takes on both positive and values for real arguments of sufficient magnitude, where the cubic term is much greater in magnitude than the other terms. The polynomial thus must be zero for some real argument, having at least one real root. It may have three, as shown in the following graph.
Graph
The simplest cubic equation is 1=x^3. It has the three roots
1 _0.5j0.866025 _0.5j_0.866025
If we set w1=._0.5j0.866025 and w2=._0.5j_0.866025, we get the following relationships:
w1=w2^2
w2=w1^2
1=w1*w2
_1=w1+w2
Thus w1 and w2 are the roots of the quadratic equation 0=_1 0 1 p.x . Using the quadratic formula above we get the expression 0.5*_1+1 _1*%:_3, which yields these complex cube roots of 1.
There is no method for completing a cube, that is, for rearranging a cubic into the form (x-r)^3. What we have to do instead is to find a quadratic relationship among its coefficients (and thus among its roots) that we can solve and substitute back into the cubic. This method was worked out by Scipione del Ferro and Tartaglia, and published by Gerolamo Cardano in 1545. The full solution for negative and complex roots was not recognized until much later. However, the appearance of complex numbers in expressions for real roots was essential to the development of complex arithmetic, raising questions in the 16th century that were not fully resolved until the 19th.
To solve a cubic equation 0=cv p. x, first we want to simplify the form of the coefficient vector cv=.d,c,b,a. As before, we divide through by the last element of cv to produce a monic polynomial. Then we make the substitution t-(2{cv)%3 for x in this monic polynomial, which has the result that the new coefficient vector has the form d,c,0 1. This form is called a depressed cubic. Note that:
(t-(2{cv)%3)=x
t=x+(2{cv)%3
For example, starting from the monic coefficient vector cv, let us define:
A significant amount of routine algebraic manipulation has been omitted above. It can be treated as an exercise, or the student can verify the equivalence numerically by assigning appropriate values to the variables and executing each expression. For example:
The other two solutions of the cubic equation require finding the other two cube roots of u^3 and v^3, which turn out to be w1 and w2 times the primary cube roots. We must be careful to match the resulting four values in pairs, observing the condition 0=p+3*u*v. The result is
x1=.(w1*u)+(w2*v)
x2=.(w2*u)+(w1*v)
These pairings work because 1=w1*w2, so (u*v)=(w1*u)*(w2*v) and (u*v)=(w2*u)*(w1*v).
However, if the discriminant is negative, using the cube root function 3&^: does not in general match the appropriate cube roots. We must use the relationship
p+3*u*v=0
3*u*v=(-p)
v=(-p)%(3*u)
There is one other case to consider, if u is 0, in which case p is 0. Then we cannot use the relationship above, but must use
Again, these are excellent approximations of the roots, with errors less than 1e_15.
Quartic Equations
Gerolamo Cardano's student Lodovico Ferrari discovered a method for solving quartic equations by means of an auxiliary cubic equation in 1540, before Cardano published the solution of the cubic. Ferrari's method uses the concept of completing the square twice. The condition for completing the second square results in the auxiliary cubic. Several other methods have been discovered since using techniques such as factorization of the polynomial, Galois theory, and algebraic geometry.
The first two steps are as for the cubic equation, to reduce the quartic to monic form (divide by the coefficient of x^4) and then to depressed form (substitute t=.x-b%4, where b is the coefficient of x^3). The new coefficient vector will have the form cvd=.ed,dd,cd,0 1. In terms of the original coefficient vector cv=.e,d,c,b,a, these have the values
If dd=0, the polynomial can be rewritten as (ed,cd,1)p. x^2, that is, as an easily-solved quadratic in x^2. If ed=0, one of the roots is 0, and we can write an equation for the other roots as (dd,cd,0 1) p. x, that is, as a depressed cubic solvable by methods discussed above.
At this point we are given that 0=(ed,dd,cd,0 1) p.x for certain unknown values of x, or that
Any of the three solutions will serve our purpose. Each solution of the cubic allows us to complete the second square, resulting in a pair of quadratic equations. Each such pair matches the roots of the quartic in pairs, in one of three possible arrangements:
Equations of Higher Degree
The methods described above fail to work for quintic (fifth-degree) equations and for all higher degrees. When one tries Ferrari's method on quintic polynomials, one does indeed get an auxiliary equation, but it is of the sixth degree, and so is of no help. The Abel-Ruffini theorem established that equations of higher degree cannot be solved in radicals, and Galois theory greatly clarified the relationship between the coefficients and the roots of any polynomial. However, these topics are far beyond the scope of this textbook. | 677.169 | 1 |
Academic Links
Mathematics
We strive to educate students in all levels of mathematics. Our goal is to teach students to be fluent in numbers and also to understand the nuances of mathematics and its role in our culture. We believe that mathematics is a universal language and mastering its many aspects is necessary to be a productive global citizen.
The Math department at University Prep combines a traditional curriculum and innovative teaching styles. In the Middle School we fuse the two by using an inquiry, project-based approach in the 6th and 7th grade, which is supplemented by traditional skill building. This allows students to learn concepts through a variety of methods, ensuring that the lessons are accessible to all students. It also means that students can also do the math that they understand so well.
In the Upper School, we follow a very traditional algebraic curriculum focusing on the fundamentals. In geometry, however, our program is a technology-based geometry program, which allows our students to learn geometry and model mathematical ideas through dynamic sketches. This experience gives the students the ability to think at a deeper level about mathematics than the static approach of more traditional geometry. This perspective is one that stays with them throughout our math sequence, as algebra and geometry come together in Pre-Calculus and Calculus.
We use a variety of assessments in all of our classes. In Middle School, especially in 6th and 7th grade, assessment tends to be project based. While students still take the traditional tests and quizzes, there are many more opportunities for them to delve deeper into the material using a more hands-on approach. Some recent projects have included, writing a math children's book to solidify prior knowledge, learning percents through sports and creating a Sports Center video, using Geometer Sketchpad to create tessellation designs, designing and drawing their dream house to learn proportions, and collecting and analyzing their daily garbage to understand statistics.
In the Upper School, most of our major assessments are traditional tests and quizzes. However, we do many other types of assessment to allow students to show what they know in a variety of ways. These include posters, presentations, experiments with write-ups, and oral tests. In the Upper School, classes end the semester with a cumulative final exam. | 677.169 | 1 |
0136020 Mathematics With Graph Theory
Adopting a user-friendly conversational -- and at times humorous -- style, these authors make the principles and practices of discrete mathematics as much fun as possible while presenting comprehensive, rigorous coverage.
Examples and exercises integrated throughout each chapter serve to pique student interest and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's students in the interesting, applicable facets of modern mathematics | 677.169 | 1 |
1.4 Variables and Equations
Numbers are abstract creatures that we use to represent how many "things" we have. Variables, in turn, can abstractly represent numbers. When there's a relationship between different variables in the form of a pattern, we can develop an equation to represent this relationship.
We started talking about counting numbers, mathematical creatures that you've worked with since you were just a little kid, and then wound talking about irrational numbers, which are numbers that you probably won't run into in the day-to-day physical world. Together, the counting numbers, integers, rational numbers, and irrational numbers, make up all of the real numbers. These are the types of numbers that we'll be using for this course.
Now that we have a sense of our abstract numbers, can we move up a level of abstraction? This is the type of question that the mathematician always asks. By representing objects from the real world as numbers, such as having 2 tables or having 3 chairs, we can use the language of mathematics to answer questions about quantity. If we combine 2 tables with 3 tables, then instead of thinking about the tables, we can first just think about adding the 2 and the 3 to get 5 and then translate back to the specific object, namely 5 tables. Perhaps we'll receive a similar benefit if we can think of numbers as specific objects and develop an abstract representation of the numbers themselves.
To see one real world benefit, let's say you're selling Apps for the iphone and you make 30 cents per App. If you sell a total of 1000 Apps, you'd make $
dollars. If you're a business person, and have to figure out how much you make on a monthly basis, you'd probably want to have some sort of spreadsheet or computer program that will compute the profit for you.
You can let x, known as a variable, represent the number that you sell without specifying a particular number –that's why "x" is more abstract than a number – and then in your spreadsheet program, use .3x to represent your profit; you then tell the program the number that you sell and you let it do the computation for you.
Using variables, we can then create equations that can then be used to model a real world situation. We can think of an equation as a way to describe a process using the language of mathematics. As an example, if you wanted your profit to be $300 and wanted to know how many units you'd need to sell in order to achieve this profit, then you could set up the equation:
300=.3x
In other words, "Find the unknown quantity x, so that .3x is equal to our desired profit of $300". We've translated a real world problem into the mathematical language: now using the rules of algebra, one branch of mathematics, we can solve for the unknown variable. In this case, we can divide both sides by .3 to get that x = 1000.
In this book we'll learn many different techniques that we can use to solveequations. But, before solving an equation, it's super important to understand how to translate the problem from English to mathematics. While there are no hard and fast rules as to how to do this, some key tips are:
Know what it is that you're actually looking for
Start with a "rough" equation – one that contains both English and math
Draw a picture if possible, labeling unknown quantities
Explore!
You're trying to construct a rectangular pen for your dear pig Wilbur. You'd like the length of the pen to be 4 more than the width so that Wilbur has ample room to run around. If x represents the width of the pen and you have 100 feet of wire available to construct the pen, then which equation represents the relationship between the unknown width and the other information given?
From our picture, we see that the two widths are each x while each length is x+4. Adding up the total number of x's (four of them) plus the non-x values (8) gives us the total perimeter, which is 100. This tells us that the equation:
4x+8=100
can be used to describe the relationship. Once we've translated the problem into the language of mathematics, we'll be able to use tools from algebra to solve for the unknown.
Truth be told, the above example probably doesn't have much of a real world application. In fact, to be completely honest, most problems that you'll see in any introductory algebra course don't have much "practical" value. However, these basic concepts are the building blocks of more advanced problem solving techniques that are used in the real world to solve some very, very complicated problems.
As an example, consider an airline looking to maximize their profit. They need to figure out how many planes they should have, the number of routes, what to charge customers, among a host of other variables. Do you think that they're just going to "guess" what number to assign each of the unknown variables in order to maximize their profit? Of course not! They use some very advanced techniques from algebra to figure out all of their unknowns (potentially hundreds), in order to maximize profit.
After working through some problems in this section, which will give you a chance to practice translating some English statements into mathematical ones, you'll begin to notice that one helpful tool in developing equations is being able to visualize what's going on. In the next section, we're going to study the number line, which will connect the concepts of numbers, variables, and representing them both visually. | 677.169 | 1 |
Assessment Rules
Curriculum Design: Outline Syllabus
Number theory: division with remainder; highest common factors and the Euclidean algorithm; lowest common multiples; prime numbers; the Fundamental Theorem of Arithmetic and the existence of infinitely many prime numbers; applications of prime factorization.
To introduce students to mathematical proofs; to state and prove fundamental results in number theory; to generalize the notion of congruence to that of an equivalence relation and explain its usefulness; to generalize the notion of a highest common factor from pairs of integers to pairs of real polynomials.
Educational Aims: General: Knowledge, Understanding and Skills
University mathematics has a rather different feel from that encountered at school; the emphasis is placed far more on proving general theorems than on performing calculations. This is because a result which can be applied to many different cases is clearly more powerful than a calculation that deals only with a single specific case.
For this reason we begin by taking a look at the language and structure of mathematical proofs in general, emphasizing how logic can be used to express mathematical arguments in a concise and rigorous manner.
We then apply these ideas to the study of number theory, establishing several fundamental results such as Bezout's Theorem on highest common factors and the Fundamental Theorem of Arithmetic on prime factorizations.
Next, we introduce the concept of congruence of integers. This, on the one hand, gives us a simplified form of integer arithmetic that enables us to answer with ease certain questions which would otherwise seem impossibly difficult; and on the other it leads naturally to the abstract idea of an equivalence relation whichhas applications in many areas of mathematics.
Finally, we show how the idea of a highest common factor can be generalized from the integers to the polynomials.
Set theory: understand and be able to use basic set-theoretic notation.
Logic: understand the use of truth tables, and be able to set them up; be able to express mathematical statements symbolically, using quantifiers and connectives, and to negate them; master the three main methods of proof (direct, contraposition and contradiction); be able to present simple mathematical proofs.
Number theory: be able to perform division with remainder, and prove the underlying theorem; know what is meant by the highest common factor of a pair of integers, and understand how to compute it using the Euclidean algorithm and prime factorization; be able to state and prove Bezout's theorem, and know how to apply it to derive related results; know what the lowest common multiple of a pair of integers is, its relation to the highest common factor, and how to compute it; know what is meant by a prime number, and how to find prime numbers using the Sieve of Eratosthenes; be able to state and prove the Fundamental Theorem of Arithmetic, and to prove that there are infinitely many prime numbers; be familiar with various applications of prime factorization.
Congruences: know what it means that two integers are congruent modulo a given number; be able to solve linear congruences, and understand the proofs of the underlying theorems; be able to state, prove, and apply the Chinese Remainder Theorem.
Relations: know what is meant by a relation, be able to decide whether or not a relation is reflexive, symmetric, or transitive; know what is meant by an equivalence relation; know what is meant by an equivalence class and a congruence class; be able to define the sum and the product of two congruence classes, and show that it is well-defined; be familiar with various applications of the arithmetic of congruence classes; be able to construct the integers from the natural numbers, the rational numbers from the integers, and the complex numbers from the real numbers.
Polynomials: know the division algorithm; know what is meant by the highest common factor of a pair of polynomials, and how to compute it using the Euclidean algorithm.
Learning Outcomes: General: Knowledge, Understanding and Skills
The student will be familiar with some fundamental concepts in logic and elementary number theory, will be able to understand and present simple mathematical proofs, and will know how to apply the theory to calculate highest common factors and solve equations involving congruences. | 677.169 | 1 |
About the book
Mathematics for the International Student: Mathematics HL has been written to reflect the
syllabus for the two-year IB Diploma Mathematics HL course. It is not our intention to define the
course. Teachers are encouraged to use other resources. We have developed the book independently
of the International Baccalaureate Organization (IBO) in consultation with many experienced
teachers of IB Mathematics. The text is not endorsed by the IBO.
This second edition builds on the strengths of the first edition. Many excellent suggestions were
received from teachers around the world and these are reflected in the changes. In some cases
sections have been consolidated to allow for greater efficiency. Changes have also been made in
response to the introduction of a calculator-free examination paper. A large number of questions,
including some to challenge even the best students, have been added. In particular, the final chapter
contains over 200 miscellaneous questions, some of which require the use of a graphics calculator.
These questions have been included to provide more difficult challenges for students and to give
them experience at working with problems that may or may not require the use of a graphics
calculator.
The combination of textbook and interactive Student CD will foster the mathematical development
of students in a stimulating way. Frequent use of the interactive features on the CD is certain to
nurture a much deeper understanding and appreciation of mathematical concepts.
The book contains many problems from the basic to the advanced, to cater for a wide range of
student abilities and interests. While some of the exercises are simply designed to build skills,
every effort has been made to contextualise problems, so that students can see everyday uses and
practical applications of the mathematics they are studying, and appreciate the universality of
mathematics.
Emphasis is placed on the gradual development of concepts with appropriate worked examples, but
we have also provided extension material for those who wish to go beyond the scope of the
syllabus. Some proofs have been included for completeness and interest although they will not be
examined.
For students who may not have a good understanding of the necessary background knowledge for
this course, we have provided printable pages of information, examples, exercises and answers on
the Student CD. To access these pages, simply click on the 'Background knowledge' icons when
running the CD.
It is not our intention that each chapter be worked through in full. Time constraints will not allow
for this. Teachers must select exercises carefully, according to the abilities and prior knowledge of
their students, to make the most efficient use of time and give as thorough coverage of work as
possible.
Investigations throughout the book will add to the discovery aspect of the course and enhance
student understanding and learning. Many Investigations could be developed into portfolio
assignments. Teachers should follow the guidelines for portfolio assignments to ensure they set
acceptable portfolio pieces for their students that meet the requirement criteria for the portfolios.
Review sets appear at the end of each chapter and a suggested order for teaching the two-year
course is given at the end of this Foreword.
The extensive use of graphics calculators and computer packages throughout the book enables
students to realise the importance, application and appropriate use of technology. No single aspect
of technology has been favoured. It is as important that students work with a pen and paper as it is
that they use their calculator or graphics calculator, or use a spreadsheet or graphing package on
computer.
The interactive features of the CD allow immediate access to our own specially designed geometry
packages, graphing packages and more. Teachers are provided with a quick and easy way to
demonstrate concepts, and students can discover for themselves and re-visit when necessary.
Instructions appropriate to each graphic calculator problem are on the CD and can be printed for students.
These instructions are written for Texas Instruments and Casio calculators.
In this changing world of mathematics education, we believe that the contextual approach shown in this
book, with the associated use of technology, will enhance the students' understanding, knowledge and
appreciation of mathematics, and its universal application.
Using the interactive student CD
The interactive CD is ideal for independent study. Frequent use will nurture
a deeper understanding of Mathematics. Students can revisit concepts taught in
class and undertake their own revision and practice. The CD also has the text of
the book, allowing students to leave the textbook at school and keep the CD at
home.
The icon denotes an Interactive Link on the CD. Simply 'click' the
icon to access a range of interactive features:
spreadsheets
video clips
graphing and geometry software
graphics calculator instructions
computer demonstrations and simulations
background knowledge (as printable pages)
For a complete list of all the active links on the Mathematics HL CORE second edition CD,
click here.
For those who want to make sure they have the prerequisite levels of understanding
for this course, printable pages of background informations, examples, exercises and
answers and provided on the CD. Click the 'Background knowledge' icon on
pages 12 and 248.
Graphics calculators: Instructions for using graphics calculators are also given on
the CD and can be printed. Instructions are given for Texas Instruments and Casio calculators.
Click on the relevant icon (TI or C) to access the instructions for the other type of
calculator.
Note on accuracy
Students are reminded that in assessment tasks, including examination papers, unless
otherwise stated in the question, all numerical answers must be given exactly or to
three significant figures.
HL and SL combined classes
HL Options
This is a companion to the Mathematics HL (Core) textbook. It offers coverage
of each of the following options:
Topic 8 – Statistics and probability
Topic 9 – Sets, relations and groups
Topic 10 – Series and differential equations
Topic 11 – Discrete mathematics
In addition, coverage of the Geometry option for students undertaking the IB Diploma
course Further Mathematics is presented on the CD that accompanies the
HL Options book.
Supplementary books
A separated book of WORKED SOLUTIONS give the fully worked solutions for every question
(discussions, investigations and projects excepted) in each chapter of the
Mathematics HL (Core) textbook. The HL (CORE) EXAMINATION PREPARATION & PRACTICE
GUIDE offers additional questions and practice exams to help students prepare for the
Mathematics HL examination. For more information email
[email protected]. | 677.169 | 1 |
Note to students
Do your older friends ever tell you they wish they had worked harder when they were in the classes that you are in now? Do you have friends in college who say they are struggling because they weren't challenged enough by the adults around them? It is hard sometimes to stay focused in school, when there are other things that seem more interesting and relevant than what you are learning in class today.
It may surprise you to know that the national organization Achieve ( reports that, when students are surveyed two years after high-school graduation, 75% express the wish that they had worked harder and had been challenged more by the adults around them. Amazingly, more than 60% say they wish they had taken more challenging mathematics courses in high school.
You are at a time in your life when you can take advantage of opportunities that those surveyed students did not. One way to do that is by challenging yourself to take lots of math. Taking rigorous mathematics courses can be a key to success in just about any career you might want to pursue when you leave school. The work isn't done only in your junior or senior year of high school, either. As you explore the resources on this site, notice how important ideas of middle school mathematics lay the foundation for your future success in Algebra I, Geometry, Algebra II, Precalculus, Calculus, and Statistics. | 677.169 | 1 |
Unit specification
Aims
This module aims to engage students with a circle of algorithmic techniques and concrete problems arising in elementary number theory and graph theory.
Brief description
Modern Discrete Mathematics is a broad subject bearing on everything from logic to logistics. Roughly speaking, it is a part of mathematics that touches on those subjects that Calculus and Algebra can't: problems where there is no sensible notion continuity
or smoothness and little algebraic structure. The subject, which is typically concerned with finite—or at the most countable—sets of objects, abounds with interesting, concrete problems and entertaining examples.
Intended learning outcomes
Students should develop the ability to think and argue algorithmically, mainly by studying examples in elementary number theory, graph theory and combinatorics.
On completion of this unit successful students will be able to:
understand proofs by induction thoroughly and be fluent in their construction; | 677.169 | 1 |
Lecture 1: Simple Equations
Embed
Lecture Details :
Introduction to basic algebraic equations of the form Ax=B
Course Description :
This is the original Algebra course on the Khan Academy and is where Sal continues to add videos that are not done for some other organization. It starts from very basic algebra and works its way through algebra II. | 677.169 | 1 |
Math Strategies
Course Description
Math Strategies is a Response to Invention aimed at assisting students who have been identified through ISAT and MAP testing data as having deficits in math. Math Strategies uses a concrete- representational- abstract (CRA) approach to learning using discovery activities in the Math Elevations curriculum. Activities will increase students' fact fluency and individual math deficits.
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 | 677.169 | 1 |
id: 05776637
dt: j
an: 2010e.00699
au: Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
ti: Enzyme kinetics and the Michaelis-Menten equation.
so: PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 20, No. 2, Special
Issue: Application activities to enhance learning in the
mathematics-biology interface, 148-168 (2010).
py: 2010
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: M65 I75
ut: difference equations; elementary differential equations; Euler's method;
linearization; parameter estimation; enzyme catalysis; Michaelis-Menten
kinetics; mass balance; law of mass action; conservation of mass;
biology; mathematical applications
ci:
li: doi:10.1080/10511970903486491
ab: Summary: The concepts presented in this article represent the cornerstone
of classical mathematical biology. The central problem of the article
relates to enzyme kinetics, which is a biochemical system. However, the
theoretical underpinnings that lead to the formation of systems of
time-dependent ordinary differential equations have been applied widely
to any biological system that involves modeling of populations. In this
project, students first learn about the general balance equation, which
is a statement of conservation within a system. They then learn how to
simplify the balance equation for several specific cases involving
chemically reacting systems. Derivations are reinforced with a concrete
experiment in which enzyme kinetics are illustrated with pennies. While
a working knowledge of differential equations and numerical techniques
is helpful as a prerequisite for this set of activities, all of the
requisite mathematical skills are introduced in the project, so the
methods would also serve as an introduction to these techniques. It is
also helpful if students have some basic understanding of chemical
concepts such as concentration and reaction rate, as typically covered
in high school or college freshman chemistry courses.
rv: | 677.169 | 1 |
Intermediate Algebra, An Individualized Approach
Online Intermediate Algebra Overview
This course assumes a degree of proficiency with Beginning and Elementary Algebra. Each new topic is introduced with a brief review of the needed knowledge from earlier courses, but the review is intended only as a refresher.
The remainder of the course extends the topics of Elementary Algebra and begins a solid development of relations, functions, and their graphing.
Every objective is thoroughly explained and developed. Numerous examples illustrate concepts and procedures. Students are encouraged to work through partial examples. Each unit ends with an exercise specifically designed to evaluate the extent to which the objectives have been learned. The student is always informed of any skills that were not mastered.
Topics include:
simplifying radical expressions and fractions
rational number exponents
polynomials
equation solving
inequalities and absolute values
linear functions
quadratic functions and relations (the conics)
systems of equations
The instruction depends only upon reasonable reading skills and conscientious study habits. With those skills and attitudes, the student is assured a successful math learning experience. | 677.169 | 1 |
Elementary Algebra - 9th edition
Summary: Ideal for lecture-format courses taught at the post-secondary level, ELEMENTARY ALGEBRA, Ninth Edition, makes algebra accessible and engaging. Author Charles ''Pat'' McKeague's passion for teaching mathematics is apparent on every page. With many years of experience teaching mathematics, he knows how to write in a way that you will understand and appreciate. His attention to detail and exceptionally clear writing style help you to move through each new concept with ease, and real-wor...show moreld applications in every chapter highlight the relevance of what you are learning | 677.169 | 1 |
Mathematics All Around, CourseSmart eTextbook, 4th Edition
Description
Mathematics All Around, Fourth Edition, is the textbook for today's liberal arts mathematics students. Tom Pirnot presents math in a way that is accessible, interesting, and relevant. Like having a teacher on call, its clear, conversational writing style is enjoyable to read and focuses on helping students understand the math, not just get the correct answers on the test. Useful features throughout the book enable students to become comfortable with thinking about numbers and interpreting the numerical world around them. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book | 677.169 | 1 |
preliminary study of calculus completed
i'll finish the 14th chapter soon and i have 16 chapters so i think i will just finish the other two chapters later. i started reviewing my notes last night and it's not quite as exciting as moving onto a new chapter. but i do eventually need to review everything i've learned, as hard as they may be. i want to get a solid database of notes so that at any time i can go back and relearn a problem that i've forgotten. it's possible that i can keep moving forward and never look back, after all i did that for the first 14 chapters and whenever i went back to review something i was able to access the needed information rather quickly. still, it's kind of bewildering confronting so many new facts and i want to try to make sense of it all. midway through the book, maybe around chapter 8 i realized that my note-taking strategy was inadequate. what i need for the more complicated algorithms, that is, those that involve more than 5 steps is for me to write out how to do each of the steps, since the book is so completely incompetent at explaining things.
throughout the book i understood very few theorems. for instance, i've seen kepler's laws explained in algebra and i understood them but when this book tried to do the same thing in calculus i didn't know what was going on. this comes as a severe disappointment since, as a philosopher, theorems were the one thing that i really wanted to understand. i've decided that doing problems mechanically is so much easier than understanding why one is doing the steps in the first place. for example, anyone can take the derivative of 2x^2 but it is much more difficult to understand why one is taking the derivative. it got to the point where i just gave up trying to understand the theorems. then again, i could rarely understand that books' explanations about anything. for some reason there is something about mathematicians and the printed word that do not go together. when mathematicians (or anyone explaining math) are forced to explain things off the cuff, orally, things for some reason become so much more clear. perhaps it's because it's easier to not know what you're talking about and write, then it is to speak and not know what you're talking about. when you're speaking, you're looking at someone and you're seeing if whether or not they are holding a straight face, moreover, you have to speak fluenty. you don't have to be thinking fluently when you're writing. you can just come up with whatever you think is clear, regardless if it takes 5 minutes to complete a sentence or not. for that reason i had to rely heavily on youtube to explain these calculus concepts. i'm afraid if i ever get up to higher math there simply won't be any youtube videos to explain things and i don't believe in taking courses in order to learn things. i learn things much better by myself. however, i can easily foresee that certain math and physics concepts become so difficult that i will really need a human who knows what they're talking about to explain it to me. it's just a fact of life that it's easier to transmit clarity in speech than in writing.
i'm rather troubled by my inability to understand theorems. i have a feeling that this is not a way to learn math. doing steps mechanically does not imply real understanding as anyone who has read searle's chinese room knows. one of these days my inability to understand theorems is going to haunt me. i'm just hoping that after reading enough math texts, getting more comfortable with the jargon, knowing more and more facts that sooner or later a light bulb will go off and it will come clear to me. | 677.169 | 1 |
200676,"ASIN":"1841465445","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.85,"ASIN":"1841465585","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":2,"ASIN":"184146581X","isPreorder":0}],"shippingId":"1841465445::cmPNQvYQ%2FoPHi8KnI2OBiPXqjweMjI5yISUYyF8w7AjeNJ%2FmGAT3FPW3diuoVVwWS7cHXXJZs%2BcUU%2BQQDgmFuvYQGGqV5vlf,1841465585::Pbp5eHZ6oeTeHda0rKF7oqQN8fCUy2uDefsZKd3sGFPC46cznCILS2WerZ3q1BwG6fdoqtxMU6EfrP9KAomBJldpwIaBmaD7,184146581X::laYrmzeDte55xtB%2B%2FHuYyPN%2FFIytmIj712yCmj3%2BstQ%2B19bheKPeLRL0k7xHGM%2B57WjXdPFsTxV838dDPM2zwLPx8VKskV series of GCSE revision books are good revision aid to benefit all levels of GCSE candidate. The book incorporates pages and pages of review exercises including every aspect of the GCSE Mathematics curriculum which are all easily accessible with handy hints and tips along the way. They include colourful and non-complicated examples and include the major points of every topic in a suitable framework. I would have liked to see a more thorough review of algebra and maybe more exercises to complete along side the notes. I feel this would be essential reading to brush up on the more less familiar concepts.
I bought this guide in the months before my GCSE exam - in my opinion, this book is the only reason I passed! It covers so much information in such a short book, and in an easy-to-remember format. The pages are colourful and make revision easier to handle, and although the jokes aren't quite as funny as they are intended to be, they keep you involved in what you're reading. The summaries qnd questions at the end of each chapter are also very useful.
This book really helped my concentrate on revising for my exam, i recomend it to all those who are unsure of the exam. It uses easy to understand words and easy to follow diagrams, if you have this book your guaranteed to pass with flying colours! | 677.169 | 1 |
Calculators are used extensively in the Algebra curriculum, and to a lesser extent, in the Geometry curriculum. Students are provided a calculator for classroom use. Calculators are also available from the DHS library for a two-day check out period. Students are not required to purchase calculators. If you wish to purchase a calculator, we recommend the TI-84 series. This calculator is the one that students will use on the TAKS test and is suitable for all High School and most college math courses. However, please do not bring personal calculators to school.
Spiral notebook of your choice to keep notes. You will keep notes for the entire year. The spiral will encourage you to keep them all in one place. You will need a folder or binder to keep all of your daily warm-ups and daily assignments, pop quizzes, etc.
Compass
Protractor
Ruler, marked in inches and centimeters
Lots of paper for homework
Map colors or crayons or markers to aid in marking diagrams to solve problems.
Dry erase markers for use on small white boards. (2 in contrasting colors should be adequate) | 677.169 | 1 |
Solving Quadratic Equations: Cutting Corners
This lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.Mathematics and Statistics2013-04-26T15:06:37Course Related MaterialsSteps to Solving Equations
This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.Mathematics and Statistics2013-04-26T15:06:34Course Related MaterialsStudent-Generated Questions for Exam Prep
Math teacher Jennifer Giudice takes a unique approach to preparing her students for their upcoming assessment. She assigns her students a homework assignment that requires them to develop 2 possible assessment questions. She uses these questions to both determine where different students are at in their understanding of quadratics and also to select questions that help her best assess their level of understanding.Ms. Giudice shares a few of the questions the following day and asks students to consider what they need to do to prepare for each of the questions.Mathematics and Statistics2013-02-26T16:56:31Course Related MaterialsAlgebra Team: Teacher Collaboration
Algebra teachers, Juliana Jones and Marlo Warburton, have common philosophies and expectations in their algebra classrooms but use their own unique teaching styles and structures to create consistent experiences for students. Collaboration is an important part of that process and allows teachers to provide common learning experiences in their classrooms despite different teaching styles and structures. This video takes a look at the warm-up, lesson, strategies for group work, classroom expectations and routines to discuss commonalities but also identify ways in which each teacher personalizes their classrooms based on their own teaching style and personality.Marlo Warburton, Juliana Jones,Mathematics and Statistics2012-11-02T13:06:40Course Related MaterialsAlgebra Team: Strategies for Group Work Jones' Warburton's Overview of Teaching StylesMy Favorite No: Learning From MistakesMathematics and Statistics2012-11-01T12:47:10Course Related MaterialsThe Factor Game (i-Math Investigations)
An online, interactive, multimedia math investigation. The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.Mathematics and Statistics2012-09-07T13:53:35Course Related MaterialsDifference of Squares
This lesson uses a series of related arithmetic experiences to prompt students to generalize into more abstract ideas. In particular, students explore arithmetic statements leading to a result that is the factoring pattern for the difference of two squares. An excellent teaching idea on how to help students walk the bridge from arithmetic to algebra.Mathematics and Statistics2012-09-07T13:53:35Course Related MaterialsQuadratic forms
This applet is an exploratory exercise for students to determine the best form for a quadratic. What do the coefficients do? Why do we spend so much time learning how to factor; is that form any better?Mathematics and Statistics2012-07-23T09:10:40Course Related MaterialsFactoring the Sum of Cubes or Difference of Cubes
Factoring the difference or sum of cubes.Mathematics and Statistics2012-07-23T09:10:17Course Related MaterialsFactorize Quadratic Polynomials by Table (Draft version)
Factorize the given quadratic polynomials. 3 levels of difficulties are provided.Mathematics and Statistics2012-07-13T14:53:49Course Related MaterialsFactoring simpleFactoringAngry Birds in Standard Form
Angry Birds in Standard FormMathematics and Statistics2012-07-13T14:53:21Course Related MaterialsAngry Birds in Factored Form
Angry Birds in Factored FormMathematics and Statistics2012-07-13T14:53:21Course Related MaterialsFactoring Quadratics with a Coefficient of One
The applet randomly generates quadratics with a coefficient of one with values of factors between -10 and 10. It also includes a check box to check the factors and a button to generate a new quadratic.Mathematics and Statistics2012-07-09T08:14:10Course Related MaterialsSolving a Quadratic by Factoring
This classroom tested applet demonstrates a step-by-step procedure for solving a quadratic equation (that will need to put into standard form) by factoring. The zero-product property may not be how you like it, but you and your students will get the idea.Mathematics and Statistics2012-07-06T21:33:02Course Related Materials | 677.169 | 1 |
Algorithmic Puzzles
Interprets puzzle solutions as illustrations of general methods of algorithmic problem solving
Contains a tutorial explaining the main ideas of algorithm design and analysis for a general reader
Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking.
The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies — exhaustive search, backtracking, divide-and-conquer and a few others — are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions
about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an elementary level, with puzzle examples, and requires neither programming nor mathematics beyond a secondary school level. Thus, the tutorial provides a gentle and entertaining introduction to main ideas in high-level algorithmic problem solving.
The second and main part of the book contains 150 puzzles, from centuries-old classics to newcomers often asked during job interviews at computing, engineering, and financial companies. The puzzles are divided into three groups by their difficulty levels. The first fifty puzzles in the Easier Puzzles section require only middle school mathematics. The sixty puzzle of average difficulty and forty harder
puzzles require just high school mathematics plus a few topics such as binary numbers and simple recurrences, which are reviewed in the tutorial.
All the puzzles are provided with hints, detailed solutions, and brief comments. The comments deal with the puzzle origins and design or analysis techniques used in the solution. The book should be of interest to puzzle lovers, students and teachers of algorithm courses, and persons expecting to be given puzzles during job interviews.
Readership: Students and teachers of algorithm courses, puzzle enthusiasts, and anyone wishing to learn more about how to solve puzzles and/or develop algorithmic thinking
Anany Levitin is a professor of Computing Sciences at Villanova University. He is the author of a popular textbook on design and analysis of algorithms, which has been translated into Chinese, Greek, Korean, and Russian. He has also published papers on mathematical optimization theory, software engineering, data management, algorithm design techniques, and computer science education.
Maria Levitin is an independent consultant specializing in web applications and data compression. She has previously worked for several leading software companies | 677.169 | 1 |
Department of Mathematics
MATH 1RA. Developmental Mathematics I
(3 units)
The first semester in a two semester sequence preparing students for college
level mathematics. See the online Schedule
of Courses for restrictions on enrollment based on the Entry Level Math
test. Properties of ordinary arithmetic, integers, rational numbers and
linear equations. CR/NC grading only; not applicable towards baccalaureate
degree requirements. F
MATH 10A. Structure and Concepts in Mathematics
I (3 units)
Prerequisite: students must meet the ELM requirement. Designed for prospective
elementary school teachers. Development of real numbers including integers,
rational and irrational numbers, computation, prime numbers and factorizations,
and problem-solving strategies. Meets B4 G.E. requirement only for liberal
studies majors. FS
MATH 45. What Is Mathematics? (3 units)
Prerequisite: students must meet the ELM requirement. Covers topics from
the following areas: (I) The Mathematics of Social Choice; (II) Management
Science and Optimization; (III) The Mathematics of Growth and Symmetry;
and (IV) Statistics and Probability. G.E. Foundation B4. FS
MATH 70. Calculus for Life Sciences (4
units)
No credit if taken after MATH 75 or 75A and B. Prerequisite: students must
meet the ELM requirement. Functions and graphs, limits, derivatives, antiderivatives,
differential equations, and partial derivatives with applications in the
Life Sciences. FS
MATH 90. Directed Study (1-3; max total
3 units)
Independently arranged course of study in some limited area of mathematics
either to remove a deficiency or to investigate a topic in more depth. (1-3
hours, to be arranged)
MATH 111. Transition to Advanced Mathematics
(3 units)
Prerequisite: MATH 76. Introduction to the language and problems of mathematics.
Topics include set theory, symbolic logic, types of proofs, and mathematical
induction. Special emphasis is given to improving the student's ability
to construct, explain, and justify mathematical arguments. FS
MATH 133. Number Theory for Liberal Studies
(3 units)
Prerequisite: MATH 10B or permission of instructor. The historical development
of the concept of number and arithmetic algorithms. The magnitude of numbers.
Basic number theory. Special numbers and sequences. Number patterns. Modular
arithmetic. F
MATH 134. Geometry for Liberal Studies
(3 units) Prerequisite: MATH 10B or permission of instructor. The use of computer
technology to study and explore concepts in Euclidean geometry. Topics include,
but are not restricted to, properties of polygons, tilings, and polyhedra.
S
MATH 137. Exploring Statistics (3 units)
Prerequisite: MATH 10B or permission of instructor. Descriptive and inferential
statistics with a focus on applications to mathematics education. Use of
technology and activities for student discovery and understanding of data
organization, collection, analysis, and inference. F
MATH 138. Exploring Algebra (3 units)
Prerequisite: MATH 10B or permission of instructor. Designed for prospective
school teachers who wish to develop a deeper conceptual understanding of
algebraic themes and ideas needed to become competent and effective mathematics
teachers. S
MATH 143. History of Mathematics (4 units)
Prerequisite: MATH 75 or 75A and B. History of the development of mathematical
concepts in algebra, geometry, number theory, analytical geometry, and calculus
from ancient times through modern times. Theorems with historical significance
will be studied as they relate to the development of modern mathematics.
S
MATH 149. Capstone Mathematics for Teachers
(4 units)
Prerequisites: MATH 151, 161, and 171. (MATH 161 and MATH 171 may be taken
concurrently.) Secondary school mathematics from an advanced viewpoint.
Builds on students' work in upper-division mathematics to deepen their understanding
of the mathematics taught in secondary school. Students will actively explore
topics in number theory, algebra, analysis, geometry.
MATH 161. Principles of Geometry (3 units)
Prerequisite: MATH 111. The classical elliptic, parabolic, and hyperbolic
geometries developed on a framework of incidence, order and separation,
congruence; coordinatization. Theory of parallels for parabolic and hyperbolic
geometries. Selected topics of modern Euclidean geometry. S
MATH 165. Differential Geometry (3 units)
Prerequisite: MATH 77 and 111 or permission of instructor. Study of geometry
in Euclidean space by means of calculus, including theory of curves and
surfaces, curvature, theory of surfaces, and intrinsic geometry on a surface.
F
MATH 232. Mathematical Models with Technology
(3 units)
Prerequisite: graduate standing in mathematics or permission of instructor.
A technology-assisted study of the mathematics used to model phenomena in
statistics, natural science, and engineering.
MATH 250. Perspectives in Algebra (3 units)
Prerequisite: graduate standing in mathematics or permission of instructor.
Study of advanced topics in algebra, providing a higher perspective to concepts
in the high school curriculum. Topics selected from, but not limited to,
groups, rings, fields, and vector spaces.
MATH 260. Perspectives in Geometry (3
units)
Prerequisite: graduate standing in mathematics or permission of instructor.
Geometry from a transformations point of view. Euclidean and noneuclidean
geometries in two and three dimensions. Problem solving and proofs using
transformations. Topics chosen to be relevant to geometrical concepts in
the high school curriculum.
MATH 270. Perspectives in Analysis (3 units)
Prerequisite: graduate standing in mathematics or permission of instructor.
An overview of the development of mathematical analysis, both real and complex.
Emphasizes interrelation of the various areas of study , the use of technology,
and relevance to the high school mathematics curriculum.
MATH 298. Research Project in Mathematics
(3 units)*
Prerequisite: graduate standing. Independent investigation of advanced character
as the culminating requirement for the master's degree. Approved for RP
grading.
MATH 299. Thesis in Mathematics (3 units)
Prerequisite: See Criteria for Thesis
and Project. Preparation, completion, and submission of an acceptable
thesis for the master's degree. Approved for RP grading. | 677.169 | 1 |
Free Coursera Calculus course with hand-drawn animated materials
Robert Ghrist from University of Pennsylvania wrote in to tell us about his new, free Coursera course in single-variable Calculus, which starts on Jan 7. Calculus is one of those amazing, chewy, challenging branches of math, and Ghrist's hand-drawn teaching materials look really engaging.
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include:
the introduction and use of Taylor series and approximations from the beginning;
Watch these next
Great post, and I am likely being pedantic, but I think it's important to distinguish between *describing* and *explaining*.
DevinC
I signed up for this course, rather than another introductory calculus course offered through Coursera, because Ghrist's approach seems radically different than the industry standard. His Funny Little Calculus Textbook starts off with functions, but immediately jumps to Taylor series, assuming the reader knows how to take the derivatives of simple polynomials. In other words, it seems more like a course about understanding calculus than doing calculus.
s2redux
Trying to figure out why George Takei agreed to read this script while wearing pants that are 2 sizes too small.
SamSam
Yay, I already signed up for this course a few months ago!
Even as a programmer I've always felt my basic calc was a bit rusty, and while I could probably just take a two-session refresher course and jump straight to Calc 2, this course looked fun. Now… hopefully I can stick with the schedule better than I could with "The History of the World Since 1300." Who would have guessed that 700 years of history would require lots of reading and lectures? (The course was very good, and I made it through four weeks on-schedule, but in the end I didn't have nearly enough time.)
I have all the prereqs; I just wish I remembered half of them. This class looks fun. Oh well.
sburns54
Holy moley! It's still as densely unapproachable to me as I remember it being when I flunked it in high school! Even with cartoons, which always grab my attention! I was lost by 1:03 seconds in! Thank goodness there are other people that can do this stuff and put it to practical use. I'll just stay in the kitchen, if anyone needs a sandwich.
SamSam
There's also a more basic Calculus One course:
The only prereqs are highschool algebra and trig.
Alissa Mower Clough
I'm getting somewhat aroused. In which sense, I really don't know.
penguinchris
I did a computer science course on Coursera in the spring that I thought was very good. I then tried another and didn't like the way it was done and gave up on it. I definitely need a calculus refresher and this looks good so I'm sold on this one, I hope it turns out well. | 677.169 | 1 |
Maths is everywhere, often where we least expect it. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the most of us - form a fascinating and integral part of our everyday lives. In The Joy of X, Strogatz explains the great ideas of maths - from negative numbers to calculus, fat tails... more...
The easy way to brush up on the math skills you need in real life Not everyone retains the math they learned in school. Like any skill, your ability to speak "math" can deteriorate if left unused. From adding and subtracting money in a bank account to figuring out the number of shingles to put on a roof, math in all of its forms factors into daily... more...
Forget the jargon. Forget the anxiety. Just remember the math. In this age of cheap calculators and powerful spreadsheets, who needs to know math? The answer is: everyone. Math is all around us. We confront it shopping in the supermarket, paying our bills, checking the sports stats, and working at our jobs. It is also one of the most fascinating-and... more...
This work presents principles of thin plate and shell theories - emphasizing novel analytical and numerical methods of solving linear and nonlinear plate and shell dilemmas, and new theories for the design and analysis of thin plate-shell structures. more...
Turbulence modelling is critically important for industries dealing with fluid flow and for applied mathematicians. This collection of lecture courses presented at a Newton Institute instructional conference on the title topic by leading researchers, has been edited or rewritten to provide a coherent account suitable for self-study. more...
The Generalized Riemann Problem (GRP) algorithm comprises common schemes of numerical simulation of compressible, inviscid time-dependent flow. This monograph, including examples illustrating the algorithm's applications, presents the GRP methodology beginning with its underlying mathematical principles. The book is accessible to researchers and graduate... more...
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak... more...
This book presents the current state of the art in computational models for turbulent reacting flows, and analyzes carefully the strengths and weaknesses of the various techniques described. The focus is on formulation of practical models as opposed to numerical issues arising from their solution. more... | 677.169 | 1 |
Streeter-Hutchison Series in Mathematics: Basic Mathematical Skills with Geometry
The "Streeter-Hutchison Series in Mathematics: Basic Mathematical Skills with Geometry, 7/e" by Baratto/Bergman is designed for a one-semester basic ...Show synopsisThe "Streeter-Hutchison Series in Mathematics: Basic Mathematical Skills with Geometry, 7/e" by Baratto/Bergman is designed for a one-semester basic math course. This successful worktext series is appropriate for lecture, learning center, laboratory, or self-paced courses. "Basic Mathematical Skills with Geometry" continues with it's hallmark approach of encouraging the learning mathematics by focusing its coverage on mastering math through practice. The "Streeter-Hutchison" series worktexts seek to provide carefully detailed explanations and accessible pedagogy to introduce basic mathematical skills and put the content in context. With repeated exposure and consistent structure of Streeter's hallmark three-pronged approach to the introduction of basic mathematical skills, students are able to advance quickly in grasping the concepts of the mathematical skill at hand | 677.169 | 1 |
The textbooks are free to read online and on mobile phones or you can order a hardcopy through us.
Why use the Siyavula textbooks?
•The curriculum broken down and delivered in an easy-to-get format
•Step-by-step guides to help you make sense of formulas and concepts.
•Explaining the definitions covered in the South African curriculum in basic terms
•A wide range of worked examples that will help you practice your skill and craft your thinking
•This textbook is free to read online and on mobile
Intelligent practice
A new online practice service which allows learners to practice the types of questions they may find in their tests and exams. This practice service is well integrated with the Siyavula textbooks and work together to ensure learners excel in Maths and Science. Learners are able to practice using their mobile phones or computers.
Why use the Siyavula practice?
•A multitude of exam style questions that covers the entire curriculum for grade 10, 11 and 12 Maths and Science.
•Intelligent practice allows learners to fill out final answer, rather than choose from multiple choice options.
•After answer is submitted, the full worked solution is given with all necessary steps and tips.
•Progress is monitored. A dashboard showing the learners frequency in practice and how well they are doing in the different chapters.
•Identify and improve on problem areas. The dashboard allows you to see specifically which areas you should be working on and which you have mastered | 677.169 | 1 |
MATHEMATICS DEPARTMENT
Course Offerings
This course is designed for the advanced math
student who is preparing to take Honors Pre-Calculus or college mathematics.
Second year algebra topics will be reviewed and extended to include
Pre-calculus concepts. Students will leave this course with a strong
analytical foundation that will allow them to be successful in a Calculus or
Statistics course in either high school or college. This course may be used
to meet the UC/CSU "C" or "G" requirement.
Algebra 1-2 is a logical and systematic extension of generalized
arithmetic. Algebra 1-2 covers the four basic operations on
the real numbers, solutions of first and second degree
equations in one variable, factoring, rational expression,
solutions of inequalities, functions and relations, graphing
linear equations and inequalities, irrational numbers, and
the quadratic formula. Fundamental operations with algebraic
representations and related applications are studied. This
course may be used to meet the UC/CSU "C" requirement.
This course is a review and extension of first year algebra.
Topics include, but are not limited to,
the study of linear, quadratic, and higher-order functions; rational
functions; exponential & logarithmic functions; inequalities; matrices;
complex numbers; and, trigonometry. This course may be used to meet the
UC/CSU "C" requirement.
Length of course/credits: 2 Terms (Semester 1
& 2); 1st and 3rd quarters earn elective credit and 2nd and
4th quarters earn math credit. This is a second year algebra
course. Topics studied will be identical to the Algebra 3-4
course with extended class time for mastery. Topics include,
but are not limited to, the study of linear, quadratic, and
higher-order functions; rational functions; exponential &
logarithmic functions; inequalities; matrices; complex
numbers; and, trigonometry. This course may be used to
meet the UC/CSU "C" requirement.
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. This course may be used to meet the
UC/CSU "C" or "G" requirement. UC approved for extra honors
credit (A=5, B=4, C=3).
In Trigonometry, the 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. This course may be used to meet
the UC/CSU "C" or "G" requirement. Statistics is a college preparatory
course which 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. This course may be used to meet the UC/CSU "C"
or "G" requirement.
This course is designed to build upon the fundamentals of computer
programming. The emphasis is on object-oriented programming
methodology, problem solving and algorithm development, and
is equivalent to a first-semester college course in Computer
Science. Topics include arrays, recursion, inheritance,
sorting and searching algorithms, and a case study of a
complex program. This course may be eligible for
college credit if the student enrolls at the appropriate
college while attending the Westview class and receives a grade of A or B all four
quarters of the year-long course. Click here to learn more about the
program. This course meets the UC/CSU "G"
requirement and the District's Computer Literacy requirement. UC approved
for extra honors credit (A=5, B=4, C=3).
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.
This course may be used to meet the UC/CSU "C" or "G"
requirement. UC approved for extra honors credit (A=5, B=4,
C=3).
This course is offered in the Fall semester, outside of the
regular 4 period day for 2.5 elective credits. It is
designed to help students review Calculus AB topics in
preparation for the AP Calculus BC course which is offered
in the Spring semester only.
This course follows AP Computer Science A. It covers a more
formal and in-depth study of algorithms, data structures,
design and abstraction. The topics include Big-O analysis,
exceptions, and advanced data structures (such as linked
lists, stacks, queues, trees, heaps, sets and maps). It is
equivalent to a second semester college course in Computer
Science. Students who enroll in this course need to also
enroll in AP Computer Science A 1-2. This course may be
eligible for college credit if the student enrolls at the
appropriate college while attending the Westview class and receives a grade of A or B all four quarters of the
year-long course. This course meets the UC/CSU "G" requirement and the
District's Computer Literacy requirement.
This is a second course in high school
mathematics with a main focus on Descriptive Geometry (two-
and three- dimensional geometry) and a minor emphasis in
geometric proofs and trigonometry. It is based on the
standards set by the State of California with a major
emphasis on measurements of two- and three-dimensional
figures, geometric constructions, Pythagorean applications,
special right triangles, rigid motions on geometric figures,
and coordinate geometry. This course is an integration
of high school geometry and Project Lead the Way curriculum
for Introduction to Engineering Design. The intent is to
integrate more geometry and/or teach geometry as a basis for
the course and use the project-based learning tools of
Introduction to Engineering Design as problem solving to
create a more in-depth learning experience for geometry
students. The focus of the course is depth of knowledge,
with less breadth than a standard geometry course. This
course may be used to meet the UC/CSU "C" math requirement.
This course teaches deductive reasoning and organized
thinking. Students study postulates, definitions, theorems
for use in formal proofs and use algebraic skills to solve
problems. Students study plane geometry and solid geometry.
Students also learn straightedge and compass constructions
and transformations. This course may be used to meet the
UC/CSU "C" requirement.
This course provides the foundation for students to proceed
on to Calculus. Reviews are done of trigonometry, geometry,
and algebra. The study of polynomials including synthetic
division, graphing theory, limits, and derivatives are
introduced. This course may be used to meet the UC/CSU "C"
or "G" requirement.
This course is designed to teach students the fundamentals
of computer programming. Topics covered include
variables and data types, methods, decision structures and
loops. The emphasis is on structured and
object-oriented programming methodology. This course
is linked with AP Computer Science A 1-2. This course
may be eligible for college credit if the student enrolls at
the appropriate college while attending the Westview class
and receives a grade of A or B all four quarters of the
year-long course. This course may be used to meet the
UC/CSU "G" requirement and the District's Computer Literacy
requirement.
This class is designed for the student who needs to master
computational skills such as fractions, decimals, and
percents. The main focus of this class is to help build the
foundational skills required to be successful in Algebra and
beyond. This course meets the PUSD math 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. This course may be
used to meet the UC/CSU "C" or "G" requirement. UC approved
for extra honors credit (A=5, B=4, C=3). | 677.169 | 1 |
Overview
Main description
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's.
problems, and practice exercises to test your skills.
This Schaum's Outline gives you
1,600 fully solved problems
Complete review of all course fundamentals
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!
Table of contents
Schaum's Outline of College Mathematics, 4ed Elements of Algebra Functions Graphs of Functions Linear Equations Simultaneous Linear Equations Quadratic Functions and Equations Inequalities Locus of an Equation The Straight Line Families of Straight Lines The Circle Arithmetic and Geometric Progressions Infinite Geometric Series Mathematical Induction The Binomial Theorem Permutations Combinations Probability Determinants of Order Two and Three Determinants of Order Systems of Linear Equations Introduction to Transformational Geometry Angles and Arc Length Trigonometric Functions of a General Angle Trigonometric Functions of an Acute Angle Reduction to Functions of Positive Acute Angles Graphs of the Trigonometric Functions Fundamental Trigonometric Relations and Identities Trigonometric Functions of Two Angles Sum, Difference, and Product Trigonometric Formulas Oblique Triangles Inverse Trigonometric Functions Trigonometric Equations Complex Numbers The Conic Sections Transformations of Coordinate Points in Space Simultaneous Quadratic Equations Logarithms Power, Exponential, and Logarithmic Curves Polynomial Equations, Rational Roots Irrational Roots of Polynomial Equations Graphs of Polynomials Parametric Equations The Derivative Differentiation of Algebraic Expressions Applications of Derivatives Integration Infinite Sequences Infinite Series Power Series Polar Coordinates Introduction to the Graphing Calculator The Number System of Algebra Mathematical Modeling
Author comments
The late Frank Ayres, Jr., Ph.D., was formerly a professor in and head of the Department of Mathematics at Dickinson College, Carlisle, Pennsylvania. He is the author or coauthor of eight Schaum's Outlines, including Calculus, Trigonometry, Differential Equations, and Modern Abstract Algebra.
Philip A. Schmidt, Ph.D., has a B.S. from Brooklyn College (with a major in mathematics), an M.A. in mathematics, and a Ph.D. in mathematics education from Syracuse University. He is currently the program coordinator in mathematics and science education at The Teachers College at Western Governors University in Salt Lake City, Utah. | 677.169 | 1 |
Geometry: A Fresh Approach (called Geometry from
here on) is a complete high-school geometry course. The student
book includes solutions to odd-numbered problems. Geometry is
intended to be a consumable worktext, but you could write your
answers on lined or graph paper to use the book for future students.
An even-numbered problem solution guide is also available. With
these two books, paper, and a pencil, your student will be ready
to tackle geometry. Algebra 1 is a prerequisite.
Geometry consists of 13 chapters and two appendices.
Lessons are written directly to the student; consequently, a parent
does not need to teach the lessons. Every chapter is made up of
several parts, and beginning in chapter 2 each chapter ends with
a mixed review. The mixed review could be used as a chapter test. Geometry does
not contain tests or final exams.
Appendix A reviews algebraic concepts and is a good starting point
for most students. Appendix B includes answers to the odd-numbered
problems.
Ms. Walters wrote Geometry, as well as Algebra 1 and Algebra
2, after years of providing one-on-one tutoring to students.
She used her knowledge of what students struggled with to write
an easy-to-use curriculum that will instruct students in what
they need to know. You won't find flashy colors, comics, or off-topic
word problems in Geometry - Ms. Walters does not ask
your student how he feels about the hypotenuse of triangle B
or any other unrelated questions. She sticks to the subject at
hand -- geometry.
I found the author's explanations to be thorough and complete,
making Geometry an excellent text for students who learn
well on their own. However, students who need more instruction
(i.e., video or direct teacher involvement) or who are easily frustrated
may not find this text is for them.
I like how Ms. Walters presents each lesson and how she starts
students using proofs in Chapter 1. Her "Direct and Indirect Proofs" lesson
contained enough explanation so that even I could understand it
(math is NOT my strong subject).
For future revisions, I hope that Ms. Walters will put all answers
into one solutions guide. I don't mind the odd problem solutions
remaining in the student book, but I really dislike having to go
back and forth to correct a lesson. This edition lacks a glossary
and an index, which are also things I'd like to see added into
future revision.
I wish I could say that my children loved this course. I don't
think that any geometry course would get that recommendation from
them. I think Geometry is a worthy addition to the selection
of curricula available to homeschoolers, and I think that it will
benefit many families. | 677.169 | 1 |
1
Chapter 1
Introduction
Nature of the problem
There is a tremendous amount of pressure placed upon students and teachers to
achieve proficient scores on end of level math testing. High expectations dealing with
math have created many different10
CHAPTER 2: MATERIALS & METHODS
DNA Extraction and Regions Sampled
Ancient maize specimens were previously collected from the Corngrowers Site and identified based on their depth of occurrence from the trench surface. These specimens were ground... | 677.169 | 1 |
Linear Algebra
Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, and comprises a central part of any course in mathematics. This textbook provides a rigorous introduction to the main concepts of linear algebra which will be suitable for all students coming to the subject for the first time.
The book is in two parts: Part One develops the basic theory of vector spaces and linear maps, including dimension, determinants, and eigenvalues and eigenvectors. Part Two goes on to develop more advanced topics and in particular the study of canonical forms for matrices. Professor Berberian is at pains to explain all the ideas underlying the proofs of results as well as to give numerous examples and applications. There is an abundant supply of exercises to reinforce the reader's grasp of the material and to elaborate on ideas from the text. As a result, this book presents a well-rounded and mathematically sound first course in linear algebra.
show more show less
Vector Spaces
Linear Mappings
Structure of Vector Spaces
Matrices
Inner Product Spaces
Determinants (2 x 2. and 3. x 3)
Determinants (n x n)
Similarity (Act I)
Euclidean Spaces (Spectral Theorem)
Equivalence of Matrices Over a Principal Ideal Ring
Similarity (Act II)
Unitary Spaces
Tensor Products
Table of Contents provided by Publisher. All Rights Reserved.
List price:
$39.95
Edition:
1992
Publisher:
Oxford University Press, Incorporated
Binding:
Trade Cloth
Pages:
376
Size:
7.69" wide x 9.56" long x 1.04 | 677.169 | 1 |
Book Description: Preempt your anxiety about PRE-ALGEBRA! Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve your dilemma in no time. Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. Operations with monomials and polynomials are also discussed. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. It's a no-brainer! You'll learn: Addition, subtraction, multiplication, and division of whole numbers, integers, fractions, decimals, and algebraic expressions Techniques for solving equations and problems Measures of length, weight, capacity, and time Methods for plotting points and graphing lines Simple enough for a beginner, but challenging enough for an advanced student, Pre-Algebra Demystified, Second Edition, helps you master this essential mathematics subject. It's also the perfect way to review the topic if all you need is a quick refresh | 677.169 | 1 |
Mathematics for Elementary Teachers
9780321447173
ISBN:
0321447174
Edition: 2 Pub Date: 2007 Publisher: Addison-Wesley
Summary ...just on the mechanics of how it works. Fully integrated activities are found in the book and in an accompanying Activities Manual. As a result, students engage, explore, discuss, and ultimately reach true understanding of the approach and of mathematics.[read more]
Ships From:Mishawaka, INShipping:Standard, Expedited, Second Day, Next Day | 677.169 | 1 |
4600/7602 Signal and Image Processing II Tutorial 3(Due date: Friday 1/5/09)1. Automatically locate the number plate in the following image. (Available as You may try a 2D cross-correl
Integration by substitutionThere are occasions when it is possible to perform an apparently dicult piece of integration by rst making a substitution. This has the eect of changing the variable and the integrand. When dealing with denite integrals, t
ELEC4600/ELEC7602 Signal and Image Processing IITutorial 1 (Due date: Friday 27/03/09)1. We wish to extract tones at 50 and 100 Hz from tones at 1000 and 1100 Hz and then downsample the output by the largest possible factor. Assume the signal cont
ELEC4600/7602 Signal and Image Processing IITutorial 5 (Extended due date: 30/5/2008) 1. Stereo reconstruction is only useful for reconstructing a simple scene from two nearby views1. It can be difficult to extend to complicated scenes with occlusio
Image AnalysisExtracting Information From Images9/04/2003ELEC4600/7602 Signal and Image Processing IIBrian Lovell1Image Analysis The first step in image analysis is generally to segment the image. The level of segmentation depends on th
MATH1050 Semester 1, 2008Week 6 Tutorial ProblemsWork through the following problems, show your tutor then record your name before the end of your Week 6 tutorial. You are encouraged to discuss these questions and your solutions with your peers a
MATH1050 Semester 1, 2008 Week 12 Tutorial Problems Work through the following problems, show your tutor then record your name before the end of your Week 12 tutorial. You are encouraged to discuss these questions and your solutions with your peers a
MATH1050 Semester 1, 2008Week 3 Tutorial ProblemsWork through the following problems and have your tutor sign your solutions and record your name before the end of your Week 3 tutorial. You are encouraged to discuss these questions and your solut
Lesson 5 Sec 8.3 Maxima and Minima of Functions of several variables (Continued) We have learned the second derivative test to determine whether a function of two variables has a relative maximum or a relative minimum in previous lecture. In this lec
COSC 235BDavid A. SykesQuiz 1February 15, 2008what can be computed 1. Computer science is the study of _. CPU 2. A _ is the "brains" of a computer that can only address data stored in main memory. letter underscore 3. A name in a Python program
COSC 235BDavid A. SykesQuiz 6April 18, 20081. Show the output of the program on the second sheet given the following user inputs [bold]:Welcome to the frog simulation. Enter the depth of the well: 10 Enter the height of the frog above the bott
Dao127-+Talk-+Spectral Analysis of 2-Colour 3-Pulse Photon Echoes on a Femtosecond Time Scale-+AbstractThe spectral analysis of photon echo signals is used to study a semiconductor-doped glass and a laser dye (RhB) in methanol solution. The d
Eco 301 Problem Set 12Name_ 10 December 20081. The demand curve for a monopolist is given by P = 350 - 7Q, and the short-run total cost curve is given by TC = 500 + 70Q. What is the profit-maximizing price and quantity? Find the monopolist's econ
Published in Gazette 22.3.2007 p 869South AustraliaNational Parks and Wildlife (Bascombe WellConservation Park-Mining Rights) Proclamation 2007under section 43 of the National Parks and Wildlife Act 1972Preamble1 The Crown land de
INFS3101/7100 Ontology and the Semantic WebWeek 12 Suggested Tutorial Solution: Advanced IssuesSemester 1, 2006Consider the rental accommodation exchange from the week 2 tutorial and the representation in the solution to the week 4 tutorial and f
CHEM 221 01 LECTURE #09b Tues., Oct. 04/05 2.10 Conformations of Alkanes: rotation about carbon-carbon bondsFor any bond:Overlap of end-on overlapping orbitals is not diminished by rotation about the internuclear axis rotation about a single bond
COSC235A Spring 2008 Quiz #1Please read each question carefully and be sure to give complete answers. Work quickly and good luck! 1. (1 pt.) Print your name: _ 2. (10 pts.) For each of the follow, indicate whether it is a valid Python identifier or
CS 235 Preliminary Student SurveyThis survey is not meant to invade your privacy. I created it to help me get to know you better. If there is a question that you feel uncomfortable answering, please ignore that question. However, returning the surve
GABAergic Influences Increase Ingestion across All Taste Categories Liz Miller Molly McGinnis Lindsey RichardsonA research thesis submitted in partial completion of PSY451 senior research thesis, at Wofford College2 Abstract Each year six million
2008The Parliament of theCommonwealth of AustraliaHOUSE OF REPRESENTATIVESPresented and read a first timeTax Laws Amendment (PoliticalContributions and Gifts) Bill 2008No. , 2008(Treasury)A Bill for an Act to amend th | 677.169 | 1 |
Secondary Mathematics WWW Resources
This
is a selective, annotated list of recommended Web sites about secondary
mathematics.
TIP:
Press Ctrl/f
and enter a part of a word or phrase in the Find what: box and
click on Find Next to search for a topic on this page. For example,
type math to search for
math, mathematics, mathematical.
Awesome
Library: Middle-High School Math
This site provides links
about teaching Algebra, By Subject and Standard, Calculus, Data Analysis,
Geometry, Graphing, Pre-Algebra, Pre-Calculus, Probability and Statistics,
& Trigonometry. The site also includes links to Assessment Information,
Math Lessons, Problem Solving, & Standards and Discussions. The Awesome
Library uses specific selection
criteria and methods for including links on the web site.
Cornell
Theory Center Math and Science Gateway: Mathematics
At this site, sponsored by Cornell University's Department of Education, you
can locate links to resources in mathematics for educators and students in
grades 9-12; topics covered include: fractals, geometry, history of mathematics,
mathematics software, commercial software, and tables/constants/definitions.
Frank
Potter's Science Gems - Mathematics
A professor of physics at the University of California at Irvine produces
an annotated list of math sites arranged by topic and grade level; subjects
include: algebra, calculus, geometry, history of mathematics, number theory,
probability and statistics, and trigonometry.
Infinite
Secrets
This PBS/NOVA Web site
about the concept of infinity explores the life of Archimedes and the recently
discovered manuscript which shows he came quite close to discovering calculus.
The site includes a number of interviews, short articles, a teacher's guide
and interactive features, including an "Approximating Pi" demonstration
that illustrates how Archimedes calculated pi around the year 250 BCE.
Interactive
Mathematics
An extensive,
award winning mathematics site which includes games, puzzles, analog gadgets,
polls, and more! Additionally a Chronology of Updates for "an insight
of this site's evolution, chronology updates may be used for word searches."
Math
in Everyday Life
Funded by Annenberg/CPB, this site
explores using math to help us in everyday life situations, such as playing
games or cooking, buying or leasing a new car, and predicting retirement savings.
Math
Forum@ Drexel
The Math Forum, a center for math education on the Internet, is funded by
the National Science Foundation. Check out the following resources from theForum:
PBS
TeacherSource PBS provides links to excellent math resources on the Web and to
recommended books for grades 9-12.
Teaching
Mathematics Teaching Mathematics provides a number of
teaching articles on topics that include: Teaching Secondary Mathematics,
Theories of Mathematical Learning, Enhancing Thinking Skills in the Sciences
and Mathematics, and Symbolizing and Communicating in Mathematics Classrooms:
Perspectives on Discourse, Tools, and Instructional Design. A person can also
search by books, journals, magazines, newspapers, or encyclopedias. Advanced
search options are also available on this site.
Webmath
Webmath offers help in Math for Everyone, General Math, K-8 Math, Algebra,
Plots & Geometry, Trig. & Calculus, and Other Stuff. "This site
has over 100 instant-answer, self-help, math solvers, ready to help you get
your math problem solved." Webmath also offers an ask the expert area
and math software for your computer. | 677.169 | 1 |
Paul C Emekwulu
Title:
Mathematical Encounters for the Inquisitive Mind
Genre:
Teaching / Educational
ISBN:
9784535510
Synopsis :
Some school books are not written strictly in line with any traditional curriculum. They
fall into the category of supplemental materials. The right supplemental materials in
mathematics are analogous to novels and other reading materials. Novels, the language
of expression notwithstanding, build language skills in the areas of vocabulary, reading
and comprehension, spelling, grammar etc. Similarly, the right supplemental materials
in mathematics build vocabulary, computational, language, reasoning and logical
thinking skills. Mathematical Encounters for the Inquisitive Mind is a unique collection
of articles written by the author over the years under different circumstances and each
has some dose of mathematical insights for the inquisitive mind. The book can help
students and the general reader to be logical in their approach to mathematics and life
situations.
Full Table of Contents is available @: | 677.169 | 1 |
Topic: this is a mathematics education question (but applies to other sciences too).
Assumtions
Assumptions
Specializing early
Topic: this is a mathematics education question (but applies to other sciences too).
Assumtions | 677.169 | 1 |
PROFESSOR: Hi, I'm Gilbert Strang, and I'm a math professor at MIT. And I hope these highlights of calculus will be helpful. I started the project this year, because the linear algebra lectures which were in class have been watched by a lot of people on OpenCourseWare. And so I looked at what there was for calculus.
And I saw two or three types of things. One was lectures, sort of very serious, too mathy. And another was supported by foundations, an effort to make math look so terrifically exciting and wonderful and connect with everything. And yet, I feel a lot of people are taking math courses, calculus, in high school, in college, and simply want a little help to see what's the main point.
And maybe that's the idea of these lectures, is to try to tell you the main point without all the heavy things that a giant textbook would do, and without all the practice that you'll get in class, and doing exercises and so on. So these are kind of short, but I hope alive. And if they help, I'm very happy.
So I guess I'm hoping everybody might watch this who'd like a little help or a second look at calculus, both high school and college students. I wanted to capture key ideas that you could use for review and see new examples and see just coming from a second person. That seems to be what succeeds with linear algebra. The videos are sort of just to add, to supplement what you're actually seeing in class and in the textbook.
I think of the textbooks as often so large and so many exercises that it's totally easy to lose the key point, what's essential about calculus and what is just kind of routine and practice. So in short videos, it has to be the essential points, the three groups of functions, like powers of x, sine and cosine of x, and e to the x. If you understand those, you've got the main ideas.
We're starting out with a first group of five videos. Maybe big picture is the words that we think of for those. And then that'll be the first group that'll be on OpenCourseWare. And then I've done 12 after that, that do sort of the rest of differential calculus, big words just meaning how to find the derivative, the slope, the speed. You'll see in the videos. And then after that could come integral calculus, if you think I should.
I don't think of a lot of prerequisites for these videos. I guess I'm always hopeful that you could watch them even if you haven't started calculus, to see what's coming, what it's about. I've taught math for a long time, and it's so easy to get into the course and jump over the opening, the introduction that tells what's important here. And that's maybe what these videos are aimed at.
FEMALE SPEAK | 677.169 | 1 |
Free Graphing Calculator
Free Graphing Calculator has a clear-cut layout, which is ideal for this type of an app. It only has five tabs, all listed at the very bottom of the screen: calculator, equations, graph, reference and more. The first three are self-explanatory. The last two have more details. The reference-tab offers many references not only applicable to algebra, but also to calculus, mechanics, fractions, geometry, language, logic, trigonometry, vectors and many more! The more-tab is where you'll find your settings, information about the full version, a place to make an in-app purchase of $0.99 to eliminate ads, as well as table, polynomial and triangle solvers!
Because Free Graphing Calculator is all about numbers and being precise, itsads do bother me. However, they only cost a buck to remove permanently, and this app is worth way more than a buck! If you need a little help with your algebra, this graphing calculator could make your grade! It's that good! It offers more than features than the paid calculator apps, and it's FREE!
Graphing Capabilities:
• Graph up to four equations at once.
• Graphs are labeled.
• You can drag the graph or pinch to zoom in or out.
• Calculator can find roots and intersections.
A unit converter: With a tap, you can enter the result of your conversion into the calculator. Currently converts different units of the following: acceleration, angle, area, density, distance, energy, force, mass, power, pressure, speed, temperature, time, and volume. Great for doing physics homework!
Constants for scientific calculations — speed of light, strength of gravity at Earth's surface, etc. etc. etc. Tapping on a constant will insert it into your calculation — i.e, you don't have to key in the value. Again, great for doing physics homework!
It can make a table of the values of any function you care to enter. You can choose the starting x value of the table, as well as how much x increases for each successive row.
Help screens linked directly to many of the available functions and constants. Tap the disclosure arrow to see the definition.
Forgot the quadratic formula? Or the double-angle formulas for sine and cosine? The math/science reference hits the high points of various subjects. Currently includes algebra, differential and integral calculus, geometry, trigonometry, vectors, vector calculus, and classical mechanics.
App Review Details
Free Graphing Calculator | 677.169 | 1 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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Math 442Homework # 1SolutionsTexas A & M UniversitySpring 20111. You are a professional modeler at Texas Department of State Health Services. You havebeen assigned to study an inuenza epidemic which occurred in a boarding school in the northof Dall
Math 442Homework # 4Due April 4Texas A & M UniversitySpring 20111. The simple pendulum consist of a particle P of mass m suspended from a xed point O bya light string of length a, which is allowed swinging in a vertical plane. If there is no frictio
Math 442Lab 1 - WorksheetTexas A & M UniversitySpring 2011In this course we will be using Matlab for numerical analysis of mathematical models. A lot ofuseful information about Matlab is available at http:/ begin we mus
Math 442Lab 2 - WorksheetTexas A & M UniversitySpring 20111. Consider a city with population of 3 106 . Suppose that one third of the people livingin that city have been infected with inuenza. In the absence of antibiotics, health ocialsestimate an
Math 442, Quiz # 5Name & ID number:(Solutions)Texas A & M UniversitySpring 2011[15 points] 1. What is the process of validating a model? When can we accept a model?First we propose a test (e.g. whether the model predictions match with the recorded d
Math 442, Quiz # 1 (solutions)Name & ID number:Texas A & M UniversitySpring 2011[30 points] 1. What are the main assumptions of the lake purication model discussed in section1.1 of the textbook?1.2.3.4.The lake has a constant volume.The lake is Research individual | 677.169 | 1 |
0471923850
9780471923855 and practice of the numerical computation of internal and external flows. In this volume, the author explains the use of basic computational methods to solve problems in fluid dynamics, comparing these methods so that the reader can see which would be the most appropriate to use for a particular problem. The book is divided into four parts. In the first part, mathematical models are introduced. In the second part, the various numerical methods are described, while in the third and fourth parts the workings of these methods are investigated in some detail. Volume 2 will be concerned with the applications of numerical methods to flow problems, and together the two volumes will provide an excellent reference for practitioners and researchers working in computational fluid mechanics and dynamics. Contents Preface Nomenclature Part 1 The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation Introduction Chapter 1 The Basic Equations of Fluid Dynamics Chapter 2 The Dynamic Levels of Approximation Chapter 3 The Mathematical Nature of the Flow Equations and their Boundary Conditions Part II Basic Discretization Techniques Chapter 4 The Finite Difference Method Chapter 5 The Finite Element Method Chapter 6 Finite Volume Method and Conservative Discretizations Part III The Analysis of Numerical Schemes Chapter 7 The Concepts of Consistency, Stability and Convergence Chapter 8 The Von Neumann Method for Stability Analysis Chapter 9 The Method of the Equivalent Differential Equation for the Analysis of Stability Chapter 10 The Matrix Method for Stability Analysis Part IV The Resolution of Discretized Equations Chapter 11 Integration Methods for Systems of Ordinary Differential Equations Chapter 12 Iterative Methods for the Resolution of Algebraic Systems Appendix Thomas Algorithm for Tridiagonal Systems Index «Show less... Show more»
Rent Numerical Computation of Internal and External Flows, Fundamentals of Numerical Discretization 1st Edition today, or search our site for other Hirsch | 677.169 | 1 |
Libros de: ECONOMIA CUANTITATIVA
Learn the science of collecting information to make effective decisions Everyday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting ...
Hirsch, Devaney, and Smale's classic "Differential Equations, Dynamical Systems, and an Introduction to Chaos" has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a ...
Volume II is devoted to generalized linear mixed models for binary, categorical, count, and survival outcomes. The second volume has seven chapters also organized in four parts. The first three parts in volume II cover ...
Although there are currently a wide variety of software packages suitable for the modern statistician, R has the triple advantage of being comprehensive, widespread, and free. Published in 2008, the second edition of Statistiques avec ...
Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How ...
Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all ...
Designed specifically for business, economics, or life/social sciences majors, "Calculus: An Applied Approach, 9E, International Edition" motivates students while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show students the real-world ...
This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine ...
Graphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical ...
This book provides analysis of stochastic processes from a Bayesian perspective with coverage of the main classes of stochastic processing, including modeling, computational, inference, prediction, decision-making and important applied models based on stochastic processes. In ...
Business Statistics: First European Edition provides readers with in-depth information on business, management and economics. It includes robust and algorithmic testbanks, high quality PowerPoint slides and electronic versions of statistical tables. Furthermore, the text features ...
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied ...
This book provides a comprehensive description of the state-of-the-art in modelling global and national economies. It introduces the long-run structural approach to modelling that can be readily adopted for use in understanding how economies work, | 677.169 | 1 |
Attend the 3rd Annual USACAS Conference
Computer Algebra Systems (CAS) have the potential to revolutionize mathematics education at the secondary level. They do for Algebra & Calculus what calculators do for arithmetic: simplify expressions, solving equations, factoring, taking derivatives, and much more.
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From the Publisher: Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Sixth reinforce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology.
Description:
Over the years, the text has been shaped and adapted
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Description:
This text bridges the gap between traditional and reform approaches
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Statistics Bridging Courses
Early in 2013 the Mathematics Learning Centre will offer short bridging courses for students planning to undertake programmes which require the study of statistics, such as Statistics and Research Methods for Psychology, and degrees/diplomas in Public Health or other postgraduate degrees.
These courses are designed for people who lack confidence when faced with mathematical tasks or as a refresher for people who want to brush up on basic mathematical skills. They may also be useful for students who have not studied Mathematics (2 Unit) at school. They are not appropriate for students who have at any time completed the higher levels of mathematics for the Higher School Certificate.
The courses aim to review the basic mathematics needs of students in a statistics course and to develop an intuitive understanding of some fundamental statistical concepts.
The program includes:
use of a scientific calculator, including the use of statistical functions
algebra, including the use of formulae and the solution of simple linear equations
introduction to concepts in probability by means of practical activities | 677.169 | 1 |
Cut The Knot!
Students' Social Choice
It's our choices, Harry, that show what we truly are, far more than our
abilities.
Albus Dumbledore, Headmaster
Hogwarts School of Witchcraft and Wizardry
Harry Potter, Year 2,
J. K. Rowling
Scholastic, 1999
The usual math sequence taken by a liberal arts major is two courses
long: some sort of intermediate algebra and one more course that is
expected to fulfill the aims of liberal arts education with regard to
mathematics. This last — the final math course — what should it
be? Years ago, this course would most certainly be of the pre-calculus
variety. It might have also been an attempt to endear mathematics on
students who gave up on the subject long, long ago by presenting its more
enticing, often recreational facets (see, for example,
a review of
[Beck], where the latter was referred to as a
magnificent fossil of a book. Sherman Stein's eminently readable
book might be in the same category. It was republished
in 1999 by Dover Publications, Inc., which places it squarely among the
venerable classics. The book can be now had at
amazon.com at a throwaway price of
$13.96, far below the expected textbook price range.)
A new trend seems to be growing roots in math departments and among
textbook publishers. I am aware of two fine representatives of this trend:
Excursions in Modern Mathematics by
P. Tannenbaum and R. Arnold and For All Practical
Purposes by COMAP. In less than a decade one underwent 4, the
other 5 editions. The books are similar in contents, execution and price
($90+).
In the Preface, the authors of
Excursions explain that the
"excursions" in this book represent a collection of topics chosen to meet a
few simple criteria:
Applicability
The connection between the mathematics presented here and
down-to-earth, concrete real-time problems is direct and
immediate.
Accessibility
Interesting mathematics need not always be highly technical and
built on layers upon layers of concepts.
Age
Modern mathematical discoveries do not have to be only within the
grasp of experts.
Aesthetics
There is an important aesthetic component in mathematics and, just
as in art and music (which mathematics very much resembles), it often
surfaces in the simplest ideas.
The following is a small sample of the topics common to the two books (I
am more familiar with the Excursions than
with the COMAP book, whose contents could be
ascertained from
the
online description.)
The Borda Method
The Borda method, named after Jean-Charles de Borda (1733-1799), is used
to select the winner of the Heismann trophy, the American and National
Baseball Leagues MVP's, Country Music Vocalist of the Year, school
principals, university presidents, and in a host of other real world
situations.
The Borda and the Plurality with Elimination (described below) methods
use preference ballots, wherein a voter lists the alternatives in
order of preference. The Borda method is about counting points. The last
alternative on a ballot receives 1 point, the next one receives 2 points
and so on. The Borda method selects the alternative with the largest point
count.
It may surprise a student to learn that the winner picked up by the
Borda method may not be the one preferred by the majority of the
voters.
(Numbers in the upper row indicate the number of votes cast for ballots
below. Letters A, B, C, D and so on denote the competing alternatives.)
Plurality with Elimination
The Plurality with Elimination is a natural extension of the majority
vote to the case of more than 2 alternatives. Alternatives with the fewest
number of (1st place) votes are dropped one after another until
only two left, of which the winner is selected by the majority rule.
The Plurality with Elimination method violates the so-called
Monotonicity Criteria. It's possible for a winner to lose the
elections after someone switched votes in its favor. To see how that may
happen, swap the first and the second alternatives on the 4th
ballot.
There are many more methods used to combine individual preferences of
the voting population into the Social Choice of the population as
a whole. Kenneth Arrow's Impossibility theorem (1951), which in its
currently common formulation asserts that no absolutely satisfactory
democratic method exists, was called by Arrow himself the General
Possibility Theorem: it pointed to a method that satisfied all the
reasonable requirements Arrow thought to impose on a Social Choice
procedure. Unfortunately, the method came out to be a dictatorship: one
fellow's social preferences become the choice of the whole population (with
or without an election).
Power Indices
The United Nations Security Council consists of five permanent members
(the US, Russia, England, France and China) and 10 nonpermanent members
elected for two year periods on a rotating basis from several country
blocks. For a motion to pass in the Security Council, it must be approved
by all five permanent members and at least 4 nonpermanent ones. The
situation is best described as a
weighted
voting system [39: 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
which indicates that
each of the five permanent members has a weight of 7 (votes),
while
each of the ten nonpermanent member has a weight of 1, and
that
for a resolution to pass in the Security Council, it must muster at
least 39 — the quota — votes.
All five permanent members have in effect veto power and thus
wield more power than is suggested by the ratio 7:1. The Banzhaf power
index has been invented to evaluated power distribution in weighted voting
systems.
A coalition of voters is called losing if the total weight of its
members does not reach the quota. Otherwise, a coalition is called
winning. A member is critical to a winning coalition if its
removal renders the coalition losing. Let there be N vote holders (players,
as they are usually called). Let Bi, I = 1, 2, ..., N, denote
the number of times the Ith player is critical. Introduce B =
B1 + ... + BN. Then the Banzhaf power index of the
Ith player is defined as BPIi =
Bi/B.
It could be shown that the Banzhaf power index of a permanent member of
the Security Council is more than 10 times greater than that of a
nonpermanent member. (The ratio goes up to about 100 for another —
Shapley-Shubik's — power index.)
Intuitively, power comes with the number of votes. More votes wield more
power. So that the following situation may come as a surprise. It is
straightforward to verify that, for the weighted system [8: 5, 3, 1,
1, 1],BPI1 = 9/19. The curious fact is
that, if the first player cedes 1 vote to the second player, such that the
weighted system becomes [8: 4, 4, 1, 1, 1], the voting power
of the first player grows. Indeed, the index BPI1 becomes
1/2 > 9/19. On the other hand, when the second player cedes a
vote to the third player, the real loser is the first player. The system
becomes [8: 5, 2, 2, 1, 1], and BPI1 drops to
10/22 <9/19.
Fair Division
Each of the players that participate in the division of goods has a
value system that tags any piece or part of the goods. A division is fair
if each of the players thinks his portion constitutes at least
1/Nth (where N is the number of players) of the total.
The problem may seem difficult, but there are several working algorithms
that apply in different situations. Not only it is possible to satisfy
everyone's idea of fairness, in many cases a tangible part of the goods
will be left over.
The method of markers applies in situations where the goods to
be divided comprise a large number of small indivisible items that could be
arranged in a line or the case where the goods naturally form a linear like
entity, e. g., a sea front strip of land.
Each of the players, unbeknownst to the others, places (N-1) markers
that divide the goods into N parts of equal (in his private estimation)
value. The markers are then combined on a single diagram. The algorithm
scans the goods left to right till it meets the leftmost of the first
markers. The owner of that marker receives the stretch from the beginning
to the marker. By construction, this is of course, in his view, a fair
part. The algorithm than scans for the leftmost of the second markers. The
owner of that marker receives the stretch between his first and second
markers, i.e. the second of the parts he designated as fair. And so on. The
last fellow receives the stretch from his last marker to the end of the
goods. In the applet below, each player is assigned a color, whereas the
black pieces belong to no one.
Kruskal's Algorithm
A number of universities and federal agencies must be connected via the
internet. Throughput and reliability of the fiber optic connections are
such that there is no need in redundant lines: it's sufficient that for any
two of the organizations involved, there exists just one (perhaps indirect,
i. e., through other organizations) communication channel. On the other
hand, the costs of connections that depend on the distance between
organizations and the terrain to dig through, may differ from one
connection to another. A very practical question is what would be the least
expensive way to build up the connection network?
After the locations of all organizations have been set up on a map, it
became obvious that not all possible connections ought to be
considered. Some organizations are too distant from each other, others are
separated by naturally impassable territory. Still, among the feasible
connections there is significant redundancy. Which combination is least
expensive?
There is a surprisingly simple algorithm to answer that
question. Kruskal's algorithm (Joseph Kruskal, 1956) proceeds in steps:
On every step mark the cheapest unmarked edge.
See that the marked edges do not form circuits (to avoid redundancy.)
Repeat 1 and 2 while possible.
(Click on connections.)
Kruskal's algorithm exemplifies one approach to problem solving. When
there are too many conditions to be satisfied, it may make sense to
temporarily drop some conditions and first try to satisfy the remaining
ones. (See, for example, a classical
geometric
construction problem.) At the outset, the requirement of having a
connected network is dropped, and the algorithm only concerns with using
the cheapest connections. But eventually a combination of the latter turns
out to be connected.
As we see, the applicability of the selected topics does not imply their
direct usability to the student. (Although the
online
summary of the COMAP book makes an astonishing
claim: "Their text, For All Practical Purposes, tackles the
question: If there were a course designed to present concepts of math that
apply to today's consumers, what should it include?" As far as I can judge,
except for the last, 20th, chapter — Models in Economics
— and chapters on statistics, there is nothing in the book of
interest to the consumer of either today or tomorrow.)
Other topics covered include additional graph algorithms, the problem of
apportionment, scheduling, growth, symmetry
and statistics. Each of the topics contributes to the notion that
mathematics is an integral part of our society and culture. Most could be
introduced with no mathematics at all. Very few require familiarity with
algebraic concepts. Most of them could be dug deeper and reveal more of
interesting mathematics and its methods. (For example, A. Taylor's book, still very popular, concentrates on
only five topics, more or less equivalent to just one of the four parts of
the Excursions, but covered in much
greater depth and by far more rigorously.)
On the whole, both books offer a nice selection of (currently)
unconventional topics. And there is a good chance that every student may
like at least one of them. (We learn about one of the courses based on the
COMAP book from the
MAA's JOMA:
The goal of the course is to get every student excited about and
involved in at least one aspect of the mathematics that we do.)
But assume that the student did love one of the topics. What then? On
reading the Excursions, I got curious
about the Social Choice theory, which led to purchasing A. Taylor'sMathematics and Politics, and the
problem of apportionment, which directly led to Balinsiki and Young'sFair
Representation. (Both are gems in their genres. One as a textbook, the
other as a comprehensive exposition.) A student, however, concerned over
fulfillment of the graduation requirements, would not have time to even
contemplate deviating from the course material. But what if there were
time? What if the student could also get credit for following his heart?
Would not then it be nice to make available to the student some material on
the level, of, say, Taylor's book. On the other hand,
I can imagine a student in one of Taylor's classes who would rather prefer
the less sophisticated chapters from the Excursions or the COMAP
book. After all, not all students are the same.
In the introduction to chapter 19, Logic and Modeling, one of the two
chapters added in the 5th edition, the authors write:
In the preface to the first edition of For All Practical
Purposes, we find the following sentence:
[This book] represents our efforts to bring the excitement of contemporary
mathematical thinking to the nonspecialist, as well as help him or her
develop the capacity to engage in logical thinking and to read
critically the technical information with which our contemporary
society abounds.
In part, For All Practical Purposes has met this challenge of
developing the capacity to think logically by illustrating how mathematical
models can be used to analyze real-world problems. But isn't this challenge
itself a real-world problem? If we want to understand what "critical
thinking" is, perhaps we can do so by constructing a mathematical model
that we can analyze.
Let's apply a similar reasoning to that final course of a liberal arts
student. We see students are being taught to make choices, fairly divide
the load and schedule jobs. Their developing capacity to think logically
can be used to analyze real-world problems. But is not selection of topics
into a course, their depth and rigor of exposition a real-world problem?
Thompson Learning provides
instructors with tools for tailoring courses to their tastes by mixing
chapters from multiple titles and by adding new material. By extension,
could not the students be permitted to create their own course they would
have a better chance of enjoying? I mean just this once, in this final
semester of their last stand vis-à-vis mathematics. You know, the
technology is out there.
The idea may not be as frivolous as it sounds. I see the topics set up
on a virtual network where connections represent a varying degree of rigor
or depth, historical background or commonality of method, relevance of
subjects, alternative approach, theory and applications. Topics are framed
into study units with practice problems and online selftests, passing which
students gain access to further topic selections. From time to time
students are required to write reports that reflect on their progress. In
class, students seek the instructor's guidance and share their ideas and
recommendations about the topics. An important graduation requirement is
the number of topics mastered. Credit is given for the student's
demonstrated ability to follow the connections and for the number of topics
mastered in depth. It's all very doable. And the opportunity is of the
once-in-a-life-time significance.
To sum up, books like Excursions in Modern
Mathematics and For All Practical
Purposes offer an excellent selection of topics. But selection of
topics and their depth is dictatorial. In that final math course of the
liberal arts graduation requirement, I think, students may be entrusted
with making a few choices of their own. Some of the students, for example,
may have a taste for recreational mathematics. | 677.169 | 1 |
This 8-day course continues the sequence from the Making Math Real Overview, 4 Operations & The 400 Math Facts, and Fractions, Decimals & Advanced Place Value courses, and provides the essential development for meeting the challenges of transitioning students from elementary math to algebra.
The cognitive demands of algebra require a strong and comprehensive developmental foundation including recognizing and extending patterns, generalizing, sequential processing, and especially, detail analysis. The specific outcome of a successful pre-algebra experience is the establishment and full integration of algebraic law that defines and supports all algebraic processes of simplifying and solving. The most crucial component of successful instruction and learning is to include all of the incremental steps in every algebraic development. Therefore, course emphasis is on the systematic incrementation and methods of instruction that address the development, refinement, and integration of students' sensory-cognitive abilities with the application and retention of algebraic problem solving and skills.
Topics include units on the four operations with integers and rational numbers, probability, number theory, ratio, proportion and percent, solving equations, and linear graphing. This course is designed for educational therapists, special educators, elementary and secondary classroom teachers, and college professors. Parents and those who consider themselves non-math majors are especially encouraged to enroll. Prior knowledge of algebra is not required.
These techniques are designed to reach the full diversity of learning styles. Extensive color-coding is a critical element of the program. Please bring 4 colored ball point pens or pencils in blue, green, red and black.
NEXT OFFERING:Pre-Algebra will return to Making Math Real's Calendar in the Spring of 2014.
Cost of the 8-day Pre-Algebra Course: $994 for tuition and reader, paid to Making Math Real Institute; $360 for optional 4 semester UC Extension academic units, paid to UC Regents on the first day of class. | 677.169 | 1 |
Algebra - 2nd edition
Summary: Algebra, Second Edition, by Michael Artin, discusses concrete topics of algebra in greater detail than most textbooks, preparing readers for the more abstract concepts. This book covers all of the topics that are important to the average mathematician, and are covered in the typical course. Linear algebra is tightly integrated throughout | 677.169 | 1 |
Search Course Communities:
Course Communities
Lesson 31: Logarithms
Course Topic(s):
Developmental Math | Logarithms
The lesson begins with an application problem to motivate the necessity and use of a logarithm. The formal definition linking logs and exponents is then introduced. Exercises in writing exponential equations as logarithms follows before a calculator based method for approximating logarithmic values is discussed. The common log, i.e. logs of base (10), is introduced and a procedure for solving common log equations with a calculator is presented, along with various caveats about proper syntax for the calculator. The lesson concludes with exponential modeling problems where logs may be employed to find the desired exponent. | 677.169 | 1 |
Matrix of a Linear Map
In this lesson our instructor talks about matrix of a linear map. First, he discusses a helpful theorem and procedure for computing to matrix. Then he talks about property of matrix of a linear map. He ends the lesson with solutions to three complete example problems.
This content requires Javascript to be available and enabled in your browser.
Matrix of a Linear Map introduces concepts early in a familiar, concrete real number setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible. | 677.169 | 1 |
Are calculus and real analysis the same thing? They are written in greek. I was wrong , the total pages are 2800 (2 theory and some problems and examples and 2 other only problems.) It uses literature from apostol,ayoub,birkhoff,comtet,ciang and lots of other[80 total].But they are extreemly hard to read. Even the most difficult textbook for calculus is easy compared to them.And they are given at engineering school | 677.169 | 1 |
study was performed using a convenience sample of 90 students at a northeastern community college to determine gender differences of math anxiety and its effect on math avoidance. Four sections of an introductory English class were given aDuring the last decade, new technologies created a deluge of potential drug targets. Sifting through thousands of potential drug targets is a major industry bottleneck. Pharmaceutical companies can save billions of dollars by identifying most...
Each year thousands of students are tracked into mathematics classes. In these particular classes, students may struggle or find their mathematics skills less academically able than their classmates and give up on the tasks that are introduced to | 677.169 | 1 |
Peer Review
Ratings
Overall Rating:
This site is an interactive learning object that utilizes the GeoGebra tool (see to investigate lines and their equations. It contains three interactive windows where the student can move points and pieces of a line construction to see the effect on the line and its equation.
Learning Goals:
To understand the relationship between the graph of a line and its equation.
Target Student Population:
Beginning algebra students.
Prerequisite Knowledge or Skills:
Knowledge of the coordinate plane and equations and their coefficients.
Type of Material:
Simulation
Recommended Uses:
An instructor can use this to present lines and equations or can assign activities for students to work on.
Technical Requirements:
JAVA enabled browser
Evaluation and Observation
Content Quality
Rating:
Strengths:
This learning object contains every aspect of a line and its equation. As a student moves a point or other piece of a line, the equation dynamically changes. For the first window, the slope and y-intercept is shown both in the equation as the coefficients and alone. The student has the ability to change the window, the fixed point, the slope and the y-intercept. For the second window, with a given fixed point, the student can change the slope and watch the effect of everything else. For the third window, with the slope fixed the y-intercept can be changed or with the y-intercept fixed, the slope can be changed. There is sound use of color coding throughout.
Concerns:
There is too much information given on each screen. A beginning algebra student will get lost in the details and will lose the main point.
The explanation of the first window does not match what the first window is all about. Two links in the bottom of the page point to non-existing locations.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
For the tactile learner, this can be and effective exploration tool. An instructor can create a set of questions that guide the student through the tool and through learning how the equation of a line is related to the graph of the line.
Concerns:
The beginning algebra student is likely to get turned of due to the number of technical displays that are given. For example there is use of delta x over delta y for the slope, which is notation that this population has not seen before. Also the equation:
LPtLsp(x) = m(x – P1) + P2
is not something beginning algebra students can comprehend.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The second and third activities are accompanied with explanations that will let the student know what can be done. The slider is simple to use and the dragging the point is also easy.
Concerns:
Since the explanation of the first activity does not match the activity, a student will get very confused about what to do.
The applet windows do not work in Slimbrowser. Two dead links in the bottom of the page create navigation problems. | 677.169 | 1 |
Who are the Math Tutors?
We are primarily students like yourself with a little more experience in math. Some of us started with Math 054 or 055 and slowly made our way to calculus, so we know what you are going through. If you prefer working with an "expert," we have Educational Technicians who have already acquired their degrees in math or sciences.
Why go to the LC for math help?
If you are having trouble understanding what is going on in your math class or cannot finish your homework, you can come for help. Helping students in distress is indeed one of our main functions, yet it would be wrong to think that having "trouble" is the only reason to come see us. Students come for everything from a little moral support to sharing insights to discussing the nature of mathematics.
What are the Tutors likely to do for you?
We will try to make the math you are doing more comprehensible. This might include working on problems with you, explaining a concept, or simply letting you know you are on the right track. A simple statement of our philosophy might be that we help you help yourself. Yes, we know how trite that sounds, but it does underscore the idea that we are a resource to aid in your understanding, not a substitute for understanding.
Will I pass my math class if I come to the Learning Center?
Coming to the Learning Center will almost certainly increase your understanding of math, which is directly related to passing the course. But that alone will not get you through--attending lectures, doing your homework, and passing exams are important too. The more you do to try and better understand the mathematics you are learning, the better you will do in your math courses.
What other services do you provide?
A grant from the Alaska State Library provides Alaskan students with free access to live one-on-one online help with assignments, papers and exam preparation in math, science, social studies and writing. Visit tutor.com via the Statewide Library Electronic Doorway on the web any day of the week from 1 pm until 12 am.
There are periodic workshops offered during the semester that range from course specific problem solving sessions to how to effectively use your calculator. During these workshops you can review course material in a group setting, moderated and assisted by a tutor. We also have a collection of math exams for review online, which will help you prepare for your tests. Textbooks and calculators are available for use at the Learning Center, and some textbooks can be checked out.
If there is a service you wish we offered, come tell us about it or call us at 796-6348. We are always open to suggestions. | 677.169 | 1 |
Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Conics; Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more. For individuals... MORE with an interest in learning algebra as it applies to their everyday lives. This latest edition of the successful Contemporary Sullivan Series features more modeling and real world data throughout the text. The usage of the Graphing Calculator remains optional, as do the new Internet Chapter Openings. Newly expanded website is more usable than ever. | 677.169 | 1 |
Journal of Applied & Computational Mathematics under the Open Access category allows free, faster and unconstrained access to the scientific research and their results. JACM encourages and also depends upon data interpretation, efforts and analysis of mathematical data. The contents of the journal are freely accessible through internet and promptly available to share the innovations of researchers and scholars for the progress of Applied and Computational Mathematics.
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods. | 677.169 | 1 |
M115A-MidtermOneAdvice
Course: MATH 172a, Fall 2012 School: UCLA Rating:
Word Count: 405
Document Preview solve a problem if you do not have the proper tools.
3. You should understand all of the proofs given in class and be able to recreate them on the midterm.
This does not mean you should go out and memorize all of the proofs. You should go and understand
the main idea, trick, and technique of each proof. Most techniques can be repeated or are useful in
other problems.
4. If you are asked to prove something from lecture, you should try to give the proof done in lecture and
cannot use material after the proof given in lecture. If you are asked to prove something new, anything
from class is fair game.
5. Manage your time during the test. When proving result a on the midterm, you should include as much
detail as you deem necessary. If you are unsure whether to go into more detail, leave it and come back
to the problem if you have time.
6. You should try to have an intuition about how to approach problems. This is the most dicult thing
to do in this course and, if you can do this, you should most denitely succeed. When trying to solve
a problem, you should think about what you are given and what the givens imply, think about what
you are trying to do and how you could do it, think about what techniques we have and which might
be useful, and think about which tools (i.e. results and theorems) you have and how they might be
applied.
7. Do not give up on a problem. Most problems in this course do not involve an absurdly dicult trick
and can be solved by reasoning using the denitions and results done in class.
8. Get a good night sleep the night before the midterm. If you are too tired to think because you crammed
all night, the cramming with not be eective and you will not be able to think criticallyCommon Notation and Symbols in Linear AlgebraPaul SkoufranisSeptember 20, 2011The following is an incomplete list of mathematical notation and symbols that may be used MATH 115A.Shorthand Notation:for allthere existstherefores.t.such that=impli
MATH 115A - Practice Final ExamPaul SkoufranisNovember 19, 2011Instructions:This is a practice exam for the nal examination of MATH 115A that would be similar to the nalexamination I would give if I were teaching the course. This test may or may not
MATH 115A - Practice Midterm OnePaul SkoufranisOctober 9, 2011Instructions:This is a practice exam for the rst midterm of MATH 115A that would be similar to a midterm I wouldgive if I were teaching the course. This test may or may not be an accurate
MATH 115A - MATH 33A Review QuestionsPaul SkoufranisSeptember 13, 2011Instructions:This documents contains a series of questions designed to remind students of the material discussed inMATH 33A. It is recommended that students work through these ques
University of California, Los AngelesMidterm Examination 2November 9, 2011Mathematics 115A Section 5SOLUTIONS1. (6 points) Each part is worth 3 points. For each of the following statements, prove or nd a counterexample.(a) Let V and W be nite dimens
Problem Set 1Math 115A/5 Fall 2011Due: Friday, September 30Please note a typo was corrected in problem 3.Read Chapter 2 of the supplemental material in the text.Problem 1Consider the set Mnn (R) of all n n matrices with real entries with the operati
Problem Set 6Math 115A/5 Fall 2011Due: Friday, November 18Problem 1 (4.4.6)Prove that if M Mnn (F ) can be written in the formM=AB0C,where A and C are square matrices, then det(M ) = det(A) det(C ).Problem 2 (5.1.3)For each of the following mat
Problem Set 7Math 115A/5 Fall 2011Due: Monday, November 28Please note a typo was corrected in problem 2.Problem 1 (5.2.3)For each of the following linear operators T on a vector space V , test T for diagonalizability,and if T is diagonalizable, nd a
Problem Set 8Math 115A/5 Fall 2011Due: Friday, December 2Problem 1 (6.2.2)In each part, apply the Gram-Schmidt process to the given subset S of the inner productspace V to obtain an orthogonal basis for span(S ). Then normalize the vectors in the bas
Section 1.3, exercise 12Prove that the upper triangular matrices form a subspace of Mmn (F).Proof. Let W be the set of upper triangular matrices in the vector space Mmn (F). SinceMmn (F) is a vector space, it contains a zero vector and this vector is t
Life Science 15: Concepts and IssuesLecture 2: Intro to Life Science/Science as a Religion1/12/12I. Age of ScienceII. Who am I?III. Scientific ThinkingScientific MethodOrganizedEmpiricalMethodicalStructured way of finding info about observable e
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Life Science Final Review:1. Happiness: why is rate/direction of change more important than absolutelevel? How does this relate to material acquisitions? The emotion of happiness is a tool our genes use to cause u to behavein ways that will benefit th
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Strategic ManagementDoes Strategy Matter? 2005 Robert H. Smith School of BusinessUniversity of MarylandDifferences in Industry ProfitabilityThe average return on invested capital varies markedly fromindustry to industry.Between 1992 and 2006, for e | 677.169 | 1 |
To introduce students
to a sophisticated mathematical subject where elements of different
branches of mathematics are brought together for the purpose of solving an
important classical problem.
Intended Learning Outcomes:
On successful
completion of the course students will:
Have deepened their knowledge about
fields
Have acquired sound understanding of the
Galois correspondence between intermediate fields and subgroups of the
Galois group
Be able to compute the Galois correspondence
in a number of simple examples
Appreciate the insolubility of polynomial
equations by radicals.
Pre-requisites:
212,252,312 (ex-UMIST) MT2262, UM3121 (ex-VUM)
Dependent Courses:
None
Course
Description:
Galois theory is one of
the most spectacular mathematical theories. It gives a beautiful
connection of the theory of polynomial equations and group theory. In
fact, many fundamental notions of group theory originated in the work of
Galois. For example, why some groups are called "soluble" ? Because they
correspond to the equations which can be solved ! (Meaning by a solution
some formula based on the coefficients and involving algebraic operations
and extracting roots of various degrees.) Galois theory explains why we
can solve quadratic, cubic and quartic equations, but no similar formulae
exist for equations of degree greater than 4. It also gives complete
answer to ancient questions such as divising of a circle into n equal arcs
using ruler and compasses. In modern exposition, Galois theory deals with
"field extensions", and the central topic is the "Galois correspondence"
between extensions and groups. Galois theory is a role model for
mathematical theories dealing with "solubility" of a wide range of
problems. | 677.169 | 1 |
It depends what course youre doing, economics at research level has high maths requirements. Finance is also quite high, although slightly less so unless you are doing something like asset pricing. Other b-school degrees shouldnt have especially high requirements.
(Original post by career)
Well, it is hard to say if that knowledge is really required or if it will be reviewed anyway. That being said, in my experience, lectures are much more enjoyable when you already have some knowledge of what is being taught so that you can understand not only after you fill in the gaps but also during the actual lectures. I assumed the "reading list" is given to achieve this goal.
Thanks for the replies guys. Also not sure how how many textbooks to buy, they recommend 3 per module but I was wondering if I could get away with buying 1 and use the library for the bits of the course my books won't cover.
(Original post by Ghost6)This is wrong for two reasons. First, those are introductory (graduate level) lecture notes so they arent going to be too advanced, theoretical economics at research level obviously requires a deeper grasp of mathematics (here are two papers from the last issue of Econometrica for instance: 12, scroll down to the Appendices). The amount of math in non-theoretical and empirical papers is of course a lot lower, so this is very subfield dependent. Second, as in physics, the point of the courses isnt the math as such, but learning how its used. The focus of those courses is economic modelling, and they assume that you are somewhat familiar with the math used. If you are not comfortable enough with the mathematical background, and need to learn it as you go along, then it will be harder to learn about the economic part since you are basically learning two things at once. | 677.169 | 1 |
SIMMS IM LEVEL I - Research Project Help - T. DeBuff
High School freshman-level integrated mathematics research projects, to be used with the Systemic Initiative for Montana Mathematics and Science Integrated Math (SIMMS IM), curriculum Level I. View project descriptions and find links to sites that will
...more>>
Society of Actuaries
Actuaries are professionals trained in mathematics, statistics, and economic techniques that allow them to put a financial value on future events. This skill is of great value to insurance companies, investment firms, employee benefits consulting firms,
...more>>
Softmath - Neven Jurkovic
Developers of Algebrator, an automated tutor based on Maxima CAS that provides step-by-step solutions to algebra, trigonometry, and statistics problems, and exports answers to MathML. Demo and purchase Algebrator; use Softmath's free online software to
...more>>
Software for mathematics education - Piet van Blokland
Software for mathematical education that draws on David Tall's philosophy of teaching: use Graphic Calculus to visualize, explore, and conceptualize the graph of a linear function; analyze the data and simulations included with VUStat to learn statistics
...more>>
So Much Data - William D. May
Based on the book So Much Data, So Little Math, tools for learning to do simple data analysis on data sets. Features the online calculation tools "Easy Correlation Calculations" and "Easy Trend Prediction," with explanations, as well as an example of
...more>>
Songs for Teaching - S. Ruth Harris, LLC
Lyrics to music that teaches or reinforces math facts and concepts, including addition, subtraction, multiplication, division, algebra, and geometry. Some songs have links to sound files as well.
...more>>
The SPSS Decision Maker - Maurits Kaptein
This is a website that guides you through a number of steps to select a statistical technique. Developed for those who do know the basic concepts of research statistics and experimental design but need help determining the final test.
...more>>
Standard Deviation, Part 1 - Barbara Christopher
Can the standard deviation pick the most consistent set of numbers? or Which city's temperatures vary the least, San Diego or San Francisco? An interactive project in which students use the Internet to find statistical data for the mean, standard deviation,
...more>>
Standard Deviation, Part 2 - Barbara Christopher
Do cities closer to the ocean have more consistent temperatures? A followup to Standard Deviation, Part 1. Students use the Internet to gather temperature data from 3 cities; calculate the standard deviation and percentage error of the gathered temperatures;
...more>>
StatApplet - Marcus Kazmierczak
A simple statistics program and a short outline of the underlying mathematics. The statistics applet calculates the sample mean and sample standard deviation, and constructs a 95 percent confidence interval for data values entered.
...more>>
Statbag - Worth Swearingen
A blog repository for statistics educators: "... each teacher should have a bag of tricks. Teachers spend years developing their own favorites. While acknowledging that experience is the best teacher, one purpose of this site is to help teachers develop
...more>>
Statistical Assessment Service (STATS)
STATS is a non-profit, non-partisan resource on the use and abuse of science and statistics in the media. Its goals are to correct scientific misinformation in the media and in public policy resulting from bad science, politics, or a simple lack of information
...more>>
Statistical Consultants Ltd - Dion Walker
Data analytics and other consulting services. See, in particular, the New Zealand company's blog, which dates back to 2010 with posts such as "Battle of Britain Casualty Data," "Gretl: A free alternative to EViews," "Life expectancy at birth versus GDP
...more>>
Statistical Rules of Thumb - Gerald van Belle
This companion website to Statistical Rules of Thumb, published by John Wiley & Sons, Inc., offers free PDFs of chapter two ("Sample Size") and more than a dozen "monthly rules of thumb," such as "Use Text for a Few Numbers, Tables for Many Numbers,
...more>> | 677.169 | 1 |
I'm just wondering if someone can give me a few pointers here so that I can understand the concepts behind problem solver-maths. I find solving problems really tough. I work in the evening and thus have no time left to take extra classes. Can you guys suggest any online resource that can help me with this subject?
Hey. I imagine I can help. Can you elucidate some more on what your troubles are? What specifically are your troubles with problem solver-maths? Getting a good teacher would have been the greatest thing. But do not worry. I think there is a way out. I have come across a number of math programs. I have tried them out myself. They are pretty smart and good quality. These might just be what you need. They also do not cost a lot. I think what would suit you just fine is Algebra Buster. Why not try this out? It could be just be the answer for your problems.
I have used quite a lot of programs to grapple with my difficulties with trinomials, least common denominator and system of equations. Of them, my experience with Algebra Buster has been the best. All I needed to do was to just key in the problem. Punch the solve key. The answer showed up almost instantaneously with an easy to understand steps indicating how to reach the answer. It was simply too easy. Since then I have depended on this Algebra Buster for my difficulties with Algebra 2, Algebra 2 and Intermediate algebra. I would highly recommend you to try out Algebra Buster. | 677.169 | 1 |
Intermediate Algebra Concepts and Applications
9780201708486
0201708485
Summary: The Sixth Edition of Intermediate Algebra: Concepts and Applications continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen hardback series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. With this revi...sion, the authors have maintained all the hallmark features that have made this series so successful, including its five-step problem-solving process, student-oriented writing style, real-data applications, and wide variety of exercises. Among the features added or revised are new Aha! exercises that encourage students to think before jumping in to solve a problem, 20% new and added real-data applications, and 50% more new Skill Maintenance Exercises. This series not only provides students with the tools necessary to learn and understand math, but also provides them with insights into how math works in the world around them.[read more] | 677.169 | 1 |
If your work involves math that can't easily be done in a spreadsheet, MathCad 6.0 from MathSoft (617 577-1017) may be the tool for you. Both the Standard ($129) and programmable Plus ($349) versions let you do complicated numerical or symbolic calculations on a sort of computerized scratch pad. Results can then be pasted into other Windows applications. While less sophisticated than computer algebra systems such as Wolfram Research's Mathematica, MathCad is much easier to learn and use.BY STEPHEN H. WILDSTROM | 677.169 | 1 |
Math Department
Department Chair: Mrs. Joyce Heller
Our primary goal in teaching mathematics is to help students learn the art of reasoning and problem solving, skills that will aid them throughout their educational and professional careers. The ability to evaluate data, turn it into information, and reach timely and pertinent decisions is crucial in achieving success in any field of endeavor. The Ma'ayanot mathematics program helps students learn how to think logically and creatively, perform mathematical calculations both manually and with the use of graphing calculators, and master mathematical functions and concepts.
COURSE OF STUDY:
Entering students take a placement examination in mathematics regardless of their previous mathematical background in elementary school. A multi-track math program allows Ma'ayanot to serve the individual needs of all students. All students are required to take three years of math in high school and they are strongly encouraged to take a fourth year as an elective. PSAT and SAT preparation is incorporated into the curriculum. All students take Algebra I, Algebra II/Trigonometry, and Geometry. Pre-Calculus and AP Calculus AB or BC are offered in the junior and senior years. Students with strong aptitude and interest in mathematics are encouraged to participate in extracurricular math programs, competitions, and research projects in advanced mathematics.
All math courses in the high school program require students to have a TI-83 graphing calculator to be used as a tool for learning and doing mathematics.
Tracking: All mandatory Math classes are tracked (9th - 11th grade), but all students can choose to take Math electives in the senior year. Math classes are tracked independently of other disciplines.
ALGEBRA I
This course is designed to help student understand the basic concepts of elementary algebra and acquire important manipulative algebraic skills. The syllabus has been developed on a level appropriate to the mathematical maturity and sophistication of all students. Enrichment is provided throughout for those students capable of proceeding at a faster pace.
The basic concepts of this course are carefully developed with the use of simple language and symbolism. Explanations and problems lead to the statement of general principles and procedures. Model problems and solutions are detailed in class, helping students to apply these principles independently. Daily exercises cover almost every type of difficulty and tests cover students' understanding of basic concepts as well as mastery of manipulative skills.
GEOMETRY
The geometry syllabus is written to provide appropriate materials to help both teacher and student achieve the following objectives of a modern geometry course.
To develop an understanding of geometric relationships in a plane and in space.
To develop an understanding of the meaning and nature of proof.
To teach the method of deductive proof in both mathematical and non-mathematical situations.
To develop the ability to think creatively and critically in both mathematical and non-mathematical situations.
To integrate geometry with arithmetic, algebra and numerical trigonometry.
ALGEBRA II/TRIGONOMETRY
The major objective of the Algebra II/Trigonometry syllabus is the integration of intermediate algebra, plane trigonometry and coordinate geometry. To achieve this goal, trigonometric content is presented at an early stage and carried along simultaneously with work in algebra. Such a presentation is more effective than one in which the teaching of trigonometry is deferred until intermediate algebra has been completed.
Proper integration of algebra and trigonometry enables a student to make a smooth transition from working with algebraic expressions and equalities to working with trigonometric expressions and equalities. The comprehensive presentation of coordinate geometry also serves as an effective means of integrating intermediate algebra and plane trigonometry. This is accomplished by emphasizing the fundamental ideas underlying the graphs of linear functions, quadratic functions and trigonometric functions.
PRE-CALCULUS
Pre-calculus can serve as preparation for calculus or as a fourth year to the normal curriculum. Topics covered prepare students not only for calculus but for all future college level mathematics courses. During the year, students cover diverse topics, such as examining relations and functions, mathematical induction, polynomial equations, linear programming, conic sections, complex numbers, polar coordinates, sequences and series. Students make extensive use of the graphing calculator to develop mathematical models for real world applications.
Pre-calculus is a required course for students who entered high school with accelerated mathematics and must complete a third year of high school mathematics at Ma'ayanot. It is a prerequisite for students wishing to take calculus either at Ma'ayanot or in college. It is an elective for seniors who would like to explore mathematical concepts in greater depth or expect to need some mathematics in their college studies.
ADVANCED PLACEMENT CALCULUS
Calculus AB is primarily concerned with developing the students' understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations are important.
Technology is used regularly by students and teachers to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results.
Through the use of unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, the course becomes a cohesive whole.
The course represents college level mathematics for which most colleges grant advanced placement credit according to the results of an Advanced Placement Examination. The AB course enables a student to obtain credit for the first semester of college calculus.
Calculus BC represents college level mathematics, for which a student may qualify for two semesters of college credit, based upon the results of the Advanced Placement Examination.
ADVANCED PLACEMENT STATISTICS
The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:
Students who successfully complete the course and examination may receive credit and/or advanced placement for a one-semester introductory college statistics course.
REAL WORLD FINANCE
This course was designed for seniors who are interested in a pragmatic finance course. The course explores all aspects of investments, including savings accounts, CDs, stocks, bonds, mutual funds, planning for retirement, alternative investment vehicles, and creating a balanced investment portfolio. Forms of credit such as credit cards, student loans, mortgages, and car loans are studied, in addition to life, health, car, homeowners, and ancillary insurance. Planning a household budget, balancing a checkbook, online banking and bill paying, and income taxes round out the course. | 677.169 | 1 |
Prerequisite: Placement through the assessment process or MATH 075 or MATH 075SP or equivalent
Note: In this computer-assisted self-paced class, students study from the textbook, online, during weekly face-to-face meetings and take a combination of online and in-class exams. The online labs require computer access and may be completed either on or off campus. The face-to-face meetings will be held in the DVC Math Lab (for lab schedule go to for Pleasant Hill or for SRC). Students are encouraged to complete MATH 110SP in one semester, or take up to 2 semesters. MATH 110SP is equivalent to MATH 110; students who have completed MATH 110 will not receive credit for MATH 110SP.
This course is a computer-assisted self-paced equivalent to MATH 110. The topics include linear equations and inequalities, development and use of formulas, algebraic expressions, systems of equations, operations on polynomials, factoring, graphs, and an introduction to quadratic equations. | 677.169 | 1 |
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This article discusses about the latest version of openSIS, one of the most popular student information system round the globe. Recently OS4ED launched openSIS ver5.2, the developers of the product demands that this will be better, faster and more secured compared to previous versions.
A System of equations is basically a collection of Linear Equations and includes the same Set of the variables in each and every equation of the system. This system of equations is also known as the Linear System.
A number which is divided by itself and by 1 is called a prime number. Prime number can also be defined as the Odd Numbers which are not divided by any odd number except 1 and itself. Prime numbers are mainly 1, 2, 3, 5, 7, and 11 and so on.
Numbers starting with 1, 2, 3, 4.…… are called Natural Numbers. Natural numbers are denoted by 'N'. These numbers are put into different groups. The group may be of Even Numbers, odd numbers, prime numbers or even composite numbers.
When we deal with algebra, we mainly focus on equations and expression. These two terms can be defined as the heart of the algebra, as whenever we solve any problem we have to solve different equations.
The elements are subdivided into molecules which further divided into atoms. The atoms for long considered to be indivisible but with the discovery of the sub atomic particle, like electrons and protons, it was understood that there were more smallest and fundamental particles then the atom. | 677.169 | 1 |
MATH 500: Fundamentals of Mathematics
This course provides students with a thorough foundation in the topics of whole numbers, fractions, decimals, ratios and proportions, percents, geometric figures and measurement. (Offered in lab and lecture formats.) Lecture: 3 hours
Credits:0
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Thanks, enjoy the course! Come back and let us know how you like it by writing a review. | 677.169 | 1 |
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Discrete Mathematics Study Materials
Discrete Mathematics
Lectures Ppt
Click on the blue colored links to download the lectures.
Course Description
This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.
Lecture 1:What kinds of problems are solved in discrete math?What are proofs? Examples of proofs by contradiction, and proofs by induction:Triangle numbers, irrational numbers, and prime numbers. (3.1-3.2) | 677.169 | 1 |
Mathematics for Elementary Teachers
9780470105832
ISBN:
0470105836
Edition: 8 Pub Date: 2008 Publisher: Wiley, John & Sons, Incorporated
Summary: Now in its eighth edition, this book masterfully integrates skills, concepts, and activities to motivate learning. It emphasizes the relevance of mathematics to help readers learn the importance of the information being covered [more | 677.169 | 1 |
A rigorous, concise development of the concepts of modern matrix structural analysis, with particular emphasis on the techniques and methods that form the basis of the finite element method. All relevant concepts are presented in the context of two-dimensional (planar) structures composed of bar (truss) and beam (frame) elements, together with simple discrete axial, shear and moment resisting spring elements. The book requires only some basic knowledge of matrix algebra and fundamentals of strength of materials. | 677.169 | 1 |
Math
Math is an important subject in the context of high school education. If the students are able to succeed in this subject then the overall success in the high school curriculum would be relatively easy. Perhaps, the subject is more important in the long term running. Having a good concept in the math curriculum of high school standards would prepare the learners well for college and career. Education Services Aug offers online math solutions that are very engaging and interesting, which enables the high school learners to succeed in math whether it be in algebra or calculus. Our math curriculum is aligned to the standard that is followed in the courses recognized in the United States.
The basic structure of the coursework is to motivate the students and generate interests in the subject. We encourage the students in various problem solving standards. It is important to read the problems and understand them. There should be perseverance on their part in solving these problems. The learners should be able to reason conceptually and express them quantitatively. Arguments against each problem should be viable and made from the understanding of the concepts. It is also healthy to be critical of other's arguments as well. Our interactive learning process provides the students with modeling and visualizing techniques for mathematics. The learners are familiarized with the use of appropriate tools at strategic moments. Education Services Aug secondary math solutions instill in the learners the importance of attending to precision. The students are taught to look for and use the structures in the problems and also to express regularity in reasoning again and again.
Our comprehensive and flexible online courses allow the students to learn at the pace that is best suited to them. We offer an extensive coverage of the course structure. Education Services Aug math coursework includes Advanced Calculus, Algebra, Consumer Mathematics, Pre-Algebra, Pre-Calculus and Geometry. Apart from that we also offer many skill based packages like Data Skills, Foundation Mathematics, Math Problem solving and Trigonometry skills packages. Based on this programs students are taught to think independently and intuitively. The aim is to make math an easy subject so that students can relate to it and not feel threatened by it. Education Services Aug also provides assessments in order to have an idea about the gaps in the understanding of the concepts of each learner which would benefit the educators to channelize them in the correct path to success. | 677.169 | 1 |
Next year I will be starting a degree in game programming. I have been told to brush up on my math. Which chapters of math text books should I read over?
The course is described as:
The Qantm Bachelor of Interactive
Entertainment (with a Major in Games
Programming) focuses on specific areas which
are critical to developing knowledge
and skills in games programming for
interactive entertainment. Students of
the Major in Games Programming learn
C++ programming, work with
mathematical functions and artificial
intelligence to design and program
games for a variety of devices. To
broaden students' perspectives on the
games development pipeline, the major
includes specialised courses in script
writing, character development, games
design, agent systems and 2D and 3D
animation.
While, the topics are similar, there a differences, the inclusion of a course description allows for more distinct answers relevant to my unique situation. – fauxCoderOct 19 '09 at 1:09
@Ngu Soon Hui, this is not a duplicate of that question. I'd say that the other questions is potentially a subset of this one. For example, path finding requires knowledge of graph theory. – Bob CrossOct 19 '09 at 1:32
@cdiggins, why lambda calculus? This is a serious question: I don't understand how this would be useful to someone who was specifically writing games. – Bob CrossOct 19 '09 at 12:50
LC is useful to understand the underpinnings of functional programming. I think all programmers should know it. Then again, one can do what I did, and learn it after learning functional programming in practice. – cdigginsOct 20 '09 at 3:14
Having studied that course at Qantm a few years back ('06 graduate), I know approximately what you're in for ;)
All the maths you will need will be taught as part of the course - however it is done at a blazing pace, and if you miss any of the tutorials you will need to scramble and get your head around it yourself. I remember missing the class on collision detection, and boy was that painful.
All the answers given already are spot-on for the useful concepts for game math. One extra thing you might want to get on top of early is state machines (for AI).
Although this article's audience is someone who is preparing for an interview, I still believe the first section in this article (Math) gives you an idea of what you should know, or at least be comfortable with. | 677.169 | 1 |
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