text
stringlengths 6
976k
| token_count
float64 677
677
| cluster_id
int64 1
1
|
|---|---|---|
Learning basic mathematics is easy and engaging with this combined text/workbook! BASIC COLLEGE MATHEMATICS is infused with Pat McKeague's passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague's proven "EPAS" approach (Example, Practice Problem, Answer, and Solution) moves you through each new concept with ease while helping you break up problem solving into manageable steps. Real-world applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including a Digital Video Companion CD-ROM and access to Basic MathematicsNOW, a personalized online learning companion.
Want the streamlined approach to statistics? ESSENTIALS OF STATISTICS FOR BUSINESS AND ECONOMICS, ABBREVIATED EDITION explains updated statistical methods in simple ways. This Homework Edition isPat McKeague's eighth edition of INTEMEDIATE ALGEBRA is the book for the modern student like you. Like its predecessors, the eighth edition is clear, concise, and patient in explaining the concepts. ... | 677.169 | 1 |
Khan Academy Video Course: Calculus
Description
Welcome to calculus, the study of change. Through limits, functions, derivatives, integrals, and infinite series, calculus provides systems to examine change and make predictions based on what we can calculate. This course covers topics that you'd find in first and second-semester calculus courses at the college level, and serves as a gateway to advanced mathematical analysis. A solid understanding of pre-calculus is essential for success. Good luck!
Note that given the length of these lessons, you may want to adjust your settings to receive one or two lessons a week.
Opening Lines (Experimental)
Today's Calculus lesson (in video) from the Khan Academy is: Introduction to Limits: To view other Khan Academy videos, you can find them at their website here: Enjoy! P.S. Note that given the length of these lessons, you may want to adjust your settings to receive one or two lessons a ... | 677.169 | 1 |
Features: - Outcomes at the start of every chapter - A dynamic full colour design that clearly distinguishes theory, examples, exercises, and features - Carefully graded exercises with worked examples and solutions linked to each - Cartoons offering helpful hints - Working mathematically strands that are fully integrated. These also feature regularly in challenging sections designed as extension material which also contain interesting historical and real life context - A Chapter review to revise and consolidate learning in each chapter - Speed skills sections to revise and provide mental arithmetic skills - Problem solving application strategies with communication and reasoning through an inquiry approach - a comprehensive Diagnostic test providing a cumulative review of learning in all chapters, cross referenced to each exercise - Integrated technology activities - Literacy skills develop language skills relevant to each chapter - Fully linked icons to accompanying CD-ROM.
The student CD-ROM accompanying this textbook can be used at school or at home for further explanation and learning.
Each CD-ROM contains: - Interactive diagnostic text – perfect revision for all Stage 4 work. The regenerative nature of the program allows for an almost limitless number of varied tests of equal difficulty. This test can be used prior to commencing Stage 5 work. - Dynamic geometry activities using WinGeom and Cabri software for student investigations - Using technology with formatted Excel spreadsheets - Full textbook with links to the above.
A.Kalra and J. Stamell
Connections Maths is a comprehensive, full colour, 6-book series that meets all the requirements of the new Years 7–10 course. The series will engage, motivate and support students of all abilities. The page design, the vibrant use of colour, and the range of photos and cartoons make each page an interactive learning experience. Each textbook is accompanied by a student CD-ROM. | 677.169 | 1 |
Buy now
Detailed description * Highlights from the history of geometry are intertwined with explanations on how to read and write proofs. * This is the first book to present the works of Euclid and Hilbert in addition to other geometers in chronological order, all in an effort to show how the subject matter developed over time. * Hints and both partial and complete solutions are included at the end of the book as an aid for selected exercises. * An important contribution to the teaching of geometry, this book proves that learning to read and write proofs is a crucial aspect of the subject. * This book develops ideas with careful attention to logic and follows the development of the field through time. * An Instructor's Solutions Manual is available upon request. | 677.169 | 1 |
Exam duration:
Aid:
Evaluation:
Qualified Prerequisites:
General course objectives:
To provide the student with a solid framework for understanding and applying a number of geometric shapes and techniques as they are used in engineering and architectural design contexts as exemplified below.
For ship building engineers: Propeller geometries via deformations of standard profiles and the construction of ship hulls.
For architectural engineers: Classical geometric concepts and basic operations for shape design and form description in plane and space.
To apply 2x2 and 3x3 matrices and their properties to analyze simple geometric constructions in plane and space and thereby obtain and practice the essential understanding of coordinate transformation techniques.
To define and to calculate precise modifications of a given geometric object.
To apply computer experiments as an integrated part of the course for illustrations, learning, and calculations.
Learning objectives:
A student who has met the objectives of the course will be able to:
Calculate on a vectorial basis the area and volume
Apply matrix calculus to construct and and analyze deformations of basic objects and explain the induced change in area and volume
Find parametrizations of simple geometric objects in plane and space
Calculate and explain the notions of area and volume for parametrized objects
Apply simple parametrizations or other representations to construct triangulations of surfaces and domains in space and compare the respective areas and volumes
Apply basic kinematic concepts to analyse simple motions in the plane
Calculate and explain the notions of arclength and curvature for curves in the plane
Apply extrudition, offsetting, and projection to construct new geometric objects from old ones
Course literature:
Remarks:
The course provides a basic foundation for the understanding of the geometric operations which are applied in FEM modelling, machine element design, architectural engineering, and sculptural design | 677.169 | 1 |
Tags: wolfram.
Wolfram Mathematica 8.0 Windows | 926.5 MB What is Mathematica? Almost any job related to the calculation results, and that is what Mathematica is not-from building a web of hedge funds, - - download rapidshare appz megaupload fileserve mediafire warez li
What is Mathematica? Almost any job related to the calculation results, and that is what Mathematica is not-from building a web of hedge funds, trading or textbook publishers interactive technology to develop image recognition algorithm is embed - Free so
Mathematica 8 introduce free form input language-a completely new way to calculate. Enter plain English, the results are not immediately required syntax. It's a new entry point into the work - The home of warez rapidshare
What Is Mathematica? Almost any workflow involves computing results, and that's what Mathematica does—from building a hedge fund trading website or publishing interactive engineering textbooks to developing embedded image recognition algorithms or - The | 677.169 | 1 |
Chestnut Mountain Precalculus is built off a healthy curiosity for the world around us. These are concepts that when explained properly can prompt a further desire for learning in the future. Let's get the ball rolling.
...Physical | 677.169 | 1 |
Integral Calculus
It is not an exaggeration that the fort of Mathematics is Calculus and the most important part of it is Integral Calculus. It is quite a lot scoring and should be taken very seriously in the preparation of IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations. The Calculus is said to be complete only if you have mastered the topic of Integral Calculus.
Since the prerequisite to the preparation of Integral Calculus is the study of Differential Calculus, we can judge a student in Calculus by seeing his comfort level and proficiency in Integral Calculus. The importance of Integral Calculus is not just restricted to Mathematics but it is of profound importance in the major part of Physics and Physical Chemistry. The major portions of study of Integral Calculus include Indefinite Integral and Definite Integral and they are rightly termed as tools which are further used in its applications under the topics of Area. The topic of Area is the one which used the most in Physics and should be taken very seriously. The next topic of Differential Equations is also quite important. Since the syllabus do not demand differential equations of higher order so it is easy for the students to have proficiency in the subject.
It is true that most of the students fear from Integral calculus, but all the high rank holders in IIT JEE are always very comfortable in the topic. It is advised to do a practice in Integral Calculus at an early stage as it is one of the new topics which students study while preparing for IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations. | 677.169 | 1 |
Student Responsibilities:
One cannot benefit from or contribute to a class discussion or activity unless one is physically present (this a necessary condition, not a sufficient one). Attendance is required. Call me (796-3658) if you will not be in class. A valid excuse is necessary to miss class. Unexcused absences may lower your grade for the course.
Assigned readings of the texts and handouts need to be done if meaningful discussion can occur.
Your active participation makes the course go. Math is not a spectator sport. Assigned problems and textbook exercises are ways for you to develop problem solving skills and reflect on your learning. Do the problems when they are assigned.
Content
I. Logic and Proofs
A. Propositions and Connectives
B. Conditional and Biconditionals
C. Quantifiers
D. Basic Proof Methods I
E. Basic Proof Methods II
F. Proofs Involving Qunatifiers
II. Set Theory
A. Basic Concepts
B. Set Operations
C. Extended Operations and Indexing
D. Induction
III. Relations
A. Cartesian Products
B. Equivalence Relations
C. Renaming
D. Partitions
IV. Functions
A. Functions as Relations
B. Constructions
C. One-to-One, Onto Functions
V. Cardinality (if time permits)
A. Equivalent Sets
B. Infinite Sets
C. Countable Sets
Evaluation
I will use a 90 – 80 – 70 – 60 framework for grading. I will give you written assignments on Thursday and these will be due to the following Thursday. You may consult each other but the write-up is your responsibility. I suggest you go to separate rooms to write up your answers.
There will be three exams in class. I need to see what you can do all by yourself. The dates will be determined during the first week of class.
A Note to You
Mathematics can be an intellectual adventure, a powerful tool, and a creative experience Some of you may have had mathematics courses that were based on the transmission, or absorption, view of teaching and learning. In this view, students passively It is one way to make sense of the world.
Consequently, I have three goals when I teach. The first is to help you develop mathematical structures that are more complex, abstract, and powerful than the ones you currently possess so that you will be capable of solving a wide variety of meaningful problems. The second is to help you become autonomous and self- motivated Hopefully.
As
So
You may find this experience frustrating at times. Persevere! Eventually I hope you will own personally the mathematical ideas you once knew unthinkingly or only peripherally (and sometimes anxiously). I want you to become competent and confident using mathematical ideas and techniques.
In training a child to activity of thought, above all things we must beware of what I will call "inert ideas" - that is to say, ideas that are merely received into the mind without being utilized, or tested, or thrown into fresh combinations . . . Education with inert ideas is not only useless: it is, above all things, harmful. Except at rare intervals of intellectual ferment, education in the past has been radically infected with inert ideas . . . Let us now ask how in our system of education we are to guard against this mental dryrot. We enunciate two educational commandments, "Do not teach too many subjects," and again, "What you teach, teach thoroughly." . . . Let the main ideas which are introduced into a child's education be few and important, and let them be thrown into every combination possible. The child should make them his own, and should understand their application here and now in the circumstances of his actual life. From the very beginning of his education, the child should experience the joy of discovery. (Alfred North Whitehead, The Aims of Education)
Americans With Disability Act. If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski (MC 320, 796-3085) within ten days to discuss your accommodation needs. | 677.169 | 1 |
Traditionally, an Algebra 1 course focuses on rules or specific strategies for solving standard types of symbolic manipulation problems-usually to simplify or combine expressions or solve equations. For many students, symbolic rules for manipulation are memorized with little attempt to make sense of why they work. They retain the ideas for only a short time. There is little evidence that traditional experiences with algebra help students develop the ability to "read" information from symbolic expression or equations, to write symbolic statements to represent their thinking about relationships in a problem, or to meaningfully manipulate symbolic expressions to solve problems.
In the United States, algebra is generally taught as a stand-alone course rather than as a strand integrated and supported by other strands. This practice is contrary to curriculum practices in most of the rest of the world. Today, there is a growing body of research that leads many United States educators to believe that the development of algebraic ideas can and should take place over a long period of time and well before the first year of high school. Developing algebra across the grades and integrating it with other strands helps students become proficient with algebraic reasoning in a variety of contexts and gives them a sense of the coherence of mathematics. Transition to High School in Implementing CMP.
The Connected Mathematics program aims to expand student views of algebra beyond symbolic manipulation and to offer opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. The development of algebra in Connected Mathematics is consistent with the recommendations in the NCTM Principles and Standards for School Mathematics 2000 and most state frameworks.
Algebra in Connected Mathematics focuses on the overriding objective of developing students' ability to represent and analyze relationships among quantitative variables. From this perspective, variables are not letters that stand for unknown numbers. Rather they are quantitative attributes of objects, patterns, or situations that change in response to change in other quantities. The most important goals of mathematical analysis in such situations are understanding and predicting patterns of change in variables. The letters, symbolic equations, and inequalities of algebra are tools for representing what we know or what we want to figure out about a relationship between variables. Algebraic procedures for manipulating symbolic expressions into alternative equivalent forms are also means to the goal of insight into relationships between variables. To help students acquire quantitative reasoning skills, we have found that almost all of the important tasks to which algebra is usually applied can develop naturally as aspects of this endeavor. (Fey, Phillips 2005)
There are eight units which focus formally on algebra. Titles and descriptions of the mathematical content for these units are:
Variables and Patterns
Introducing Algebra
Representing and analyzing relationships between variables, including tables, graphs, words, and symbols
Frogs, Fleas, and Painted Cubes
Quadratic Relationships
Examining the pattern of change associated with quadratic relationships and comparing these patterns to linear and exponential patterns, recognizing, representing, and analyzing quadratic functions in tables graphs, words, and symbols; determining and predicting important features of the graph of a quadratic functions, such as the maximum/minimum point, line of symmetry, and the x-and y-intercepts; factoring simple quadratic expressions
Say It With Symbols
Making Sense of Symbols
Writing and interpreting equivalent expressions; combining expressions; looking at the pattern of change associated with an expression; solving linear and quadratic equations
Linear Systems and Inequalities
Even though the first primarily algebra unit occurs at the start of seventh grade, students study relationships among variables in grade 6.
There also are opportunities in 6th and in 7th grade for students to begin to examine and formalize patterns and relationships in words, graphs, tables, and with symbols.
In Shapes and Designs (Grade 6), students explore the relationship between the number of sides of a polygon and the sum of the interior angles of the polygon. They develop a rule for calculating the sum of the interior angle measures of a polygon with N sides.
In Covering and Surrounding (Grade 6), students estimate the area of three different- size pizzas and then relate the area to the price. This problem requires students to consider two relationships: one between the price of a pizza and its area and the other between the area of a pizza and its radius. Students also develop formulas and procedures-stated in words and symbols-for finding areas and perimeters of rectangles, parallelograms, triangles, and circles.
In Bits and Pieces I, II and III (Grade 6), students learn, through fact families, that addition and subtraction are inverse operations and that multiplication and division are inverse operations. This is a fundamental idea in equation solving. They use these ideas to find a missing factor or addend in a number sentence.
In Data About Us (Grade 6), students repre- sent and interpret graphs for the relationship between variables, such as the relationship between length of an arm span and height of a person, using words, tables, and graphs.
In Accentuate the Negative (Grade 7), students explore properties of real numbers, including the commutative, distributive, and inverse properties. They use these properties to find a missing addend or factor in a number sentence.
In Filling and Wrapping (Grade 7), students develop formulas and procedures-stated in words and symbols-for finding surface area and volume of rectangular prisms, cylinders, cones, and spheres.
Developing Functions
In a problem-centered curriculum, quantities (variables) and the relationships between variables naturally arise. Representing and reasoning about patterns of change becomes a way to organize and think about algebra. Looking at specific patterns of change and how this change is represented in tables, graphs, and symbols leads to the study of linear, exponential, and quadratic relationships (functions).
Linear Functions
In Moving Straight Ahead, students investigate linear relationships. They learn to recognize linear relationships from patterns in verbal, tabular, graphical, or symbolic representations. They also learn to represent linear relationships in a variety of ways and to solve equations and make predictions involving linear equations and functions. Problem 1.3 illustrates the kinds of questions students are asked when they meet a new type of relationship or function-in this case, a linear relationship. In this problem students are looking at three pledge plans that students suggest for a walkathon.
Moving Straight Ahead. p. 9
Whereas many algebra texts choose to focus almost exclusively on linear relationships, in Connected Mathematics students build on their knowledge of linear functions to investigate other patterns of change. In particular, students explore inverse variation relationships in Thinking With Mathematical Models, exponential relationships in Growing, Growing, Growing, and quadratic relationships in Frogs, Fleas, and Painted Cubes. Examples are given below which illustrate the different types of functions students investigate and some of the questions they are asked about these functions. By contrasting linear relationships with exponential and other relationships, students develop deeper understanding of linear relationships.
Inverse Functions
In Thinking With Mathematical Models, students are introduced to inverse functions.
Thinking With Mathematical Models. p. 32
Exponential Functions
In Growing, Growing, Growing, students are given the context of a reward figured by placing coins called rubas on a chessboard in a particular pattern, which is exponential. The coins are placed on the chessboard as follows.
Place 1 ruba on the first square of a chessboard, 2 rubas on the second square, 4 on the third square, 8 on the fourth square, and so on, until you have covered all 64 squares. Each square should have twice as many rubas as the previous square.
In this problem students use tables, graphs, and equations to examine exponential relationships and describe the pattern of change for this relationship.
Growing, Growing, Growing. p. 7
Quadratic Functions
In Problem 1.3 from Frogs, Fleas and Painted Cubes, students use tables, graphs, and equations to examine quadratic relationships and describe the pattern of change for this relationship.
Frogs, Fleas and Painted Cubes. p. 10
As students explore a new type of relationship, whether it is linear, quadratic, inverse, or exponential, they are asked questions like these:
What are the variables? Describe the pattern of change between the two variables.
Describe how the pattern of change can be seen in the table, graph, and equation.
Decide which representation is the most helpful for answering a particular question. (see Question D in Problem 1.3 Frogs and Fleas and Painted Cubes above)
Describe the relationships between the different representations (table, graph, and equation).
Compare the patterns of change for different relationships. For example, compare the patterns of change for two linear relationships, or for a linear and an exponential relationship.
After students have explored important relationships and their associated patterns of change and ways to represent these relationships, the emphasis shifts to symbolic reasoning.
Equivalent Expressions
Students use the properties of real numbers to look at equivalent expressions and the information each expression represents in a given context and to interpret the underlying patterns that a symbolic statement or equation represents. They examine the graph and table of an expression as well as the context the expression or statement represents. The properties of real numbers are used extensively to write equivalent expressions, combine expressions to form new expressions, predict patterns of change, and to solve equations. Say It With Symbols pulls together the symbolic reasoning skills students have developed through a focus on equivalent expressions. It also continues to explore relationships and patterns of change. Problem 1.1 in Say It With Symbols introduces students to equivalent expressions.
Say It With Symbols. p. 6
In Problem 2.1 students revisit Problem 1.3 from Moving Straight Ahead (see above) to combine expressions. They also use the new expression to find information and to predict the underlying pattern of change associated with the expression.
Say It With Symbols. p. 24
Solving Equations
Equivalence is an important idea in algebra. A solid understanding of equivalence is necessary for understanding how to solve algebraic equations. Through experiences with different functional relationships, students attach meaning to the symbols. This meaning helps student when they are developing the equation-solving strategies integral to success with algebra.
In CMP, solving linear equation is an algebra idea that is developed across all three grade levels, with increasing abstraction and complexity. In grade six, students write fact families to show the inverse relationships between addition and subtraction and between multiplication and division. The inverse relationships between operations are the fundamental basis for equation solving. Students are exposed early in sixth grade to missing number problems where they use fact families. Below is a description of fact families and a few examples of problems where students use fact families to solve algebraic equations in grades 6 and 7. These experiences precede formal work on equation solving.
In Bits and Pieces II (Grade 6), Bits and Pieces III (Grade 6), and Accentuate the Negative (Grade 7), students use fact families to find missing addends and factors.
Bits and Pieces II. p. 22
Bits and Pieces III. p. 28
Accentuate the Negative. p. 30
In Variables and Patterns (Grade 7), students solve linear equations using a variety of methods including graph and tables. As students move through the curriculum, these informal equation- solving experiences prepare them for the formal symbolic methods, which are developed in Moving Straight Ahead (Grade 7), and revisited throughout the five remaining algebra units in eighth grade.
Moving Straight Ahead. p. 85
Say It With Symbols (Grade 8), pulls together the symbolic reasoning skills students have developed through a focus on equivalent expressions and on solving linear and quadratic equations.
Say It With Symbols. p. 42
Shapes of Algebra (Grade 8), explores solving linear inequalities and systems of linear equations and inequalities. By the end of Grade 8, students in CMP should be able to analyze situations involving related quantitative variables in the following ways:
identify variables
identify significant patterns in the relationships among the variables
represent the variables and the patterns relating these variables using tables, graphs, symbolic expressions, and verbal descriptions
translate information among these forms of representation
Students should be adept at identifying the questions that are important or interesting to ask in a situation for which algebraic analysis is effective at providing answers. They should develop the skill and inclination to represent information mathematically, to transform that information using mathematical techniques to solve equations, create and compare graphs and tables of functions, and make judgments about the reasonableness of answers, accuracy, and completeness of the analysis. | 677.169 | 1 |
Encyclopedia of Mathematics & Society
Published by Salem Press
Presents articles showing the math behind our daily lives. Explains how and why math works, and allows readers to better understand how disciplines such as algebra, geometry, calculus, and others affect what we do every day | 677.169 | 1 |
CMAT - Comprehensive Mathematical Abilities Test
Browse titles:
Products
Based on state and local curriculum guides, and math education tools used in schools, the CMAT is a major advance in the accurate assessment of math taught in today's schools. Contains six core subtests (addition, subtraction, multiplication, division, problem solving, and charts, tables, & graphs) and six supplemental subtests. | 677.169 | 1 |
Job Title
Math Teacher
Summary
Teach courses
pertaining to mathematical concepts, statistics, and actuarial science and to
the application of original and standardized mathematical techniques in
solving specific problems and situations. | 677.169 | 1 |
books.google.ch - This... Geometry
Computational Geometry:
This and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.
Bewertungen von Nutzern
Review: Computational Geometry: Algorithms and Applications
Review: Computational Geometry: Algorithms and Applications
Nutzerbericht - Willy Van den driessche - Goodreads
Beauty is the first test. This is a very beautiful book (form) with a beautiful contents. The book explains in a very throrough way some of the fundamental algoritms in "computational geometry". You ...Vollständige Rezension lesen | 677.169 | 1 |
Questions About This Book?
The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included.
Related Products
Numerical Methods
Numerical Methods
Numerical Methods/Book and Disk With Instructional Manual
Student Solutions Manual for Faires/Burden's Numerical Methods, 3rd
Student Solutions Manual for Faires/Burden's Numerical Methods, 4th
Summary
This book emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. In this book, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally. | 677.169 | 1 |
Area Calculation
Area calculationis one of the most important chapters of Integral Calculus. It takes a real test of the skills of Integration and that too Definite Integral in particular. The chapters of Indefinite and Definite Integral are prerequisite to study the topic ofArea Calculationin Integral calculus.
This chapter is devoted to the application of definite integration forcalculating the areaof the regions bounded by specified or derived curves. Comprehensive material is provided with the consideration of wide variety of regions. Efforts are made to present the subject matter in the most lucid manner in order to involve the students actively and intellectually. A large number of solved examples, both of objective type and subjective type, are so chosen as to cover all the possible variations of question likely to be encountered by the students in different competitive examinations.
We have learnt that the definite integral between two values of Independent variable represents the area of the curve bound by the curve, the axis of the independent variable. Further, as we can calculate the area under one curve and the area under another curve then we can calculate the area between two curves. Depending upon the nature of the curves, this area can have different shapes and thus the tool of definite integral can be employed to calculate the area of different shapes. As a matter of fact, you will realize that the standard formulae to calculate the areas of different shapes can be derived by definite integral by choosing the appropriate curves.
Area Calculation is important from the perspective of scoring high in IIT JEE as there are few fixed pattern on which a number Multiple Choice Questions are framed on this topic. You are expected to do all the questions based on this to remain competitive in IIT JEE examination. It is very important to master these concepts as this this helps in many of the problems in Physics in your preparation for IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations. | 677.169 | 1 |
7th Grade Math
For Students: The Important Files (documents and power points) are located at the bottom of the page
Overview of 7th Grade MathAtStudentsStudents will review basic geometry vocabulary and concepts. They will learn how to set up equations given geometric information to solve for a variable. They will also learn properties of circles-- pi, radius, diameter-- and how to calculate their area and circumference.
GRAPHING: Students will be introduced | 677.169 | 1 |
A Friendly Introduction to Number Theory, Coursesmart eTextbook, 4th Edition
Description
For one-semester undergraduate courses in Elementary Number Theory.
A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.
Table of Contents
Preface
Flowchart of Chapter Dependencies
Introduction
1. What Is Number Theory?
2. Pythagorean Triples
3. Pythagorean Triples and the Unit Circle
4. Sums of Higher Powers and Fermat's Last Theorem
5. Divisibility and the Greatest Common Divisor
6. Linear Equations and the Greatest Common Divisor
7. Factorization and the Fundamental Theorem of Arithmetic
8. Congruences
9. Congruences, Powers, and Fermat's Little Theorem
10. Congruences, Powers, and Euler's Formula
11. Euler's Phi Function and the Chinese Remainder Theorem
12. Prime Numbers
13. Counting Primes
14. Mersenne Primes
15. Mersenne Primes and Perfect Numbers
16. Powers Modulo m and Successive Squaring
17. Computing kth Roots Modulo m
18. Powers, Roots, and "Unbreakable" Codes
19. Primality Testing and Carmichael Numbers
20. Squares Modulo p
21. Is -1 a Square Modulo p? Is 2?
22. Quadratic Reciprocity
23. Proof of Quadratic Reciprocity
24. Which Primes Are Sums of Two Squares?
25. Which Numbers Are Sums of Two Squares?
26. As Easy as One, Two, Three
27. Euler's Phi Function and Sums of Divisors
28. Powers Modulo p and Primitive Roots
29. Primitive Roots and Indices
30. The Equation X4 + Y4 = Z4
31. Square–Triangular Numbers Revisited
32. Pell's Equation
33. Diophantine Approximation
34. Diophantine Approximation and Pell's Equation
35. Number Theory and Imaginary Numbers
36. The Gaussian Integers and Unique Factorization
37. Irrational Numbers and Transcendental Numbers
38. Binomial Coefficients and Pascal's Triangle
39. Fibonacci's Rabbits and Linear Recurrence Sequences
40. Oh, What a Beautiful Function
41. Cubic Curves and Elliptic Curves
42. Elliptic Curves with Few Rational Points
43. Points on Elliptic Curves Modulo p
44. Torsion Collections Modulo p and Bad Primes
45. Defect Bounds and Modularity Patterns
46. Elliptic Curves and Fermat's Last Theorem
Further Reading
Index
*47. The Topsy-Turvey World of Continued Fractions [online]
*48. Continued Fractions, Square Roots, and Pell's Equation [online]
*49. Generating Functions [online]
*50. Sums of Powers [online]
*A. Factorization of Small Composite Integers [online]
*B. A List of Primes [online]
*These chapters are available online | 677.169 | 1 |
Mathematics
Introduction
Mathematics is a science that involves abstract concepts and language. Students develop their mathematical thinking gradually through personal experiences and exchanges with peers. Their learning is based on situations that are often drawn from everyday life. In elementary school, students take part in learning situations that allow them to use objects, manipulatives, references and various tools and instruments. The activities and tasks suggested encourage them to reflect, manipulate, explore, construct, simulate, discuss, structure and practise, thereby allowing them to assimilate concepts, processes and strategies1 that are useful in mathematics. Students must also call on their intuition, sense of observation, manual skills as well as their ability to express themselves, reflect and analyze. By making connections, visualizing mathematical objects in different ways and organizing these objects in their minds, students gradually develop their understanding of abstract mathematical concepts. With time, they acquire mathematical knowledge and skills, which they learn to use effectively in order to function in society.
In secondary school, learning continues in the same vein. It is centred on the fundamental aims of mathematical activity: interpreting reality, generalizing, predicting and making decisions. These aims reflect the major questions that have led human beings to construct mathematical culture and knowledge through the ages. They are therefore meaningful and make it possible for students to build a set of tools that will allow them to communicate appropriately using mathematical language, to reason effectively by making connections between mathematical concepts and processes, and to solve situational problems. Emphasis is placed on technological tools, as these not only foster the emergence and understanding of mathematical concepts and processes, but also enable students to deal more effectively with various situations. Using a variety of mathematical concepts and strategies appropriately provides keys to understanding everyday reality. Combined with learning activities, everyday situations promote the development of mathematical skills and attitudes that allow students to mobilize, consolidate and broaden their mathematical knowledge. In Cycle Two, students continue to develop their mathematical thinking, which is essential in pursuing more advanced studies.
This document provides additional information on the knowledge and skills students must acquire in each year of secondary school with respect to arithmetic, algebra, geometry, statistics and probability. It is designed to help teachers with their lesson planning and to facilitate the transition between elementary and secondary school and from one secondary cycle to another. A separate section has been designed for each of the above-mentioned branches, as well as for discrete mathematics and analytic geometry. Each section consists of an introduction that provides an overview of the learning that was acquired in elementary school and that is to be acquired in the two cycles of secondary school, as well as content tables that outline, for every year of secondary school, the knowledge to be developed and actions to be carried out in order for students to fully assimilate the concepts presented. A column is devoted specifically to learning acquired in elementary school.2 Where applicable, the cells corresponding to Secondary IV and V have been subdivided to present the knowledge and actions associated with each of the options that students may choose based on their interests, aptitudes and training needs: Cultural, Social and Technical option (CST), Technical and Scientific option (TS) and Science option (S).
Information concerning learning acquired in elementary school was taken from the Mathematics program and the document Progression of Learning in Elementary School - Mathematics, to indicate its relevance as a prerequisite and to define the limits of the elementary school program. Please note that there are no sections on vocabulary or symbols for at the secondary level, these are introduced gradually as needed. | 677.169 | 1 |
MPPET Maths Syllabus-1
Engineering Entrance
,
MPPET
Maths Syllabus Madhya Pradesh Professional Examination Test (MPPET):
I : ALGEBRA
Unit 1 Sets,Relations and Functions
Sets and their Representations, Union, intersection and complements of sets and the algebraic properties, Relations, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.
Unit 2 Complex Numbers
Complex number in the form a+ib and their representation in a plane. Argand diagram. Algebra of complex numbers, Modulus and Arguments (or amplitude) of a complex number, square root of a complex number. Cube roots of unity, triangle-inequality.
Unit 3 Matrices and Determinants
Determinants and matrices of order two and three, properties of determinants. Evaluation of determinants. Area of triangles using determinants, Addition and multiplication of matrices, adjoint and inverse of matrix. Test of consistency and solution of simultaneous linear equations using determinants and matrices.
Unit 4 Quadratic Equations
Quadratic equation in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots; Symmetric functions of roots.
Unit 5 Permutation & Combination
Fundamental principle of counting; Permutation as an arrangement. Meaning of P(n,r) and C(n,r) Simple applications.
Unit 6 Mathematical Induction and its applications-
Unit 7 Binomial Theorem and its Applications
Binomial Theorem for a positive integral index; general term and middle term; Binomial Theorem for any index. Properties of Binomial Co-efficients. Simple applications for approximations.
Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Integral as limit of a sum. Properties of definite integrals. Evaluation of indefinite integrals; Determining areas of the regions bounded by simple curves.
Unit 11 Differential Equations
Ordinary differential equations, their order and degree. Solution of differential equations by the method of separation of variables. Solution of homogeneous and linear differential equations. III : TWO AND THREE DIMENSIONAL GEOMETRY
Unit 12 Two dimensional Geometry
Recall of Cartesian system of Rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points and section formula, centroid and in-centre of a triangle. Locus and its equation, translation of axes, slope of a line; parallel and perpendicular lines. Intercepts of a line on the coordinate axes.
Unit 12 The straight line and pair of straight lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrency of three lines, distance of point from a line, coordinates of orthocentre and circumcentre of triangle, equation of family of lines passing through the point of intersection of two lines homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to represent of pair of lines, point of intersection and angle between two lines represented by S=O and the factors of S.
Unit 12 Circles & system of Circles
Standard form of equation of a circle, general form of the equation of a circle its radius and centre, equation of a circle in the parametric form, equations of a circle. When the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to the circle. Length of the tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.
Unit 12 Conic Section
Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y=mx+c to be a tangent and point(s) of tangency.
Unit 13 Three dimensional Geometry
Coordinates of the point in space, distance between the points; Section formula, direction ratios and direction cosines, angle between two intersecting lines, equations of a line and plane in different forms; intersection of a line and a plane, coplanar lines, equation of a sphere, its centre and radius. Diameter form of the equation of a sphere. IV : VECTORS
Unit 14 Vector Algebra
Vector and Scalars, addtion of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, vector triple product. Application of vectors to plane geometry.
V : STATISTICS
Unit 15 Measures of Central Tendency and Dispersion
Calculation of Mean, median and mode of grouped and unpgrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Unit 16 Probability
Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Probability distribution of a random variable; Binomial distribution and its properties. VI : TRIGONOMETRY
Resultant of Coplanar forces; moments and couples. Equilibrium of three concurrent forces.
Unit 19 Dynamics
Speed and velocity, average speed, instantaneous speed, acceleration and retardation, resultant of two velocities, relative velocity an its simple applications. Motion of a particle along a line moving with constant acceleration. Motion under gravity. Laws of motion, Projectile motion. | 677.169 | 1 |
Synopsis
This book provides a clear picture of the use of applied mathematics as a tool for improving the accuracy of agricultural research. For decades, statistics has been regarded as the fundamental tool of the scientific method. With new breakthroughs in computers and computer software, it has become feasible and necessary to improve the traditional approach in agricultural research by including additional mathematical modeling procedures.
The difficulty with the use of mathematics for agricultural scientists is that most courses in applied mathematics have been designed for engineering students. This publication is written by a professional in animal science targeting professionals in the biological, namely agricultural and animal scientists and graduate students in agricultural and animal sciences. The only prerequisite for the reader to understand the topics of this book is an introduction to college algebra, calculus and statistics. This is a manual of procedures for the mathematical modeling of agricultural systems and for the design and analyses of experimental data and experimental tests. It is a step-by-step guide for mathematical modeling of agricultural systems, starting with the statement of the research problem and up to implementing the project and running system experiments.
Found In
eBook Information
ISBN: 9780080535883 | 677.169 | 1 |
Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers)
- Write numbers in scientific notation and translate back into standard form
- Find the common factors and greatest common factor of two or more numbers
- Determine multiples and least common multiple of two or more numbers
- Determine the prime factorization of a given number and write in exponential form
- Simplify expressions using order of operations - Note: Expressions may include absolute value and/or integral exponents greater than 0.
- Add, subtract, multiply and divide integers
- Recognize and state the value of the square root of a perfect square (up to 225)
- Determine the square root of non-perfect squares using a calculator
- Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies
Algebra:
- Translate two-step verbal expressions into algebraic expressions
- Add and subtract monomials with exponents of one
- Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
- Solve one-step inequalities (positive coefficients only)
Geometry:
- Calculate the radius or diameter, given the circumference or area of a circle
- Calculate the volume of prisms and cylinders, using a given formula and a calculator
- Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones and pyramids)
- Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
- Find a missing angle when given angles of a quadrilateral
- Identify the right angle, hypotenuse, and legs of a right triangle
- Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
- Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
- Graph the solution set of an inequality (positive coefficients only) on a number line
Measurement:
- Calculate distance using a map scale
- Convert capacities and volumes within a given system
- Calculate unit price using proportions
- Draw central angles in a given circle using a protractor and display data (circle graphs) | 677.169 | 1 |
Algebra 1 Common Core
Semester 2 Plan
These are the objectives that are placed into my gradebook. This assessment strategy has been introduced to my students' parents at open house. These are the skills that I will be assessing, but my teaching will often go deeper and cover more concepts. Having this focus allows students the freedom to know exactly what will be on the tests/assessments while exploring mathematics. | 677.169 | 1 |
I am an actuary and one of the topics covered in our syllabus was Finite Difference, which is basically the same as Discrete Math. Discrete math can cover many different topics and is a fairly advanced topic. I have assisted students at a high school on Discrete Math as it is taught there | 677.169 | 1 |
Introduction to Mathematical Thought: From the Discrete to the Continuous MATH 111 SP
In this course we seek to illustrate for the students several major themes. One of the most important is the fact that mathematics is a living, coherent discipline, a creation of the human mind, with a beauty and
integrity
of its own that transcends, but, of course, includes, the applications to which it is put. We will try to provide a somewhat seamless fusion of the discrete and the continuous through the investigation of various
natural
questions as the course develops. We try to break down the basically artificial distinctions between such things as algebra, geometry, pre-calculus, calculus, etc. The topics will be elementary, particularly as they
are
taken up, but will be developed to the point of some sophistication. One challenge to the students will be to assimilate their previous experience in mathematics into this context. In this way we hope and expect that
some
of the beauty will show through.
MAJOR READINGS
Notes will be provided. There may be additional readings as well.
EXAMINATIONS AND ASSIGNMENTS
The focus of the course will be on weekly homework and in-class discussions.
ADDITIONAL REQUIREMENTS and/or COMMENTS
This course is a First-year initiative course, open only to first-year students. Sophomores may be allowed to add the course if it is not full. Since the flow of ideas in the course is one of its fundamental features,
class attendance is required. The
course carries an NSM designation. | 677.169 | 1 |
This course of study includes an emphasis on problem-solving and communication skills. Competency in basic math skills is expected. Topics of study include data representation, equations, inequalities, linear and quadratic functions, graphing systems, rational expressions, relations and functions, and geometry. A scientific calculator is required.
PERMISSION
Copyright Notice: No materials on any of the Bellingham Schools' web pages may be copied without express
written permission unless permission is clearly stated on the page. | 677.169 | 1 |
Search Course Communities:
Course Communities
Probability
Course Topic(s):
Probability | Basic Probability, basic rules
This is a brief article on probability that includes interpretations of probability and a few probability rules: the addition rule, the inclusion-exclusion rule, and the law of total probability. There are links to related Wolfram MathWorld articles. | 677.169 | 1 |
AQA GCSE Maths – Practice book sample pages for 2010 Specification
Description: This sample is taken from the new AQA GCSE Maths practice book, this chapter covers Arcs, Cones and Spheres, and sectors of arcs and cones. It also indicates to the student which questions, if answered…
(More)
Description: This sample is taken from the new AQA GCSE Maths practice book, this chapter covers Arcs, Cones and Spheres, and sectors of arcs and cones. It also indicates to the student which questions, if answered correctly would give the student an A and differentiates this from an A* answer.
To see more sample material or order your FREE Evaluation pack, simply visit us now at | 677.169 | 1 |
The course was designed with the goal that a student completing the course will have a thorough knowledge of the most basic and essential math skills as well as develop skills for critical thinking and problem solving. Throughout this course you will be manipulating numbers in a way that will help you understand how to use them on paper as well as everyday life. The course is designed to help you realize the importance of mathematics. It is my hope that you will take the skills that you learn and begin to utilize them in your daily life. | 677.169 | 1 |
Course
Number: MA.IB6HL
Course Name: IB Math 6 HL Prerequisite: Geometry Course Description:
Higher Level Mathematics is intended for students who have a strong background and ability in mathematics. Those students intending to study mathematics, physics, engineering or technology at the college or university level should take this course. Those intending to study chemistry, economics or business should consider it, also. Students will study topics from number theory through probability and calculus. One optional topic will be chosen. Graphing calculators are required for this course. (12/94) Course Length: 2
semesters Period Length: 1 Grade Level: 9-12
grade(s) Credit Per Semester: 1.0 (Math requirement or Elective) | 677.169 | 1 |
College Algebra
The scope of this learning experience is to study basic mathematical concepts required for adult learners at a college or university level. Learners will become proficient at solving linear and quadratic equations, graphing linear and quadratic equations, functions, exponents and logarithms, and applying these concepts to real world problems.
Idizzla 19:50, 27 July 2007 (UTC) If you wish to participate with this course, please add your name below after registering an account on Wikiversity with your account signature by editing this page and adding *~~~~
Mirwin 09:39, 18 August 2006 (UTC) I can help out with some mentoring or tutoring where materials are difficult to understand and possibly help fill gaps in available materials. I have a B.S. in Engineering Physics so I have done quite a bit of practical algebra even if it is a bit rusty in spots. Participants drop queries or requests for assistance on my talk page and we will create some appropriate space from there to work from.
--MarkyParky 22:58, 25 August 2006 (UTC) I can help out when people are stuck on some problem, or just need something explained from a different perspective. | 677.169 | 1 |
@book {IOPORT.00043540,
author = {Solomentsev, E.D.},
title = {Functions of a complex variable and their applications. Textbook. (Funktsii kompleksnogo peremennogo i ikh primeneniya. Uchebnoe posobie.)},
year = {1988},
isbn = {5-06-003145-6},
pages = {168 p.},
publisher = {Moskva: Vysshaya Shkola},
abstract = {The author addresses his book to students of higher technical schools as well as to engineers wishing to enrich their mathematical background. The book contains an introduction to the theory of complex functions as well as its main applications such as operational calculus, problems of stability of linear systems and plane vector fields. The theory is illustrated by examples and exercises.},
reviewer = {J.Siciak},
identifier = {00043540},
} | 677.169 | 1 |
This is a site dedicated to students to help succeed in predominately in College Algebra. The topics on this page is what students need to master before or the first week of Math 1111. However, it can also be helpful in other courses as well as Learning Support and Precalculus. If a student needs further assistance, it is suggested they view the main math tutoring page titled "Math" located to the left. It is full of helpful links, tutoring information, and COMPASS test notes/videos.
How to Use These Videos:
The videos are best used in sequence. Meaning, they can be viewed in any order; however, if you are unfamiliar with an explanation or term within a topic, you may go back to previous videos that will help you understand the concept as a whole. | 677.169 | 1 |
This scientific calculator is configurable and contains most of the normal functions such as trigonometric and logarithmic functions, conversions, constants, memories and binary and hexadecimal notation.
It tries to figure out the best position of the menu, clear and equal but... | 677.169 | 1 |
This study examined understanding of linear functions held by students with visual impairments. The purpose of this study was to determine students' level of knowledge and type of understanding of linear function and to describe students' abilities in using the four main representational forms of a function: (a) description, equations, tables, and graphs. Other aspects studied were students' preferred representation of function and students' perceived influences in his or her mathematics education. Participants in this study included four high school and four college students who were receiving educational services for a visual impairment and who had completed at least one course in algebra.
Data collection and analysis followed a qualitative research design. Three instruments were used for data collection, (a) the Mathematics Education Experiences and Visual Abilities (MEEVA) Interview, (b) the Function Knowledge Assessment (FKA), and (c) the Function Competencies Assessment (FCA). The MEEVA provided demographic information and responses provided information on students' previous educational experiences in mathematics. The FKA and the FCA were mathematics assessments that consisted of problems related to linear functions and their applications. Student responses from the FKA and the FCA provided information on student knowledge of linear functions and student abilities when solving word problems involving linear functions. Instruments were given orally and responses were audio recorded. Each participant met with the researcher one-on-one on two different occasions to complete the three data collection instruments.
Data analysis followed the tenets of the Constant Comparative Method (Glaser & Strauss, 1967). Student responses to the MEEVA, FKA, and FCA were transcribed and coded for student understanding in the four function competencies, (a) modeling, (b) interpreting, (c) transcribing, and (d) reifying as described by O'Callaghan (1998). Students' level of knowledge of linear function was further described by students' ability to comprehend and apply knowledge when solving word problems, as described by Wilson (1971).
Results indicate that the understanding of modeling and interpreting problems involving linear functions of high school and college students with visual impairments was stronger than that of either translating between representational forms of a function or the ability to reify the function concept. A positive relationship was observed between students' graphing abilities and his or her overall understanding of function. Results also show that students were most comfortable with gaining information on functions through tables and were least comfortable gaining information through graphs. The perceived influences on students' mathematics education were that of individualized education and the use of appropriate materials that allowed for independent access to the | 677.169 | 1 |
John Carzoli, PhD
Mathematica is a software package that does much more than mathematics. Through the 20+ year history of the program it has
developed from a text-based mathematics equation-solving and plotting program to a full-fledged graphical user interface front-end
resting on top of a kernal that is capable of solving an extremely vast breadth and depth of problems in mathematics, phyiscs, engineering,
and most other sciences. In fact, if there is a discipline where data is used in any way, Mathematica can be used to present and/or analyze that
data in many different ways. Mathematica can even be used in areas where mathematics is not normally discussed. For example, you can input text
from a poem or play and do an analysis on the word count, structure and other possibly interesting things. I've seen some neat examples of this kind of analysis and I will post links to them when I find them.
Here is a list of resources for using Mathematica starting from the basics to the more advanced. | 677.169 | 1 |
MATH
►Rick Geiser
►Jen Lawrence
►Matt Zuercher
INTEGRATED MATH II
This course is designed for students who took Integrated Math I. Integrated II completes the second year class format.
ALGEBRA I Algebra I will provide instruction in the following topics: quadratic equations, linear equations, inequalities, polynomials, factoring, functions and graphs, and coordinate geometry. Algebra I is the first course in the college preparatory program. A scientific calculator (TI 30XIIS), not graphing calculator, is required for this course.
GEOMETRY
The course embodies the objectives of geometry and the logic upon which it is based. Through definitions, postulates, and theorems, the student will learn direct and indirect methods of finding lengths, angle measures, perimeters, areas, and volumes of geometric figures. Constructions and projects are offered to enhance concepts. Since the course stresses deductive reasoning, it is highly recommended for college preparatory students. A scientific calculator (TI 30XIIS), not a graphing calculator, is required for this course.
ALGEBRA II
This is the third course in the college preparatory math program. In addition to a more detailed study of Algebra I topics, Algebra II introduces matrices, radicals, complex numbers and quadratic relations and systems. A scientific calculator is required for this course.
TRIGONOMETRY
Trigonometry is the study of the sine, cosine, tangent, and their reciprocal functions in relation to right triangles. Students will investigate the properties of the trig functions and their inverses, study their graphs and transformations, solve trigonometric equations, and verify/prove identities. Students will also learn techniques to solve both right and non-right triangles. The course is a prerequisite or co-requisite for Pre-Calculus. Students are encouraged to take the course while also taking Algebra II or in the fall while taking Pre-Calculus. A graphing calculator is highly suggested.
PRE-CALCULUS
This is the 4th course in the college preparatory math program. This course offers a detailed study of circular and trigonometric functions, matrices, theory of education, Polar coordinates, complex numbers, vectors, sequences and series, exponential and logorithmic functions, and intro to calculus. Graphing calculator is strongly suggested!
ADVANCED PLACEMENT CALCULUS AB (Calculus AB)
This is the fifth course in the college preparatory math program. Topics include limits and their properties, differentiation and its applications, integration, exponential & logarithmic functions, integration techniques & applications, parametric equations, etc. Graphing calculator is strongly suggested! Students may take the AP exam in May with the possibility of testing out of college math classes. The cost is approximately $89.00.
***AP Calculus is offered on a five point grade point average system, requiring the taking of the AP Calculus exam in May. The option of taking this course on a four point grade point system eliminates the AP Calculus exam requirement.
TRANSITIONS
Transitions to college mathematics is designed to be a mathematics course for seniors who will need to take college courses in mathematics and have completed Algebra I, Geometry, and Algebra II/Algebra II Basic. A commitment to do many problems on a daily basis is essential. Algebra and Geometry concepts are presented in concrete problem settings, approached arithmetically through numerical computation. A scientific calculator is required for this course.
BRIDGING THE GAP TO COLLEGE MATH
Instead of learning in the traditional classroom, students are pre-tested (COMPASS or ACT) and
placed into the course at the level that is right for them. From there, students work through a series of online modules, progressing at their own pace, and practicing skills in class and at home through a combination of online tools and instructor support. This course is designed to help students identify the areas they need to strengthen and develop their skills so they are ready for college algebra and equipped for success in college. Bridging the Gap to College Math is based on the concept of "mastery learning", which involves practicing a skill until it is learned and can be demonstrated. When the student is ready, he/she takes a post-test. With a score of at least 85%, the student demonstrates mastery competence and is ready to progress to the next module. Instructors are available during class time to answer questions and guide the students. Columbus State Community College is our partner for this course. If a student attends CSCC upon high school graduation, they will earn placement into the appropriate credit bearing math course instead of a non-credit remedial course. | 677.169 | 1 |
AcademicsCalculus I (NSC2)
Course Outline: This course will follow
the first five chapters of Calculus by James Stewart, published
by Brooks/Cole. Explorations in Calculus, an interactive,
multimedia CD program by Joe Mazur et al, published by Springer-Verlag
and four videos available through the library, called Views
of Calculus, will provide useful extra material. The program
will follow a strict schedule that includes drill and practice
routines for developing a familiarity with the common tools
of calculus alongside discussions surrounding the concepts
behind the subject. Thus assignments from Stewart's Calculus,
together with additional material from Explorations in Calculus,
Views of Calculus and other sources, will prompt class discussion
surrounding the concepts, while daily problem sets will reinforce
a command of the material. This is a four-credit course and
there is much to learn. Please keep in mind that this course
requires a daily commitment. The best way to successfully
learn the material is to stay ahead of the game and work through
the assignments before final class discussion.
Grades: Here is the breakdown for how your grade
will be calculated: 20% Class participation and attendance;
40% Graded homework assignments; 40% Final exam.
Homeworks: Bold numbered problems in the attached
homework assignment sheet are to be handed in for grading.
Plain text numbered problems are more drill and practice material
that should be worked through to keep up with course material.
You are expected to complete the current assignment after
the topic is introduced in class and before class discussion
of the assignment itself. By noon each Friday you are expected
to hand in your solutions to the appropriate bold numbered
questions (exactly which questions these are will be announced
during the previous week); but you may wish to discuss any
assignments that you find difficult. | 677.169 | 1 |
This is a module framework. It can be viewed online or downloaded as a zip file. It is as taught in 2009-2010. This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associated theory, with a strong emphasis on rigorous proof. This module is suitable for study at undergraduate level 2. Dr Joel Feinstein, School of Mathematical Sciences Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area | 677.169 | 1 |
The aim of this course is to acquaint the students with applications of calculus in business and economics. The course includes: limits and derivative, Minima and maxima and its applications in business and economics, definite and indefinite integrals, applications of integrals in business and economics.
COURSE OBJECTIVES
Mathematics intends that students will:
Develop mathematical skills and apply them
Develop the ability to communicate mathematics with appropriate symbols and language
Develop patience and persistence when solving problems
Develop and apply business and economics skills in the study of mathematics | 677.169 | 1 |
Once considered an "unimportant" branch of topology, graph theory has come into its own through many important contributions to a wide range of fields — and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, theorems, and examples from graph theory. The authors present a collection of interesting results from mathematics that involve key concepts and proof techniques; covers design and analysis of computer algorithms for solving problems in graph theory; and discuss applications of graph theory to the sciences. It is mathematically rigorous, but also practical, intuitive, and algorithmic. | 677.169 | 1 |
In math, as in any form of communication, there are rules that are agreed upon so that everyone can understand exactly what is being communicated. Oral and written languages use vocabulary, grammar, and sentence structure to communicate effectively. Mathematics uses its own form of these entities as well. Learning the language of mathematics is a key aspect of understanding the concepts being communicated. Numbers (analogous in some ways to the alphabet in which a language is written) and how these numbers are combined (much as letters are combined in the spelling of words) are the foundation for the study of algebra. This chapter will introduce the basic building blocks of algebra and give you a sturdy foundation for your future study. | 677.169 | 1 |
Mathematics in Education
Turns your Sudden Motion Sensor-equipped laptop into a three-axis seismograph. Turns your Sudden Motion Sensor-equipped laptop into a three-axis seismograph. It shows a scrolling chart of the three axes of acceleration, reading up to five hundred...
Terrific Triangles is a math facts drill-and-practice program that teaches fact families for both addition/subtraction and multiplication/division. Terrific Triangles is a math facts drill-and-practice program that teaches fact families for both...
The award-winning periodic table of the elements for the Macintosh. The award-winning periodic table of the elements for the Macintosh. In addition to the usual information found in such programs, The Atomic Mac also contains a wealth of nuclear...
Solve mathematical models applied to technical problems of various type. Solve mathematical models applied to technical problems of various type. Documents can be realized and used as calculation models for a specific mathematical technical...
Do you have a homework assignment that needs the complete working out for a matrix question, and requires that it be neatly typed out? Do you have a homework assignment that needs the complete working out for a matrix question, and requires that...
Controls up to 4 USB or Firewire connected cameras during an eclipse so that you can be free to concentrate on observing the event visually. Controls up to 4 USB or Firewire connected cameras during an eclipse so that you can be free to...
Visualization tool for the N-body problem. Visualization tool for the N-body problem. The first program of its kind for Mac OS X, it has an intuitive interface, beautiful graphics and an accurate and fast core physics engine. Cavendish is named...
A Cocoa application dedicated to the processing of astronomical digital images taken through a telescope. A Cocoa application dedicated to the processing of astronomical digital images taken through a telescope. It is a a€sUniversal binarya€t...
Pythagorean Theorem is a text-based program that uses the formula A2 B2 = C2 to calculate the length of any side of a right triangle, provided you enter the other two. Pythagorean Theorem is a text-based program that uses the formula A2 B2 = C2 to...
Marketiva specializes in providing traders with high quality online trading services. Marketiva specializes in providing traders with high quality online trading services. With a team of dedicated financial specialists and technical support...
AlgeXpansion is an aplication that teaches algebraic expansion. AlgeXpansion is an aplication that teaches algebraic expansion. The program is capable of generating hundreds of sums for drills to ensure that the student masters the skills. It...
This program puts a set of problems on the screen. This program puts a set of problems on the screen. Each consists of two digits, and they are to be added or multiplied. There is no penalty for wrong answers. As soon as the user provides the...
Control engineers and instrumentation technicians require software tools to test communications both to and from Programmable Logic Controllers (PLCs), Remote Terminal Units (RTUs), and other logic solving devices. Control engineers and...
The best matrices calculator there is. The best matrices calculator there is.It is a calculator for real and complex matrices.It is not just a calculator you can write your own programs on it. Can do all manipulations on matrices. It can do add,...
A professional numerology decoding program that is easy to use. A professional numerology decoding program that is easy to use. It enables you to enter names, dates, letters, or numbers in any combination. Q-Decode will then break down the data...
Teaches the concepts of digital electronic circuits. Teaches the concepts of digital electronic circuits. The integrated schematic entry and simulation software was designed specifically for educational use and can be applied in minutes. Probes,...
An easy-to-use utility for backing up and restoring Garmin GPS waypoints and routes. An easy-to-use utility for backing up and restoring Garmin GPS waypoints and routes. All GPS waypoint and route data can be completely restored or you can select...
A word-processor-like editor specifically designed for use in high school and college-level algebra-based physics courses. A word-processor-like editor specifically designed for use in high school and college-level algebra-based physics courses.... | 677.169 | 1 |
Mathematics for Business, CourseSmart eTextbook, 9th Edition
Description
For courses in business mathematics at the freshman/sophomore levels, including courses where instructors demand somewhat more rigor than competitive texts permit.
Mathematics for Business provides solid, practical, up-to-date coverage of the mathematical techniques students must master to succeed in business today. This Ninth Edition takes a more integrated, holistic approach, and places far greater emphasis on analysis. Business statistics coverage has been moved towards the front, where students are taught to read and interpret graphs and tables; these skills are repeatedly reinforced throughout. Scores of new examples include visual Stop & Think sections that help students understand current events. This text includes algebra where needed to impart real understanding, and covers crucial topics other books ignore, including reading financial statements.
Table of Contents
PART I. BASIC MATHEMATICS
1. Problem Solving and Operations with Fractions
2. Equations and Formulas
3. Percent
4. Business Statistics
PART II. BASIC BUSINESS APPLICATIONS
5. Banking Services
6. Payroll
7. Taxes
8. Risk Management
PART III. MATHEMATICS OF RETAILING
9. Mathematics of Buying
10. Markup
11. Markdown and Inventory Control
PART IV. MATHEMATICS OF FINANCE
12. Simple Interest
13. Notes and Bank Discount
14. Compound Interest
15. Annuities and Sinking Funds
16. Business and Consumer Loans
PART V. ACCOUNTING AND OTHER APPLICATIONS
17. Depreciation
18. Financial Statements and Ratios
19. Securities and Distribution of Profit and Overhead
Appendix A: Calculator Basics
Appendix B: The Metric System
Appendix C: Powers of e
Appendix D: Interest Tables
Answers to Selected Exercises | 677.169 | 1 |
Elementary Curves and Surfaces
Course description: The course is designed as an informal introduction
to the geometry of curves and surfaces in space. This involves the concept
of torsion (twisting out of a plane) and curvature (away from a line) of
curves, and the curvature (away from a plane) of surfaces. A feature of
the course is the use of the computer algebra package Mathematica (for
which Manchester University has a site licence and student versions are available for personal
use) to do all the calculus and graphics in computer lab sessions. All materials are available on line. Lecture Notes (PDF format).
Recommended text:
A. Gray. Modern Differential Geometry of Curves and Surfaces.
Boca Raton: CRC Press, Second Edition, 1998. Mathematica Packages: Alfred Gray's Mathematica packages for curves and surfaces are free and
available locally, together with others that we use, see Beginning
Mathematica . Introductory Mathematica Notebook: ==>Download and open in Mathematica
Breakdown of Lectures: Lecture Notes 5 Elementary theory of curves, their curvature and torsion
7 Elementary theory of surfaces and their curvature
12 Computer laboratory sessions investigating properties of curves
and surfaces.
Coursework Assignments: ==>Download and open in Mathematica Assignment 1 Complete and submit by end of Week 4 Assignment 2 Complete and submit by end of Week 8 Assignment 3 Complete and submit by end of Week 11 | 677.169 | 1 |
Students learn the form and elements of the parabola equation in concept before applying the concepts using a small catapult. Data is collected in a catapult competition and is used to solve the equation in context.
Small Catapult with projectile object (contact Sierra College STEM project for assembly of a catapult). Algebra 2 textbook or Pre Calculus textbook to assist student with exploration of parabolic equations. Other materials (need enough for each group in class): ball, long tape measure, yard stick, data collection handout (see attachment), video camera (optional; students could use their phones to video the trajectory if allowed). | 677.169 | 1 |
West New York Calculus begins with learning to translate verbal phrases into symbols. This leads to the topic of formulas and equations. In particular, proportions are solved and linear and quadratic equations are solved and graphed | 677.169 | 1 |
Additional product details
Best-selling authors, James Stewart, Lothar Redlin, and Saleem Watson refine their focus on problem solving and mathematical modeling to provide students with a solid foundation in the principles of mathematical thinking. The authors explain critical concepts simply and clearly, without glossing over difficult points to provide complete coverage of the function concept, and integrate a significant amount of graphing calculator material to help students develop insight into mathematical ideas. | 677.169 | 1 |
Sign up for a free eduslide account !
Channels / School Education / Maths
Fundamental skills of mathematics will be applied to such topics as functions, equations and inequalities, probability and statistics, logarithmic and exponential relationships, quadratic and polynomial ... | 677.169 | 1 |
Suchresultat
The ideal review for your geometry course. More than 40 million students have trusted Schaum s Outlines for their expert knowledge and helpful solved problems. Written by a renowned expert in this field, Schaum's Outline of Geometry covers what you need to know for your [...]
The ideal review for your elementary mathematics course More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math [...]
. When you need just the essentials of elementary algebra, this Easy Outlines book is there to help. If you are looking for a quick nuts-and-bolts overview of elementary algebra, it's got to be Schaum's Easy Outline. This book is a pared-down, simplified, and tightly [...]
. When you need just the essentials of geometry, this Easy Outlines book is there to help. If you are looking for a quick nuts-and-bolts overview of geometry, it's got to be Schaum's Easy Outline. This book is a pared-down, simplified, and tightly focused version of its [...]
Takes you through elementary maths, including algebra and geometry. This easy-to-follow study guide provides sample problems that show you step-by-step how to solve the kind of problems you may find on your exams. It also includes practice problems (with answers supplied) [...] | 677.169 | 1 |
INTEGRAL tool for mastering ADVANCED CALCULUS
Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn.
Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you'll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you're mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering.
This fast and easy guide offers:
Numerous detailed examples to illustrate basic concepts
Geometric interpretations of vector operations such as div, grad, and curl
Coverage of key integration theorems including Green's, Stokes', and Gauss'
Quizzes at the end of each chapter to reinforce learning
A time-saving approach to performing better on an exam or at work
Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won't want to function without! | 677.169 | 1 |
Quadratic Functions
4th six weeks
Targeted TEKS:
A.1A, A.2A,B, A.3A, A.4A,C, A.9A,B,C,D, A.10A, B
Quadratics Galore
As students move into quadratic equations, there are much more vocabulary and techniques to be learned involving solving equations. This PBL unit is designed to make the experience meaningful and present students with various ways to use quadratic functions. It also relates the new concepts with previously learned concepts. | 677.169 | 1 |
This review of arithmetic and elementary algebra is designed to prepare the student to study MATH 100 (Mathematical Sampler) or MATH 101 (Finite Mathematics). The course is designed as a self-directed study experience. The student will have access to textbook explanations and online resources to gain mastery of the material. Appropriate testing is done with the tutors in the Mathematics Resource Center (MaRC). A nominal registration fee is charged. | 677.169 | 1 |
Join the thousands of students that have used our Algebra Video Tutorials since 2004 to master the subject!
There is no easier way to learn Algebra than to have a calm teacher show you each and every step. We don't focus on shortcuts - we focus on you truly understanding the subject so that every step makes sense!
The Matrix Algebra Tutor is a 7 hour course spread over 2 DVD disks that teaches the student how to perform Matrix operations. These topics are usually taught at the end of a high school algebra sequence, in college algebra, or in a linear algebra class. Every topic in this course is taught by working example problems that begin with the easier problems and gradually progress to the harder problems. Every problem in taught in step by step detail ensuring that all students understand the content.
The skills learned in this course will aid the student in more advanced areas of math and science. These skills are used time again in more advanced courses such as Physics and Calculus. The teaching method employed on this DVD ensures that the student immediately gains confidence in his or her abilities and improves homework and exam taking skills. | 677.169 | 1 |
Difference and Differential Equations in Mathematical Modelling demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.
...
A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.
way and using an easy to follow format, it will help boost your understanding and develop your analytical skills. Focusing on the core areas of numeracy, it will help you learn to answer questions without using of a calculator and...
This book makes quantitative finance (almost) easy! Its new
visual approach makes quantitative finance accessible to a broad
audience, including those without strong backgrounds in math or
finance. Michael Lovelady introduces a simplified but powerful
technique for calculating profit probabilities and graphically
representing the outcomes. Lovelady's "pictures" highlight key
characteristics of structured securities such as the increased
likelihood of profits, the level of virtual dividends being
generated, and market risk exposures. After explaining his visual
approach, he applies it to one...
Based on the award winning Wiley Encyclopedia of Chemical Biology, this book provides a general overview of the unique features of the small molecules referred to as "natural products", explores how this traditionally organic chemistry-based field was transformed by insights from genetics and biochemistry, and highlights some promising future directions. The book begins by introducing natural products from different origins, moves on to presenting and discussing biosynthesis of various classes of natural products, and then looks at natural products as models and the possibilities of using...
Quantitative Techniques: Theory and Problems adopts a fresh and novel approach to the study of quantitative techniques, and provides a comprehensive coverage of the subject. Essentially designed for extensive practice and self-study, this book will serve as a tutor at home. Chapters contain theory in brief, numerous solved examples and exercises with exhibits and tables.
...
The book is meant for an introductory course on Heat and Thermodynamics. Emphasis has been given to the fundamentals of thermodynamics. The book uses variety of diagrams, charts and learning aids to enable easy understanding of the subject. Solved numerical problems interspersed within the chapters will help the students to understand the physical significance of the mathematical derivations.
...
Applied Mathematical Methods covers the material vital for research in today's world and can be covered in a regular semester course. It is the consolidation of the efforts of teaching the compulsory first semester post-graduate applied mathematics course at the Department of Mechanical Engineering at IIT Kanpur for two successive years.
...
Economics, far from being the "dismal science," offers us valuable lessons that can be applied to our everyday experiences. At its heart, economics is the science of choice and a study of economic principles that allows us to achieve a more informed understanding of how we make our choices, whether these choices occur in our everyday life, in our work environment, or at the national or international level. This book represents a common sense approach to basic macroeconomics, and begins by explaining key economic principles and defining important terms used in macroeconomic discussion. It uses...The UK Clinical Aptitude Test (UKCAT) is used by the majority of UK medical and dentistry schools to identify the brightest candidates most suitable for training at their institutions.
With over 600 questions, the best-selling How to Master the UKCAT, 4th edition contains more practice than any other book. Questions are designed to build up speed and accuracy across the four sections of the test, and answers include detailed explanations to ensure that you maximize your learning.
Now including a brand new mock test to help you get in some serious score improving practice, How to Master the...
As advancements in technology continue to influence all facets of society, its aspects have been utilized in order to find solutions to emerging ecological issues. Creating a Sustainable Ecology Using Technology-Driven Solutions highlights matters that relate to technology driven solutions towards the combination of social ecology and sustainable development. This publication addresses the issues of development in advancing and transitioning economies through creating new ideas and solutions; making it useful for researchers, practitioners, and policy makers in the socioeconomic sectors....Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.
...
Praise for the Third Edition
"This book provides in-depth coverage of modelling techniques used throughout many branches of actuarial science. . . . The exceptional high standard of this book has made it a pleasure to read." —Annals of Actuarial Science
Newly organized to focus exclusively on material tested in the Society of Actuaries' Exam C and the Casualty Actuarial Society's Exam 4, Loss Models: From Data to Decisions, Fourth Edition continues to supply actuaries with a practical approach to the key concepts and techniques needed on the job. With updated material and extensive... | 677.169 | 1 |
Ankit1010 wrote:All right, Real Analysis is a proof-based course. If you have not had one of those before, it will be quite different from your other math classes. No longer will the professor tell you how to solve problems and then ask you to solve them. Now you will have to prove that the techniques to solve those problems are actually valid. You should be familiar with proof by induction, proof by contradiction, and proof by contraposition.
The course will start out covering thing that you've known since elementary school, but have probably never studied rigorously before. For example, in the section about field axioms, you might be asked to formally prove that 0·1=0. You might have to rigorously define what it means for a real number to be "positive", and prove that the positive numbers are closed under addition, multiplication, and division, but not subtraction.
From the list of topics you provide, it seems likely your course will not make you prove that such a thing as the real numbers actually exists. Instead it will implicitly take the stance, "If a complete ordered Archimedean field exists, these are the properties it must have."
Most of the course will stem from a few major ideas. One of these is the least upper bound property, meaning every bounded set of real numbers has a least upper bound in the reals. Another is trichotomy, meaning for any two real numbers x and y, exactly one of "x=y", "x<y", and "x>y" is true.
There will be a lot of topics dealing with limits from the ε-δ definition. This will probably be couched in the language of neighborhoods and balls, and likely will constitute your first introduction to the study of metric spaces. The course will start slowly, then progress quickly, until at the end you will be rigorously proving calculus theorems that you might not have seen before.
Qaanol wrote:And it really is a ton of fun. If you like that sort of thing, anyways.
Ben-oni wrote:Practice proofs. Look up any of the terms listed that your not familiar with. That should do you good for now.
Qaanol wrote:... AsI've actually done several proof-based courses before and am very comfortable with writing and understanding formal proofs. Let me clarify what I meant in the question - I want to know what textbooks/problem sets/video lectures/resources I can use to start learning the material that will be taught DURING the class, not the general areas I should cover for background knowledge. The fact is that my GPA that needs a lot of work, and next semester promises to be tough so I'm trying to effectively teach myself everything we do in class over the summer to get a head-start.
Understanding Analysis by Stephen Abbot is a very good book for self studies and the toc is suspiciously close to your course description. A good textbook in combination with wikipedia and will probably do the trick.
Alright, thanks for the advice! Understanding Analysis looks like a great book, I'll definitely pick up a copy, and I'll find out which text we'll be using for the class soon too. It will likely be either Principles of Mathematical Analysis by Rudin or Understanding Analysis. I love stack exchange, and that coupled with this forum for more serious difficulties should be enough to resolve any problems.
Ankit1010 wrote:I'm taking undergrad Real Analysis I at college next semester, and I want some advice on how I can start preparing for the course over summer since I need to do well on it.
I had a wonderful academic experience in that course. There were two factors I've identified.
1) I had a fabulous teacher. You have some control over that if there's more than one section and you can find reviews. This is difficult material ... and for someone who wants to do advanced math or physics, it's absolutely essential to nail this course. So get the best teacher you can.
And along these lines ... buddy up to the TA's. The TA's are grad students who still remember what it's like to not understand this material ... so they can be incredibly helpful. Join a study group. Go to TA office hours. Be friendly. Hang around with the other students. It really helps to grapple with this material with other people.
2) I took it during summer school and took nothing else. In fact I was taking an upper division computer science class and just dropped it. I did nothing but real analysis. And it really made a difference. This is a very labor-intensive course. You just have to do epsilon proofs till they come out your ears. Because the course involves concepts that are deep; and techniques that are precise. You really have to put some time into this class.
That would be my advice. Sign up with a good prof; hang out with the TA'S and other students; and clear the decks in the rest of your life so that you can spend all your time thinking about real analysis. | 677.169 | 1 |
PREREQUISITE:
Placement, Grade of C or better in an elementary algebra course, or consent of
the Department
TEXT: Explorations in College Algebra, Kime and Clark, (2nd
Edition) and a graphing calculator resource manual.
SUPPLIES:Texas Instruments TI-83 Graphing
Calculator (note: If you are purchasing a calculator for this class, you are
required to purchase the TI-83. If you already have a graphing calculator,
consult your instructor about its acceptability)
EXPECTED
STUDENT COMPETENCIES TO BE ACQUIRED: The successful student at the end
of the course will be able produce well-written correct solutions for problems
similar to those assigned for homework in this course.
ASSIGNMENTS:
Homework will be assigned daily and will occasionally be collected as a check on
how you are keeping up. Although most of the homework assignments will not be
collected, that doesn't mean you don't have to do it! A major part of learning
mathematics involves DOING
mathematics! Also, homework is useful in preparing for the type of questions,
which may appear on quizzes or exams.Many
homework problems will be given on quizzes and some on tests.
Evaluations:There will be given two tests and one final
exam during this short summer term.There will also be given quizzes once or twice a week depending on
whether a test is given that week or not.
GRADING:
Your success in meeting the course objectives will be measured by your scores
on homework, quizzes, lab activities, two one-hour exams (June 10 and June 24),
and a cumulative final exam (July 2, 8:00AM).
The weights of the various components of your grade in
determining your final course gradeare shown below, along with the grade
scale for the course.
WEIGHTS:
GRADE SCALE
1. Two exams (50%)
90-100
A
70-74
C
2. Quizzes, homework (20%)
85-89
B+
65-69
D+
3. Cumulative Final Exam (30%)
80-84
B
60-64
D
75-79
C+
0-59
F
NOTES:
One quiz/homework
grade will be dropped to determine your final quiz average.They will be no makeup quizzes.There will be no makeup tests, except under
special (documented) circumstances.In
the case you cannot an exam at the scheduled time, contact the instructor as
soon as possible after (or before the test), to arrange a make up.Exams not made up within 2 days of the
scheduled date will be recorded 0.
SPECIAL NOTES:
If you have a physical, psychological, and/or learning disability which might affect
your performance in this class, please contact the Office of Disability
Services, 126A B&E, (803) 641-3609, and/or see me, as soon as possible. The
Disability Services Office will determine appropriate accommodations based on
medical documentation.
ATTENDANCE
POLICY: I may occasionally take attendance. It is highly recommended
that the student not miss any class, especially for the very fast pace the
summer sessions. However, the Attendance Policy established by the Department
of Mathematical Sciences states
that the maximum number of unexcused absences allowed in this class before a
penalty is imposed is four for a regular semester.
ACADEMIC CODE OF
HONESTY: Please read and review the Academic Code of Conduct relating to Academic
Honesty located in the Student Handbook. If you are found to be in violation of
this Code of Honesty, a grade of F(0) will be given
for the work. Additionally, a grade of F may be assigned for the course and/or
further sanctions may | 677.169 | 1 |
Reviewing for the AP Statistics Exam with Fathom
Description
Are you looking for some review activities for the AP® Statistics Exam that will enhance students' understanding and refresh their memories? This webinar will focus on short and informative lessons using Fathom that will strengthen your students' skills in preparation for the three-hour exam. The lessons focus on concepts from throughout the AP® Statistics curriculum, from descriptive statistics through inference. The activities can be used in an AP® or general statistics class.
Presenter
Beth Benzing is a moderator of the Teaching Statistics using Fathom online course. She has been teaching AP® Statistics for 12 years and is a reader for the AP® Statistics exam. She has taught a statistics institute for the Math and Science Partnership Program at Arcadia University and will be teaching a statistics institute at West Chester University this summer. Beth sits on the board of a regional affiliate of NCTM in the Philadelphia area. She is a regular presenter at local, state, and national math conferences. She teaches at Strath Haven High School in Wallingford, PA, a southwest suburb of Philadelphia where she lives with her husband and three children. | 677.169 | 1 |
MATHEMATICAL PROBLEM SOLVING
by
James W. Wilson, Maria L. Fernandez, and Nelda Hadaway
Your problem may be modest; but if it challenges your
curiosity and brings into play your inventive faculties, and
if you solve it by your own means, you may experience the tension
and enjoy the triumph of discovery. Such experiences at a susceptible
age may create a taste for mental work and leave their imprint
on mind and character for a lifetime. (26, p. v.)
Problem solving has a special importance in the study of mathematics.
A primary goal of mathematics teaching and learning is to develop
the ability to solve a wide variety of complex mathematics problems.
Stanic and Kilpatrick (43) traced the role of problem solving
in school mathematics and illustrated a rich history of the topic.
To many mathematically literate people, mathematics is synonymous
with solving problems -- doing word problems, creating patterns,
interpreting figures, developing geometric constructions, proving
theorems, etc. On the other hand, persons not enthralled with
mathematics may describe any mathematics activity as problem
solving.
Learning to solve problems is the principal reason for studying
mathematics.
National Council of Supervisors of Mathematics (22)
When two people talk about mathematics problem solving, they
may not be talking about the same thing. The rhetoric of problem
solving has been so pervasive in the mathematics education of
the 1980s and 1990s that creative speakers and writers can put
a twist on whatever topic or activity they have in mind to call
it problem solving! Every exercise of problem solving research
has gone through some agony of defining mathematics problem solving.
Yet, words sometimes fail. Most people resort to a few examples
and a few nonexamples. Reitman (29) defined a problem as when
you have been given the description of something but do not yet
have anything that satisfies that description. Reitman's discussion
described a problem solver as a person perceiving and accepting
a goal without an immediate means of reaching the goal. Henderson
and Pingry (11) wrote that to be problem solving there must be
a goal, a blocking of that goal for the individual, and acceptance
of that goal by the individual. What is a problem for one student
may not be a problem for another -- either because there is no
blocking or no acceptance of the goal. Schoenfeld (33) also pointed
out that defining what is a problem is always relative to the
individual.
How long is the groove on one side of a long-play (33 1/3
rpm) phonograph record? Assume there is a single recording and
the Outer (beginning) groove is 5.75 inches from the center and
the Inner (ending) groove is 1.75 inches from the center. The
recording plays for 23 minutes.
Mathematics teachers talk about, write about, and act upon,
many different ideas under the heading of problem solving. Some
have in mind primarily the selection and presentation of "good"
problems to students. Some think of mathematics program goals
in which the curriculum is structured around problem content.
Others think of program goals in which the strategies and techniques
of problem solving are emphasized. Some discuss mathematics problem
solving in the context of a method of teaching, i.e., a problem
approach. Indeed, discussions of mathematics problem solving often
combine and blend several of these ideas.
In this chapter, we want to review and discuss the research on
how students in secondary schools can develop the ability to solve
a wide variety of complex problems. We will also address how instruction
can best develop this ability. A fundamental goal of all instruction
is to develop skills, knowledge, and abilities that transfer to
tasks not explicitly covered in the curriculum. Should instruction
emphasize the particular problem solving techniques or strategies
unique to each task? Will problem solving be enhanced by providing
instruction that demonstrates or develops problem solving techniques
or strategies useful in many tasks? We are particularly interested
in tasks that require mathematical thinking (34) or higher order
thinking skills (17). Throughout the chapter, we have chosen to
separate and delineate aspects of mathematics problem solving
when in fact the separations are pretty fuzzy for any of us.
Although this chapter deals with problem solving research at the
secondary level, there is a growing body of research focused on
young children's solutions to word problems (6,30). Readers should
also consult the problem solving chapters in the Elementary and
Middle School volumes.
Research on Problem Solving
Educational research is conducted within a variety of constraints
-- isolation of variables, availability of subjects, limitations
of research procedures, availability of resources, and balancing
of priorities. Various research methodologies are used in mathematics
education research including a clinical approach that is frequently
used to study problem solving. Typically, mathematical tasks or
problem situations are devised, and students are studied as they
perform the tasks. Often they are asked to talk aloud while working
or they are interviewed and asked to reflect on their experience
and especially their thinking processes. Waters (48) discusses
the advantages and disadvantages of four different methods of
measuring strategy use involving a clinical approach. Schoenfeld
(32) describes how a clinical approach may be used with pairs
of students in an interview. He indicates that "dialog between
students often serves to make managerial decisions overt, whereas
such decisions are rarely overt in single student protocols."
A nine-digit number is formed using each of the digits 1,2,3,...,9
exactly once. For n = 1,2,3,...,9, n divides the first n digits
of the number. Find the number.
The basis for most mathematics problem solving research for
secondary school students in the past 31 years can be found in
the writings of Polya (26,27,28), the field of cognitive psychology,
and specifically in cognitive science. Cognitive psychologists
and cognitive scientists seek to develop or validate theories
of human learning (9) whereas mathematics educators seek to understand
how their students interact with mathematics (33,40). The area
of cognitive science has particularly relied on computer simulations
of problem solving (25,50). If a computer program generates a
sequence of behaviors similar to the sequence for human subjects,
then that program is a model or theory of the behavior. Newell
and Simon (25), Larkin (18), and Bobrow (2) have provided simulations
of mathematical problem solving. These simulations may be used
to better understand mathematics problem solving.
Constructivist theories have received considerable acceptance
in mathematics education in recent years. In the constructivist
perspective, the learner must be actively involved in the construction
of one's own knowledge rather than passively receiving knowledge.
The teacher's responsibility is to arrange situations and contexts
within which the learner constructs appropriate knowledge (45,48).
Even though the constructivist view of mathematics learning is
appealing and the theory has formed the basis for many studies
at the elementary level, research at the secondary level is lacking.
Our review has not uncovered problem solving research at the secondary
level that has its basis in a constructivist perspective. However,
constructivism is consistent with current cognitive theories of
problem solving and mathematical views of problem solving involving
exploration, pattern finding, and mathematical thinking (36,15,20);
thus we urge that teachers and teacher educators become familiar
with constructivist views and evaluate these views for restructuring
their approaches to teaching, learning, and research dealing with
problem solving.
A Framework
It is useful to develop a framework to think about the processes
involved in mathematics problem solving. Most formulations of
a problem solving framework in U. S. textbooks attribute some
relationship to Polya's (26) problem solving stages. However,
it is important to note that Polya's "stages" were more
flexible than the "steps" often delineated in textbooks.
These stages were described as understanding the problem, making
a plan, carrying out the plan, and looking back. To Polya (28), problem solving was a major theme of doing mathematics
and "teaching students to think" was of primary importance.
"How to think" is a theme that underlies much of genuine
inquiry and problem solving in mathematics. However, care must
be taken so that efforts to teach students "how to think"
in mathematics problem solving do not get transformed into teaching
"what to think" or "what to do." This is,
in particular, a byproduct of an emphasis on procedural knowledge
about problem solving as seen in the linear frameworks of U. S.
mathematics textbooks (Figure 1) and the very limited problems/exercises
included in lessons.
Clearly, the linear nature of the models used in numerous textbooks
does not promote the spirit of Polya's stages and his goal of
teaching students to think. By their nature, all of these traditional
models have the following defects:
1. They depict problem solving as a linear process.
2. They present problem solving as a series of steps.
3. They imply that solving mathematics problems is a procedure
to be memorized, practiced, and habituated.
4. They lead to an emphasis on answer getting.
These linear formulations are not very consistent with genuine
problem solving activity. They may, however, be consistent with
how experienced problem solvers present their solutions and answers
after the problem solving is completed. In an analogous way, mathematicians
present their proofs in very concise terms, but the most elegant
of proofs may fail to convey the dynamic inquiry that went on
in constructing the proof.
Another aspect of problem solving that is seldom included in textbooks
is problem posing, or problem formulation. Although there has
been little research in this area, this activity has been gaining
considerable attention in U. S. mathematics education in recent
years. Brown and Walter (3) have provided the major work on problem
posing. Indeed, the examples and strategies they illustrate show
a powerful and dynamic side to problem posing activities. Polya
(26) did not talk specifically about problem posing, but much
of the spirit and format of problem posing is included in his
illustrations of looking back.
A framework is needed that emphasizes the dynamic and cyclic nature
of genuine problem solving. A student may begin with a problem
and engage in thought and activity to understand it. The student
attempts to make a plan and in the process may discover a need
to understand the problem better. Or when a plan has been formed,
the student may attempt to carry it out and be unable to do so.
The next activity may be attempting to make a new plan, or going
back to develop a new understanding of the problem, or posing
a new (possibly related) problem to work on.
The framework in Figure 2 is useful for illustrating the dynamic,
cyclic interpretation
of Polya's (26) stages. It has been used in a mathematics problem
solving course at the University of Georgia for many years. Any
of the arrows could describe student activity (thought) in the
process of solving mathematics problems. Clearly, genuine problem
solving experiences in mathematics can not be captured by the
outer, one-directional arrows alone. It is not a theoretical model.
Rather, it is a framework for discussing various pedagogical,
curricular, instructional, and learning issues involved with the
goals of mathematical problem solving in our schools.
Problem solving abilities, beliefs, attitudes, and performance
develop in contexts (36) and those contexts must be studied as
well as specific problem solving activities. We have chosen to
organize the remainder of this chapter around the topics of problem
solving as a process, problem solving as an instructional goal,
problem solving as an instructional method, beliefs about problem
solving, evaluation of problem solving, and technology and problem
solving.
Problem Solving as a Process
Garofola and Lester (10) have suggested that students are largely
unaware of the processes involved in problem solving and that
addressing this issue within problem solving instruction may be
important. We will discuss various areas of research pertaining
to the process of problem solving.
Domain Specific Knowledge
To become a good problem solver in mathematics, one must develop
a base of mathematics knowledge. How effective one is in organizing
that knowledge also contributes to successful problem solving.
Kantowski (13) found that those students with a good knowledge
base were most able to use the heuristics in geometry instruction.
Schoenfeld and Herrmann (38) found that novices attended to surface
features of problems whereas experts categorized problems on the
basis of the fundamental principles involved.
Silver (39) found that successful problem solvers were more likely
to categorize math problems on the basis of their underlying similarities
in mathematical structure. Wilson (50) found that general heuristics
had utility only when preceded by task specific heuristics. The
task specific heuristics were often specific to the problem domain,
such as the tactic most students develop in working with trigonometric
identities to "convert all expressions to functions of sine
and cosine and do algebraic simplification."
Algorithms
An algorithm is a procedure, applicable to a particular type
of exercise, which, if followed correctly, is guaranteed to give
you the answer to the exercise. Algorithms are important in mathematics
and our instruction must develop them but the process of carrying
out an algorithm, even a complicated one, is not problem solving.
The process of creating an algorithm, however, and generalizing
it to a specific set of applications can be problem solving. Thus
problem solving can be incorporated into the curriculum by having
students create their own algorithms. Research involving this
approach is currently more prevalent at the elementary level within
the context of constructivist theories.
Heuristics
Heuristics are kinds of information, available to students
in making decisions during problem solving, that are aids to the
generation of a solution, plausible in nature rather than prescriptive,
seldom providing infallible guidance, and variable in results.
Somewhat synonymous terms are strategies, techniques, and rules-of-thumb.
For example, admonitions to "simplify an algebraic expression
by removing parentheses," to "make a table," to
"restate the problem in your own words," or to "draw
a figure to suggest the line of argument for a proof" are
heuristic in nature. Out of context, they have no particular value,
but incorporated into situations of doing mathematics they can
be quite powerful (26,27,28).
Theories of mathematics problem solving (25,33,50) have placed
a major focus on the role of heuristics. Surely it seems that
providing explicit instruction on the development and use of heuristics
should enhance problem solving performance; yet it is not that
simple. Schoenfeld (35) and Lesh (19) have pointed out the limitations
of such a simplistic analysis. Theories must be enlarged to incorporate
classroom contexts, past knowledge and experience, and beliefs.
What Polya (26) describes in How to Solve It is far more
complex than any theories we have developed so far.
Mathematics instruction stressing heuristic processes has been
the focus of several studies. Kantowski (14) used heuristic instruction
to enhance the geometry problem solving performance of secondary
school students. Wilson (50) and Smith (42) examined contrasts
of general and task specific heuristics. These studies revealed
that task specific hueristic instruction was more effective than
general hueristic instruction. Jensen (12) used the heuristic
of subgoal generation to enable students to form problem solving
plans. He used thinking aloud, peer interaction, playing the role
of teacher, and direct instruction to develop students' abilities
to generate subgoals.
Managing It All
An extensive knowledge base of domain specific information,
algorithms, and a repertoire of heuristics are not sufficient
during problem solving. The student must also construct some decision
mechanism to select from among the available heuristics, or to
develop new ones, as problem situations are encountered. A major
theme of Polya's writing was to do mathematics, to reflect on
problems solved or attempted, and to think (27,28). Certainly
Polya expected students to engage in thinking about the various
tactics, patterns, techniques, and strategies available to them.
To build a theory of problem solving that approaches Polya's model,
a manager function must be incorporated into the system. Long
ago, Dewey (8), in How We Think, emphasized self-reflection in
the solving of problems.
Recent research has been much more explicit in attending to this
aspect of problem solving and the learning of mathematics. The
field of metacognition concerns thinking about one's own cognition.
Metacognition theory holds that such thought can monitor, direct,
and control one's cognitive processes (4,41). Schoenfeld (34)
described and demonstrated an executive or monitor component to
his problem solving theory. His problem solving courses included
explicit attention to a set of guidelines for reflecting about
the problem solving activities in which the students were engaged.
Clearly, effective problem solving instruction must provide the
students with an opportunity to reflect during problem solving
activities in a systematic and constructive way.
The Importance of Looking Back
Looking back may be the most important part of problem solving.
It is the set of activities that provides the primary opportunity
for students to learn from the problem. The phase was identified
by Polya (26) with admonitions to examine the solution by such
activities as checking the result, checking the argument, deriving
the result differently, using the result, or the method, for some
other problem, reinterpreting the problem, interpreting the result,
or stating a new problem to solve.
Teachers and researchers report, however, that developing the
disposition to look back is very hard to accomplish with students.
Kantowski (14) found little evidence among students of looking
back even though the instruction had stressed it. Wilson (51)
conducted a year long inservice mathematics problem solving course
for secondary teachers in which each participant developed materials
to implement some aspect of problem solving in their on-going
teaching assignment. During the debriefing session at the final
meeting, a teacher put it succinctly: "In schools, there
is no looking back." The discussion underscored the agreement
of all the participants that getting students to engage in looking
back activities was difficult. Some of the reasons cited were
entrenched beliefs that problem solving in mathematics is answer
getting; pressure to cover a prescribed course syllabus; testing
(or the absence of tests that measure processes); and student
frustration.
The importance of looking back, however, outweighs these difficulties.
Five activities essential to promote learning from problem solving
are developing and exploring problem contexts, extending problems,
extending solutions, extending processes, and developing self-reflection.
Teachers can easily incorporate the use of writing in mathematics
into the looking back phase of problem solving. It is what you
learn after you have solved the problem that really counts.
Problem Posing
Problem posing (3) and problem formulation (16) are logically
and philosophically appealing notions to mathematics educators
and teachers. Brown and Walter provide suggestions for implementing
these ideas. In particular, they discuss the "What-If-Not"
problem posing strategy that encourages the generation of new
problems by changing the conditions of a current problem. For
example, given a mathematics theorem or rule, students may be
asked to list its attributes. After a discussion of the attributes,
the teacher may ask "what if some or all of the given attributes
are not true?" Through this discussion, the students generate
new problems.
Brown and Walter provide a wide variety of situations implementing
this strategy including a discussion of the development of non-Euclidean
geometry. After many years of attempting to prove the parallel
postulate as a theorem, mathematicians began to ask "What
if it were not the case that through a given external point there
was exactly one line parallel to the given line? What if there
were two? None? What would that do to the structure of geometry?"
(p.47). Although these ideas seem promising, there is little explicit
research reported on problem posing.
Problem Solving as an Instructional Goal
What is mathematics?
If our answer to this question uses words like exploration,
inquiry, discovery, plausible reasoning, or problem solving, then
we are attending to the processes of mathematics. Most of us would
also make a content list like algebra, geometry, number, probability,
statistics, or calculus. Deep down, our answers to questions such
as What is mathematics? What do mathematicians do? What do mathematics
students do? Should the activities for mathematics students model
what mathematicians do? can affect how we approach mathematics
problems and how we teach mathematics.
The National Council of Teachers of Mathematics (NCTM) (23,24)
recommendations to make problem solving the focus of school mathematics
posed fundamental questions about the nature of school mathematics.
The art of problem solving is the heart of mathematics. Thus,
mathematics instruction should be designed so that students experience
mathematics as problem solving.
The National Council of Teachers of Mathematics recommends
that --
l. problem solving be the focus of school mathematics in the
1980s.
An Agenda for Action (23)
We strongly endorse the first recommendation of An Agenda for
Action. The initial standard of each of the three levels addresses
this goal.
Curriculum and Evaluation Standards (24)
Why Problem Solving?
The NCTM (23,24) has strongly endorsed the inclusion of problem
solving in school mathematics. There are many reasons for doing
this.
First, problem solving is a major part of mathematics. It is the
sum and substance of our discipline and to reduce the discipline
to a set of exercises and skills devoid of problem solving is
misrepresenting mathematics as a discipline and shortchanging
the students. Second, mathematics has many applications and often
those applications represent important problems in mathematics.
Our subject is used in the work, understanding, and communication
within other disciplines. Third, there is an intrinsic motivation
embedded in solving mathematics problems. We include problem solving
in school mathematics because it can stimulate the interest and
enthusiasm of the students. Fourth, problem solving can be fun.
Many of us do mathematics problems for recreation. Finally, problem
solving must be in the school mathematics curriculum to allow
students to develop the art of problem solving. This art is so
essential to understanding mathematics and appreciating mathematics
that it must be an instructional goal.
Teachers often provide strong rationale for not including problem
solving activities is school mathematics instruction. These include
arguments that problem solving is too difficult, problem solving
takes too much time, the school curriculum is very full and there
is no room for problem solving, problem solving will not be measured
and tested, mathematics is sequential and students must master
facts, procedures, and algorithms, appropriate mathematics problems
are not available, problem solving is not in the textbooks, and
basic facts must be mastered through drill and practice before
attempting the use of problem solving. We should note, however,
that the student benefits from incorporating problem solving into
the mathematics curriculum as discussed above outweigh this line
of reasoning. Also we should caution against claiming an emphasize
on problem solving when in fact the emphasis is on routine exercises.
From various studies involving problem solving instruction, Suydam
(44) concluded:
If problem solving is treated as "apply the procedure,"
then the students try to follow the rules in subsequent problems.
If you teach problem solving as an approach, where you must think
and can apply anything that works, then students are likely to
be less rigid. (p. 104)
Problem Solving as an Instructional Method
Problem solving as a method of teaching may be used to accomplish
the instructional goals of learning basic facts, concepts, and
procedures, as well as goals for problem solving within problem
contexts. For example, if students investigate the areas of all
triangles having a fixed perimeter of 60 units, the problem solving
activities should provide ample practice in computational skills
and use of formulas and procedures, as well as opportunities for
the conceptual development of the relationships between area and
perimeter. The "problem" might be to find the triangle
with the most area, the areas of triangles with integer sides,
or a triangle with area numerically equal to the perimeter. Thus
problem solving as a method of teaching can be used to introduce
concepts through lessons involving exploration and discovery.
The creation of an algorithm, and its refinement, is also a complex
problem solving task which can be accomplished through the problem
approach to teaching. Open ended problem solving often uses problem
contexts, where a sequence of related problems might be explored.
For example, the problems in the investigations in the insert evolved from considering
gardens of different shapes that could be enclosed with 100 yards
of fencing:
Suppose one had 100 yards of fencing to enclose a garden.
What shapes could be enclosed? What are the dimensions of each
and what is the area? Make a chart.
What triangular region with P = 100 has the most area?
Find all five triangular regions with P = 100 having integer
sides and integer area. (such as 29, 29, 42)
What rectangular regions could be enclosed? Areas? Organize a
table? Make a graph?
Which rectangular region has the most area? from a table? from
a graph? from algebra, using the arithmetic mean-geometric mean
inequality?
What is the area of a regular hexagon with P = 100?
What is the area of a regular octagon with P = 100?
What is the area of a regular n-gon with P = 100? Make a table
for n = 3 to 25. Make a graph. What happens to 1/n(tan 180/n)
as n increases?
What if part of the fencing is used to build a partition perpendicular
to a side? Consider a rectangular region with one partition?
With 2 partitions? with n partitions? (There is a surprise in
this one!!) What if the partition is a diagonal of the rectangle?
What is the maximum area of a sector of a circle with P = 100?
(Here is another surprise!!! -- could you believe it is r2 when
r = 25? How is this similar to a square being the maximum rectangle
and the central angle of the maximum sector being 2 radians?)
What about regions built along a natural boundary? For example
the maximum for both a rectangular region and a triangular region
built along a natural boundary with 100 yards of fencing is 1250
sq. yds. But the rectangle is not the maximum area four-sided
figure that can be built. What is the maximum-area four-sided
figure?
Many teachers in our workshops have reported success with a
"problem of the week" strategy. This is often associated
with a bulletin board in which a challenge problem is presented
on a regular basis (e.g., every Monday). The idea is to capitalize
on intrinsic motivation and accomplishment, to use competition
in a constructive way, and to extend the curriculum. Some teachers
have used schemes for granting "extra credit" to successful
students. The monthly calendar found in each issue of The Mathematics
Teacher is an excellent source of problems.
Whether the students encounter good mathematics problems depends
on the skill of the teacher to incorporate problems from various
sources (often not in textbooks). We encourage teachers to begin
building a resource book of problems oriented specifically to
a course in their on-going workload. Good problems can be found
in the Applications in Mathematics (AIM Project) materials
(21) consisting of video tapes, resource books and computer diskettes
published by the Mathematical Association of America. These problems
can often be extended or modified by teachers and students to
emphasize their interests. Problems of interest for teachers and
their students can also be developed through the use of The
Challenge of the Unknown materials (1) developed by the American
Association for the Advancement of Science. These materials consist
of tapes providing real situations from which mathematical problems
arise and a handbook of ideas and activities that can be used
to generate other problems.
Beliefs about Mathematics Problem Solving
The importance of students' (and teachers') beliefs about mathematics
problem solving lies in the assumption of some connection between
beliefs and behavior. Thus, it is argued, the beliefs of mathematics
students, mathematics teachers, parents, policy makers, and the
general public about the roles of problem solving in mathematics
become prerequisite or co-requisite to developing problem solving.
The Curriculum and Evaluation Standards makes the point
that "students need to view themselves as capable of using
their growing mathematical knowledge to make sense of new problem
situations in the world around them" (24, p. ix.). We prefer
to think of developing a sense of "can do" in our students
as they encounter mathematics problems.
Schoenfeld (36,37) reported results from a year-long study
of detailed observations, analysis of videotaped instruction,
and follow-up questionnaire data from two tenth-grade geometry
classes. These classes were in select high schools and the classes
were highly successful as determined by student performance on
the New York State Regent's examination. Students reported beliefs
that mathematics helps them to think clearly and they can be creative
in mathematics, yet, they also claimed that mathematics is learned
best by memorization. Similar contrasts have been reported for
the National Assessment (5). Indeed our conversations with teachers
and our observations portray an overwhelming predisposition of
secondary school mathematics students to view problem solving
as answer getting, view mathematics as a set of rules, and be
highly oriented to doing well on tests.
Schoenfeld (37) was able to tell us much more about the classes
in his study. He makes the following points.
The rhetoric of problem solving has become familiar over
the past decade. That rhetoric was frequently heard in the classes
we observed -- but the reality of those classrooms is that real
problems were few and far between . . . virtually all problems
the students were asked to solve were bite-size exercises designed
to achieve subject matter mastery: the exceptions were clearly
peripheral tasks that the students found enjoyable but that they
considered to be recreations or rewards rather than the substance
they were expected to learn . . . the advances in mathematics
education in the [past] decade . . . have been largely in our
acquiring a more enlightened goal structure, and having students
pick up the rhetoric -- but not the substance -- related to those
goals. (pp. 359-9)
Each of us needs to ask if the situation Schoenfeld describes
is similar to our own school. We must take care that espoused
beliefs about problem solving are consistent with a legitimately
implemented problem solving focus in school mathematics.
Technology and Problem Solving
The appropriate use of technology for many people has significant
identity with mathematics problem solving. This view emphasizes
the importance of technology as a tool for mathematics problem
solving. This is in contrast to uses of technology to deliver
instruction or for generating student feedback.
Programming as Problem Solving
In the past, problem solving research involving technology
has often dealt with programming as a major focus. This research
has often provided inconclusive results. Indeed, the development
of a computer program to perform a mathematical task can be a
challenging mathematical problem and can enhance the programmer's
understanding of the mathematics being used. Too often, however,
the focus is on programming skills rather than on using programming
to solve mathematics problems. There is a place for programming
within mathematics study, but the focus ought to be on the mathematics
problems and the use of the computer as a tool for mathematics
problem solving.
A ladder 5 meters long leans against a wall, reaching over
the top of a box that is 1 meter on each side. The box is against
the wall. What is the maximum height on the wall that the ladder
can reach? The side view is:
Assume the wall is perpendicular to the floor. Use your calculator
to find the maximum height to the nearest .01 meter.
Iteration
Iteration and recursion are concepts of mathematics made available
to the secondary school level by technology. Students may implement
iteration by writing a computer program, developing a procedure
for using a calculator, writing a sequence of decision steps,
or developing a classroom dramatization. The approximation of
roots of equations can be made operational with a calculator or
computer to carry out the iteration.
For example, the process for finding the three roots of
is not very approachable without iterative techniques. Iteration
is also useful when determining the maximum height, h, between
a chord and an arc of a circle when the length S of the arc and
the length L of the chord are known. This may call for solving
simultaneously and using iterative techniques to find the radius
r and and central angle ø in order to evaluate h = r -
r cos ø. Fractals can also be explored through the use
of iterative techniques and computer software.
Exploration
Technology can be used to enhance or make possible exploration
of conceptual or problem situations. For example, a function grapher
computer program or a graphics calculator can allow student exploration
of families of curves such as
for different values of a, b, and c.
A calculator can be used to explore sequences such as
for different values of a. In this way, technology introduces
a dynamic aspect to investigating mathematics.
Thomas (46) studied the use of computer graphic problem solving
activities to assist in the instruction of functions and transformational
geometry at the secondary school level. The students were challenged
to create a computer graphics design of a preselected picture
using graphs of functions and transformational geometry. Thomas
found these activities helped students to better understand function
concepts and improved student attitudes.
Evaluation of Problem Solving
As the emphasis on problem solving in mathematics classrooms
increases, the need for evaluation of progress and instruction
in problem solving becomes more pressing. It no longer suffices
for us to know which kinds of problems are correctly and incorrectly
solved by students. As Schoenfeld (36) describes:
All too often we focus on a narrow collection of well-defined
tasks and train students to execute those tasks in a routine,
if not algorithmic fashion. Then we test the students on tasks
that are very close to the ones they have been taught. If they
succeed on those problems, we and they congratulate each other
on the fact that they have learned some powerful mathematical
techniques. In fact, they may be able to use such techniques
mechanically while lacking some rudimentary thinking skills.
To allow them, and ourselves, to believe that they "understand"
the mathematics is deceptive and fraudulent. (p. 30)
Schoenfeld (31) indicates that capable mathematics students
when removed from the context of coursework have difficulty doing
what may be considered elementary mathematics for their level
of achievement. For example, he describes a situation in which
he gave a straightforward theorem from tenth grade plane geometry
to a group of junior and senior mathematics majors at the University
of California involved in a problem solving course. Of the eight
students solving this problem only two made any significant progress.
We need to focus on the teaching and learning of mathematics and,
in turn, problem solving using a holistic approach. As recommended
in the NCTM's An Agenda for Action (23), "the success
of mathematics programs and student learning [must] be evaluated
by a wider range of measures than conventional testing" (p.
1). Although this recommendation is widely accepted among mathematics
educators, there is a limited amount of research dealing with
the evaluation of problem solving within the classroom environment.
Classroom research: Ask your students to keep a
problem solving notebook in which they record on a weekly basis:
(1) their solution to a mathematics problem.
(2) a discussion of the strategies they used to solve the problem.
(3) a discussion of the mathematical similarities of this problem
with other problems they have solved.
(4) a discussion of possible extensions for the problem.
(5) an investigation of at least one of the extensions they discussed.
Use these notebooks to evaluate students' progress. Then
periodically throughout the year, analyze the students' overall
progress as well as their reactions to the notebooks in order
to asses the effectiveness of the evaluation process.
Some research dealing with the evaluation of problem solving
involves diagnosing students' cognitive processes by evaluating
the amount and type of help needed by an individual during a problem
solving activity. Campione, Brown, and Connell (4) term this method
of evaluation as dynamic assessment. Students are given mathematics
problems to solve. The assessor then begins to provide as little
help as necessary to the students throughout their problem solving
activity. The amount and type of help needed can provide good
insight into the students' problem solving abilities, as well
as their ability to learn and apply new principles. Trismen (47)
reported the use of hints to diagnosis student difficulties in
problem solving in high school algebra and plane geometry. Problems
were developed such that the methods of solutions where not readily
apparent to the students. A sequence of hints was then developed
for each item. According to Trismen, "the power of the hint
technique seems to lie in its ability to identify those particular
students in need of special kinds of help" (p. 371).
Campione and his colleagues (4) also discussed a method to help
monitor and evaluate the progress of a small cooperative group
during a problem solving session. A learning leader (sometimes
the teacher sometimes a student) guides the group in solving the
problem through the use of three boards: (1) a Planning Board,
where important information and ideas about the problem are recorded,
(2) a Representation Board, where diagrams illustrating the problems
are drawn, and (3) a Doing Board, where appropriate equations
are developed and the problem is solved. Through the use of this
method, the students are able to discuss and reflect on their
approaches by visually tracing their joint work. Campione and
his colleagues indicated that increased student engagement and
enthusiasm in problem solving, as well as, increased performance
resulted from the use of this method for solving problems.
Methods, such as the clinical approach discussed earlier, used
to gather data dealing with problem solving and individual's thinking
processes may also be used in the classroom to evaluate progress
in problem solving. Charles, Lester, and O'Daffer (7) describe
how we may incorporate these techniques into a classroom problem
solving evaluation program. For example, thinking aloud may be
canonically achieved within the classroom by placing the students
in cooperative groups. In this way, students may express their
problem solving strategies aloud and thus we may be able to assess
their thinking processes and attitudes unobtrusively. Charles
and his colleagues also discussed the use of interviews and student
self reports during which students are asked to reflect on their
problem solving experience a technique often used in problem solving
research. Other techniques which they describe involve methods
of scoring students' written work. Figure 3 illustrates a final
assignment used to assess teachers' learning in a problem solving
course that has been modified to be used with students at the
secondary level.
Testing, unfortunately, often drives the mathematics curriculum.
Most criterion referenced testing and most norm referenced testing
is antithetical to problem solving. Such testing emphasizes answer
getting. It leads to pressure to "cover" lots of material
and teachers feel pressured to forego problem solving. They may
know that problem solving is desirable and developing understanding
and using appropriate technology are worthwhile, but ... there
is not enough time for all of that and getting ready for the tests.
However, teachers dedicated to problem solving have been able
to incorporate problem solving into their mathematics curriculum
without bringing down students' scores on standardized tests.
Although test developers, such as the designers of the California
Assessment Program, are beginning to consider alternative test
questions, it will take time for these changes to occur. By committing
ourselves to problem solving within our classrooms, we will further
accentuate the need for changes in testing practices while providing
our students with invaluable mathematics experiences.
Looking Ahead ...
We are struck by the seemingly contradictory facts that there
is a vast literature on problem solving in mathematics and, yet,
there is a multitude of questions to be studied, developed, and
written about in order to make genuine problem solving activities
an integral part of mathematics instruction. Further, although many may view this as primarily a curriculum
question, and hence call for restructured textbooks and materials,
it is the mathematics teacher who must create the context for
problem solving to flourish and for students to become problem
solvers. The first one in the classroom to become a problem solver
must be the teacher.
Still Wondering About ...
The primary goal of most students in mathematics classes is
to see an algorithm that will give them the answer quickly. Students
and parents struggle with (and at times against) the idea that
math class can and should involve exploration, conjecturing, and
thinking. When students struggle with a problem, parents often
accuse them of not paying attention in class; "surely the
teacher showed you how to work the problem!" How can parents,
students, colleagues, and the public become more informed regarding
genuine problem solving? How can I as a mathematics teacher in
the secondary school help students and their parents understand
what real mathematics learning is all about?
Nelda Hadaway, James W. Wilson, and Maria L. Fernandez
References
*1. American Association for the Advancement of Science. (1986).
The challenge of the unknown. New York: Norton.
11. Henderson, K. B. & Pingry, R. E. (1953). Problem solving
in mathematics. In H. F. Fehr (Ed.), The learning of mathematics:
Its theory and practice (21st Yearbook of the National Council
of Teachers of Mathematics) (pp. 228-270). Washington, DC: National
Council of Teachers of Mathematics.
22. National Council of Supervisors of Mathematics. (1978). Position
paper on basic mathematical skills. Mathematics Teacher, 71(2),
147-52. (Reprinted from position paper distributed to members
January 1977.)
23. National Council of Teachers of Mathematics. (1980). An agenda
for action: Recommendations for school mathematics in the 1980s.
Reston, VA: The Author.
24. National Council of Teachers of Mathematics. (1989). Curriculum
and evaluation standards for school mathematics. Reston, VA: The
Author.
Nelda Hadaway received a B.S. Ed., an M. Ed., and
an Ed. S. from The University of Georgia in Athens, Georgia and
the Ph. D. from Georgia State University in Atlanta. She has taught
mathematics at Hunter College High School in the New YorkCity
and presently teaches mathematics at South Gwinnett High School
in Snellville, Georgia. She is interested in integrating writing
into the teaching of mathematics to enhance problem solving.
James W. Wilson is a Professor of Mathematics Education at The
University of Georgia. He has a B.S. and M.A. from Kansas State
Teachers College, M.S. from University of Notre Dame, and M.S.
and Ph.D. from Stanford University. He has been interested in
problem solving for many years. His doctoral research dealt with
problem solving and his Problem Solving in Mathematics course
is a regular offering at The University of Georgia. Over the years,
he has also been involved in various problem solving projects
including the U.S.-Japan Joint Seminar on Problem Solving in School
Mathematics.
Maria L. Fernandez is an Associate Professor of Mathematics Education
at Florida International University. She completed both a B.S. and M.S.
in Mathematics Education at Florida International University in
Miami, Florida and the Ph. D. at the University of Georgia. She previously taught at the University of Arizona and at Florida State University. She
is interested in incorporating problem solving into the mathematics
curriculum at all levels. While teaching mathematics at the secondary
level in Miami, she integrated problem solving into the curriculum
using various strategies. Her research interests involve mathematics
visualizations in problem solving. | 677.169 | 1 |
Final Review
Sample Topics and Questions
This is not an exclusive list. It is merely meant to highlight some
of the major topics covered since the second midterm. It also includes
topics that may be appropriately asked on the two midterms. Students are also
referred to the topics listed on the review pages for the first and
second midterms.
Avoid "Catastrophic cancellation" in certain expressions.
Find the next n intervals using the bisection method for
a function.
Given the time it takes to solve a certain sized system
via Gaussian elimination, how long does it take to solve a different
sized system.
Decompose a matrix into an LU-decomposition.
Find the normal equations for a linear system.
Use the Gauss-Seidel iteration method to find several
iterations for a linear system.
Use the trapezoidal rule to approximate the integral.
Use Richardson's extrapolation to get a better approximation.
How many panels are needed to get a certain degree of
accuracy via Simpson's rule?
Use Gaussian quadrature to evaluate an integral.
Create a new quadrature formula.
Change an n-th order ODE into a coupled system of first
order ODEs.
"Solve" an ODE-BVP by discretization techniques, i.e.,
set up the appropriate linear system in matrix form. | 677.169 | 1 |
Description
The Bittinger Graphs and Models Series helps students "see the math" and learn algebra by making connections between mathematical concepts and their real-world applications. The authors use a variety of tools and techniques—including side-by-side algebraic and graphical solutions and graphing calculators, when appropriate—to engage and motivate all types of learners. Abundant applications, many of which use real data, provide a context for learning and understanding the math.
Table of Contents
Preface
1. Basics of Algebra and Graphing
1.1 Some Basics of Algebra
1.2 Operations with Real Numbers
1.3 Equivalent Algebraic Expressions
1.4 Exponential Notation and Scientific Notation
Mid-Chapter Review
1.5 Graphs
1.6 Solving Equations and Formulas
1.7 Introduction to Problem Solving and Models
Summary and Review
Test
2. Functions, Linear Equations, and Models
2.1 Functions
2.2 Linear Functions: Slope, Graphs, and Models
2.3 Another Look at Linear Graphs
2.4 Introduction to Curve Fitting: Point-Slope Form
Mid-Chapter Review
2.5 The Algebra of Functions
Summary and Review
Test
3. Systems of Linear Equations and Problem Solving
3.1 Systems of Equations in Two Variables
3.2 Solving by Substitution or Elimination
3.3 Solving Applications: Systems of Two Equations
Mid-Chapter Review
3.4 Systems of Equations in Three Variables
3.5 Solving Applications: Systems of Three Equations
3.6 Elimination Using Matrices
3.7 Determinants and Cramer's Rule
3.8 Business and Economics Applications
Summary and Review
Test
Cumulative Review: Chapters 1—3
4. Inequalities
4.1 Inequalities and Applications
4.2 Solving Equations and Inequalities by Graphing
4.3 Intersections, Unions, and Compound Inequalities
4.4 Absolute-Value Equations and Inequalities
Mid-Chapter Review
4.5 Inequalities in Two Variables
Summary and Review
Test
5. Polynomials and Polynomial Functions
5.1 Introduction to Polynomials and Polynomial Functions
5.2 Multiplication of Polynomials
5.3 Polynomial Equations and Factoring
5.4 Trinomials of the Type x2 + bx + c
5.5 Trinomials of the Type ax2 + bx + c
5.6 Perfect-Square Trinomials and Differences of Squares
5.7 Sums or Differences of Cubes
Mid-Chapter Review
5.8 Applications of Polynomial Equations
Summary and Review
Test
6. Rational Expressions, Equations, and Functions
6.1 Rational Expressions and Functions: Multiplying and Dividing
6.2 Rational Expressions and Functions: Adding and Subtracting
6.3 Complex Rational Expressions
Mid-Chapter Review
6.4 Rational Equations
6.5 Applications Using Rational Equations
6.6 Division of Polynomials
6.7 Synthetic Division
6.8 Formulas, Applications, and Variation
Summary and Review
Test
Cumulative Review: Chapters 1—6
7. Exponents and Radical Functions
7.1 Radical Expressions, Functions, and Models
7.2 Rational Numbers as Exponents
7.3 Multiplying Radical Expressions
7.4 Dividing Radical Expressions
7.5 Expressions Containing Several Radical Terms
Mid-Chapter Review
7.6 Solving Radical Equations
7.7 The Distance Formula, the Midpoint Formula, and Other Applications
7.8 The Complex Numbers
Summary and Review
Test
8. Quadratic Functions and Equations
8.1 Quadratic Equations
8.2 The Quadratic Formula
8.3 Studying Solutions of Quadratic Equations
8.4 Studying Solutions of Quadratic Equations
8.5 Equations Reducible to Quadratic
Mid-Chapter Review
8.6 Quadratic Functions and Their Graphs
8.7 More About Graphing Quadratic Functions
8.8 Problem Solving and Quadratic Functions
8.9 Polynomial Inequalities and Rational Inequalities
Summary and Review
Test
9. Exponential Functions and Logarithmic Functions
9.1 Composite Functions and Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithmic Functions
Mid-Chapter Review
9.5 Natural Logarithms and Changing Bases
9.6 Solving Exponential and Logarithmic Equations
9.7 Applications of Exponential and Logarithmic Functions
Summary and Review
Test
Cumulative Review: Chapters 1—9
10. Conic Sections
10.1 Conic Sections: Parabolas and Circles
10.2 Conic Sections: Ellipses
10.3 Conic Sections: Hyperbolas
Mid-Chapter Review
10.4 Nonlinear Systems of Equations
Summary and Review
Test
11. Sequences, Series, and the Binomial Theorem
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
Mid-Chapter Review
11.4 The Binomial Theorem
Summary and Review
Test
Cumulative Review: Chapters 1-11
Answers
Glossary
Photo Credits | 677.169 | 1 |
Download
Next: Expresiones Variables
Chapter 1: Ecuaciones y Funciones
Chapter Outline
Loading Content
Chapter Summary
Description
This chapter covers evaluating algebraic expressions, order of operations, using verbal models to write equations, solving problems using equations, inequalities, identifying the domain and range of a function, and graphs of functions. | 677.169 | 1 |
Algebra Combat, players alternate turns to see who can solve sets of single-variable linear equations with the best time and accuracy. Equations are randomly generated in one of four difficulty levels. All solutions are integers less than 40 and presented as multiple choice.
Beginners may need to jot down a step or two on a piece of paper. More advanced players will be able to solve these problems on the fly. With continued gameplay, students develop increased confidence with entry level algebraic expressions, negative integers, and quick mental calculations.
Both practice and competition modes are included. All rounds contain 5 equations to solve. Scores and times are provided following each round. A "Current Rankings" score tally also follows each competition round. Best rounds of all time are entered into the "Top Fighters" hall of fame along with the player's name, time, score, and difficulty level played.
In keeping with the cage fight theme, players are encouraged to give their fighters a cool name and type in a little "trash talk" before each round. All trash talk messages are then delivered to the opposing player at the beginning of his or her turn… ensuring matches are both spirited and entertaining. | 677.169 | 1 |
MAT-121 College Algebra
A college-level algebra course that provides an understanding of algebraic concepts, processes and practical applications. Topics include linear equations and inequalities, quadratic equations, systems of equations and inequalities, complex numbers, exponential and logarithmic expressions, and functions and basic probability.
Advisory: it is advisable to have knowledge in a course equivalent to MAT-115 Intermediate are only permitted to take one of the following courses: MAT-119, MAT-121 or MAT-128. BSBA and ASBA students should not take MAT-121. BSAST and ASAST students should take MAT-121 and MAT-129. | 677.169 | 1 |
With a new
foreword by Dan Rockmore, Chair of the Department of Mathematics
at Dartmouth College
Translated
from Japanese
by Alan Gleason
Second Edition
Published 2012
426 pages
Paperback, fully illustrated
ISBN 978-0-9643504-3-4
$29.95
The
student authors take the reader along on their adventure of discovery,
creating an interactive work that gradually moves from the very basics
("What is a right triangle?") to the more complicated mathematics of
trigonometry, exponentiation, differentiation, and integration. This
is done in a way that is not only easy to understand, but actually fun!
While it is user-friendly
enough even for those who are "math phobic," Who is Fourier?
has been enjoyed by many people in the math and science fields. The
largest percentage of our readers are professors and engineers, with
business people and students following closely. It is a must-have for
anyone interested in mathematics, physics, engineering, or complex science.
Over 60,000 copies have sold in Japan since the original publication!
"An
approach to the teaching of elementary Fourier series that
is innovative, conceptual and appealingly informal."
--Dr.
John Allen Paulos, author of Innumeracy
Want to take a
look at Who is Fourier? for yourself? Barnes & Noble and
Amazon.com typically carry our books, or you can special order it from
your favorite bookstore! | 677.169 | 1 |
Sections of the MAA
At present, the MAA has 29 sections, which are defined by ZIP or postal code. Sections are a vital component of the MAA, and a significant part of the Association's activity is centered on them. Each section holds at least one professional meeting per year, usually in the Spring.
Section meetings include, but not limited to:
Invited lectures
Contributed papers
Panel discussions
Other activities designed to promote and improve collegiate level mathematics
Programs of upcoming section meetings, if not available via the links below, may be obtained from the appropriate section secretary.
Many sections also conduct activities that involve both high school and college students. These include:
Sponsoring mathematics contests
Advising state departments of education on teacher certification in the mathematical sciences
Working with high schools and colleges on course content and curricula
Providing lecturers to colleges and high schools
Active MAA members who reside in the United States and Canada have the benefit of being affiliated with one of 29 sections.
Find My Section
Enter Zip Code or Canadian Postal Code
Borders for each section are roughly illustrated in the map below. Click map to see the full-sized version. | 677.169 | 1 |
How do structural engineers predict how much the Bay Bridge will
sway during an earthquake? How does the Federal Reserve analyze
stock market fluctuations to help determine when to cut interest
rates? What model do bio logists use to describe the rate of stem
cell growth in human embryos? The answer to all of these
questions involves mathematical objects called functions. The
study of functions is where calculus begins! We will mostly look at
functions which will be important to us in calculus namely,
polynomial, logarithmic and exponential functions.
One of the great accomplishments in modern mathematics is to
apply these functions to study real world situations. Calculus
teaches you how to use functions to study velocities and
accele rations of moving bodies, find the firing angle that gives a
cannon its greatest range, or calculate the area of irregular regions
in the plane. Calculus is a really fun subject because you will learn
to use powerful ideas that took centuries to develop. It is also a
really challenging subject because it requires solid algebra skills
and has thought provoking concepts.
Homework:
Problems will be as signed at the end of each class. It is important
for your success in the course that you attempt to do those
problems before the following class meeting. The struggle to solve
them prepares you for the following class.
You may discuss the homework by forming a group and studying
with your peers. If you need help please come to my office or go to
Sichel 105, the Academic Support and Achievement Program, and
ask for a tutor. Act fast and do not fall behind.
A completed homework assignment should be folded
lengthwise in half. On the outside front half, print your name,
the assignment number , the due date of the assignment, and
the time you spent doing the assignment. Please staple your
homework.
Attendance:
Attendance is required and roll will be taken at the
beginning of
each hour. If you are not in your seat when roll is taken, you may
be considered absent, so be on time. You are allowed to miss three
classes without affecting your grade. After your grade is dropped
one step (A- to B+, C+ to C, etc.). Thereafter, each two successive
absences your grade is dropped one step further. If there is a major
illness or incapacitation, speak to your instructor. SMC athletes are
excused to attend team commitments but are responsible for
notifying me ahead of time (see below).
Exams:
There will be three midterm examinations and a final exam.
Suppose a student receives the following grades.
First Midterm
Second Midterm
Third Midterm
Final Exam
Homework Grade
Then the lowest of the Midterm/Final Exam grades above is
dropped. If you miss a midterm exam that is the grade you drop.
The final grade for the course is the average of the remaining five
grades, in this example a B-. The Homework Grade cannot be
dropped.
Honor code:
Students are expected to abide by the SMC honor code when
taking exams and doing course work. | 677.169 | 1 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
MATH 3283W. Sequences, Series, and Foundations: Writing Intensive. Spring 2009Homework 1. Problems and Solutions I. Writing Intensive Part 1 (5 points). Check whether or not each of the following statements can be true for some values ("true" or "false")
These notes by Mikhail Safonov serve as a supplementary material to the textbook by Weyne Richter "Sequences, Series and Foundations. Math 2283 and 3283W"Sequences, Series and FoundationsChapter 1. Truth, Falsity and Mathematical Induction1 Truth Table
Math 5615H. Name (Print)October 5, 2011.Midterm Exam.60 points are distributed between 5 problems. You have 50 minutes (2:30 pm 3:20 pm) to work on these problems. No books, no notes. Calculators are permitted, however, for full credit, you need to sho
Math 5615H: Introduction to Analysis I.Fall 2011Homework #2 (due on Wednesday, September 21). 50 points are divided between 5 problems, 10 points each. #1. Let F be a field. Show that there exist not more that two different solutions solutions of the eq
Math 5615H: Introduction to Analysis I.Fall 2011Homework #4 (due on Wednesday, October 5). 50 points are divided between 5 problems, 10 points each. #1. Let f be a mapping of A to B. Show that for each B1 B and B2 B, their inverse images satisfy the pro
Math 5615H: Introduction to Analysis I.Fall 2011Homework #6 (due on Wednesday, October 19). 50 points are divided between 5 problems, 10 points each. #1. Show that for an arbitrary set E in a metric space (X, d), the set E of its limit point is closed.
Math 5615H: Introduction to Analysis I.Fall 2011Homework #7 (due on Wednesday, October 26). 50 points are divided between 4 problems. You can use the following Theorem which was proved in class. Theorem. A subset K of a metric space (X, d) is compact in
Math 5615H: Introduction to Analysis I.Fall 2011Homework #1. Problems and short Solutions. #1. Prove that 6 and 2 + 3 are NOT rational. Proof. If p := 6 Q, then p2 = 6, and we get a contradiction in the same way as in Example 1.1 in the textbook. If q :
Math 5615H: Introduction to Analysis I. Homework #2. Problems and Solutions.Fall 2011#1. Let F be a field. Show that there exist not more that two different solutions solutions of the equation x x = 1. Is it possible that there is only one solution to t
Math 5615H: Introduction to Analysis I. Homework #6. Problems and Solutions.Fall 2011#1. Show that for an arbitrary set E in a metric space (X, d), the set E of its limit point is closed. Proof. Let p be a limit point of E . Then r > 0, the set Gr := Nr
Math 5615H: Introduction to Analysis I. Homework #7. Problems and Solutions.Fall 2011You can use the following Theorems which were discussed in class. Theorem 1. A subset K of a metric space (X, d) is compact in X if and only if every infinite subset E
Math 5615H: Introduction to Analysis I. Homework #13. Problems and Solutions.Fall 2011#1. If f is a continuous mapping of a metric space X into a metric space Y , prove that f (E) f (E) for every set E X. (E denotes the closure of E). Show, by an exampl
Math 8601: REAL ANALYSIS. Fall 2010 Problems for Final Exam on Saturday, December 18, 4pm6pm, VinH 1. This Final Exam will be based on the material from the textbook, in the following Sections: 0.50.6, 1.11.5 ,2.12.5, 2.6 (Theorems 2.40, 2.41), 3.13.2, 3.
Math 8601: REAL ANALYSIS. Fall 2010 Some problems for Midterm Exam #1 on Wednesday, October 6. You will have 50 minutes (10:10 am11:00 am) to work on 5 problems, 2 of which will be selected from the following list. It is recommended to prepare solutions o
Math 8601: REAL ANALYSIS. Fall 2010 Problems for Midterm Exam #2 on Wednesday, November 17. This Midterm will be based on the material for the textbook up to (including) Section 2.3. You will have 50 minutes (10:10 am11:00 am) to work on 5 problems, 2 of
Math 8601: REAL ANALYSIS.Fall 2010Homework #1 (due on W, September 15). Updated on Sat, September 11. 50 points are divided between 5 problems, 10 points each. #1. Let F be a compact subset of Rn . Show that there are point x0 , y0 F , such that diamF :
Math 8601: REAL ANALYSIS.Fall 2010Homework #5. Problems and Solutions. #1. Let E be a Lebesgue measurable set in R1 with Lebesgue measure m(E) > 0. Show that for any < 1, there is an open interval I = (a, b) such that m(E I) > m(I). Proof. Suppose that
Math 8601. December 18, 2010. Final Exam. Problems and Solutions. #1. Let A be an arbitrary set, and for each A, let an open ball B Rn be defined. Show that there is a finite or countable subset A0 A, such that B =A A0B .Proof. The open set :=AB =j
Ed Tell Angela (Anqi) Liu #6 Response: Purpose, Audience, Design (Reading 12)Sec. 002 20415897 A public speaker must be audience-oriented (99). To be more specific, the speaker should take the audience into account when selecting, a topic, preparing,
Ed Tell Angela (Anqi) Liu #3 Response: Purpose and ResponsibilitySec. 002 20415897 Try as we may to reveal ourselves as much as possible when bonding with people, we are no longer free to disregard the context in which the communication is taking plac | 677.169 | 1 |
Supplies needed for this class are a 3 ring binder, loose paper, and dividers. This will be used exclusively for General Physics. A scientific calculator is necessary, a graphing calculator is not recquired.
This is a high school level introductory course in Physics appropriate for any student interested in science. It will emphasize concepts as well as mathematical models as they apply to our studies.
Supplies needed for this class are a three ring binder, loose paper and dividers. This will be used exclusively for AP Physics. A scientific calculator is necessary, a graphing calculator is not recquired.
This is an algebra based, introductory course in Physics equivalent to a college course as outlined by the AP College Board. | 677.169 | 1 |
MATH 112 Introductory Survey
For each of the topics listed below, rate your understanding of the topic on a scale of 1 to 10. Here a 1 corresponds to "I don't understand this topic" and a 10 correspondes to "I would feel confident teaching this topic". You may put your name on this paper if you wish, but you are not required to.
When you have finished, please use the remainder of the page to write down what you would like to learn in MATH112. | 677.169 | 1 |
Signature Math
Core Courses for Algebra Readiness and Algebra I
Solving algebra. Sounds simple when you say it, but getting students to solve algebra is a real challenge today in education. Statistics support the fact that students continue to struggle in overcoming this critical milestone in obtaining a high school diploma. Signature Math solves the algebra problem by combining 181 computer-based lessons and 35 hands-on, small-group activities to build mastery of pre-algebra and Algebra I concepts.
Signature Math is a blended learning model of one-to-one computing and teacher-led instruction that combines 35 small-group, hands-on learning activities and 181 computer-based lessons. Students build mastery of critical math concepts and experience real-world learning applications that make Algebra meaningful and relevant. Students begin by taking an assessment to determine their level of knowledge of pre-algebra and Algebra I concepts and are then assigned Individualized Prescriptive Lessons™ (IPLs). As students master each concept, they advance to the next lesson. Learning is reinforced and the concepts are applied in hands-on, Culminating Group Activities (CGAs), which are teacher-led in a whole-class learning environment. | 677.169 | 1 |
Math 132: Precalculus II
PLEASE NOTE
Beginning Summer 2009, this course will be known as Math 142; only the course
number will change.
Course Description
Math 132 is the second course in a two-quarter precalculus sequence that also includes Math 131. Topics include: polynomial, rational, trigonometric, and inverse trigonometric functions; and applications involving these functions and functions from Math 131.
Who should take this course?
Generally, students seeking to take the 151–152–153 calculus sequence take the 131–132 precalculus sequence first. Some students in programs like business take this course (in place of Math 140) and then take Math 150 instead of Math 132. You should consult the planning sheet for your program and consult an advisor to determine if this sequence is appropriate for you.
Who is eligible to take this course?
The prerequisite for this course is Math 131 with a grade of 2.0 or higher.
Is this course transferable?
This course transfers to the University of Washington as UW Math 120 if both Math 131 and Math 132 are taken; consult an advisor or see the Transfer Center to determine transferability to other institutions.
What textbook is used for this course?
The first edition of Precalculus Concepts and Functions: A Unit Circle Approach by Michael Sullivan and Michael Sullivan III; a lower-priced custom version comprising Chapters 1–7 and 9 is available through the EdCC Bookstore.
What else is required for this course?
Students are required to have a graphing calculator; the TI-83 Plus or TI-84 Plus is recommended. | 677.169 | 1 |
The text comprises explanations and examples of basic arithmetic operations applied to whole numbers and fractions, a lengthy section on commercial arithmetic, and a brief account of square and cube roots at the end. | 677.169 | 1 |
In Euclidean geometrical mathematics, there are several types of shapes and figures are
defined that are generated by the various mathematician. Form one of them; rectangle is the
geometrical shape ...
This article is mainly based on the most important and complex topics of students' education,
that is Organic Chemistry. Before proceeding further, let's talk about chemistry.
It is the study of the ...
In the real life mathematics helps in performing the various kinds of tasks. At the
administration level mathematics helps in handling of data. In mathematics we study about the
graphs, which is very ... | 677.169 | 1 |
College Algebra
Credits: 3Catalog #20804212
College Algebra includes fundamental topics covered in Intermediate Algebra with a more careful look at the mathematical details and a greater emphasis on the concept of function. It covers quadratic, polynomial, rational, exponential and logarithmic functions, equations and inequalities; the use of matrices and determinants in solving linear systems of equations, solving non-linear systems; sequences and series.
Enrollment Requirements: Prereq: Intermediate Algebra 20-804-201 or 20-804-203 with a grade of "C" or better
OR
COMPASS: Algebra 66-99 or College Algebra 1-45
Course Offerings
last updated: 09:01:45Students will receive a welcome letter one week before the class starts that includes instructions for accessing the online course. Students are expected to complete basic introductory activities before the first day of class. Coursework for this class is due weekly. Assessments for this class include proctored exams | 677.169 | 1 |
97807637149 Analysis, Revised Edition (Jones and Bartlett Books in Mathematics)
The Way Of Analysis Gives A Thorough Account Of Real Analysis In One Or Several Variables, From The Construction Of The Real Number System To An Introduction Of The Lebesgue Integral. The Text Provides Proofs Of All Main Results, As Well As Motivations, Examples, Applications, Exercises, And Formal Chapter Summaries. Additionally, There Are Three Chapters On Application Of Analysis, Ordinary Differential Equations, Fourier Series, And Curves And Surfaces To Show How The Techniques Of Analysis Are Used In Concrete Settings | 677.169 | 1 |
This course introduces the basic concepts and techniques of linear algebra and calculus which are appropriate to building science and technology. It is aimed at students without a pass at A-Level in Pure Mathematics (or its equivalent). concepts from basic linear algebra and single variable calculus.
appropriately apply mathematical methods to a range of application in building science and technology.
2
5.
the combination of CILOs 1--5
20 hours in total
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.
2
2 hours
3
2 hours
1
1 hour
4
2 hours
Learning through take-home assignments helps students understand basic concepts and techniques of linear algebra and single variable calculus, and their applications.
1--4
after-class
Learning through online examples for applications helps students apply mathematical methods to some problems in building science applications.
4
after-class
Learning activities in Math Help Centre provides students extra help.
120%Coursework
802
15-30%
Questions are designed for the first part of the course to see how well the students have learned concepts and techniques of elementary calculus and their applications.
Hand-in assignments
1--4
0-15%
These are skills based assessment to help students demonstrate advanced concepts and techniques of basic linear algebra and single variable calculus, as well as some applications in building science and technology.
Examination
5
70%
Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student's versatility in linear algebra and univariate calculus | 677.169 | 1 |
This program offers all the algebra content students need to master in an accessible, informal format.
Features
Student Edition now contains more prerequisite skills practice, a new English/Spanish Glossary, sections on Standardized Test Practice and Mixed Problem-Solving, and references to the TI-84 Plus graphing calculator
Resources are now conveniently arranged by chapter, saving you time and effort in preparing lessons
Technology
New! ExamView® Pro Testmaker CD-ROM allows you to create customized tests and study guides in minutes. Add or edit existing questions, integrate graphics, and more! Built-in state and national correlations.
New! Online Learning Center gives you access to many valuable resources connected to your Glencoe textbook. The Online Learning Center is organized into two parts—the Student Center and the Teacher Center—with links to a wide variety of appropriate online resources.
New! What's Math Got to Do With It? Real-Life Video video series engages students with relevant problem-based examples that show how math is used in real life. | 677.169 | 1 |
Mathematics
Senior School Mathematics
The school provides all our students with the opportunity to progress in Mathematics. All our students are taught basic numeracy that is directed at allowing them to use mathematical knowledge required by our society. Our college also teaches the courses that build the mathematical skills and knowledge necessary to enter University courses in Mathematics and the Sciences. '
Another of our goals is to develop an awareness of patterns and the beauty inherent in Mathematics. It can create a passion for this enriching subject.
We are progressively adopting the National Curriculum and it will be taught in grade 7 to 10 in 2012. In grade 7 and 8 students do a common course as they mature their mathematical understanding. Student's interest and demonstrated achievement are used to place students in more suitable levels by grade 9. However students are given many opportunities to change to a different level mathematics course as the need arises. There are courses that suit all our students from grades 7 to 12.
Mathematical extra curricula activities are encouraged with the annual competition in the Math's Relay and National Mathematics competitions. Teachers are always willing to provide tutorial assistance and we also have available on line tutorial assistance.
Below are examples of topics covered in Grade 11 and 12 Mathematics at St Mary's College.
Specialised Mathematics
This subject gives that extra mathematical knowledge useful for University student with their Mathematical based subjects
Complex numbers
Matrices
Integral calculus to 3D
Sequences
Mathematics Methods
This subject is required subject for doing Mathematics at University.
Differential and Integral Calculus
Functions
Statisical Distributions
Trigonometric Relations
Applied Mathematics
This subject gives most students the background needed for many University subjects from accounting to psychology etc.
Algebraic modeling
Calculus
Applied Geometry
Data Analysis
Finance
Mathematics Applied Foundation
This subject is a preparation for the pretertiary Maths Applied for students who need to improve their pass in Grade 10 Advanced Maths. It covers a lot of the topics of the pretertiary course but covers the basics underpinning them and allows students more confidently attempt Maths applied the following year.
finance
space
algebra
probability
Workplace Maths
This subject gives most numeric skills in real life and in particular simulated workplace based contexts. It is about developing self confidence using mathematics and real world applications.
core maths skills
measurement
consumer maths
technology
For information about enrolling in our Senior School, please contact the Enrolments Officer by email, telephone (03) 6234 3381, or view or download the Senior School brochure. | 677.169 | 1 |
Quantitative Problem Solving in Applied Science, Natural Sciences Mathematics and Commerce:
"Hands on, Heads up" Learning
Quantitative Problem Solving
What is "Problem Solving"?
This is a form of learning based on discovery: to solve the problem, you must both think and compute systematically.
It is different from both "exercise solving", in which past routines are applied to solve similar problems, and a "trial and error" approach is used to match correct formula for the problem.
A central idea in problem solving is the use of "concepts", which are the fundamental general ideas on which other notions may be built. In any subject, there are usually only a few basic concepts (sometimes expressed as formula), which are applied in a variety of ways or situations.
For example, basic concepts include limit of function in math, and t- test in statistics, Newton's 2nd Law in physics, mole in chemistry, and liability in accounting. Identifying and deeply understanding key concepts, and developing an organizational structure to allow you to recall how they relate to each other are essential elements in expert problem solving
The "spiral of learning" occurs when basic concepts are used repeatedly to solve a variety of problems. The central concept is the core of the spiral, and various applications spin out from, and loop back to, that concept. Frequently re-visiting those basic concepts allows you to firmly fix them in your long-term memory, where they can be quickly recalled and applied.
People learn in different ways, and have different preferred styles of relating to their world, seeking sensory input, making information meaningful, and patterns of learning. It is very helpful to understand your own preferred learning style, and use methods that both mesh with and challenge your style. See the free "Index of Learning Styles" by Felder and Silverman. and refer to the "Working with Your Preferred Learning Style" resource on the Learning Strategies web site
Self-Reflection Questions
Do you:
1. understand your own approach: strengths and weaknesses?
2. focus on concepts to increase understanding, and as an organizational framework?
3. learn material sequentially?
4. look for the "spiral of learning": repetition and expansion of basic concepts?
5. develop a systematic, methodical approach, to talk yourself through each step?
6. compute accurately, and eventually… quickly
7. persist?
8. get help when needed?
What is YOUR Approach to Quantitative Problem Solving?
Awareness of your own attitudes and habits is a good starting point to see your strengths and areas to change. Click on the "Evidence Based Components" questionnaire to assess your approach.
Characteristics of Expert Problem Solvers
1. Attitude Characteristics
* Optimistic: you believe "I can do it"
* Confident: the problem really does have a reasonable, but perhaps difficult, solution
* Willing to persevere: you aim for a complete and well reasoned solution, not an immediate or superficial one
* Concern for accuracy in reading: you concentrate, re-read and paraphrase to increase understanding, and translate unfamiliar words or terms
* Concern for accuracy in thinking: you work at a moderate to slow pace initially, perform operations carefully, check answers periodically, and draw conclusions at the end not part way through.
2. Skill Characteristics
* Systematic approach: you have a plan to follow, which
i. reduces the panic
ii. allows you to monitor your thought processes
iii. helps isolate errors in logic or computation
* Sound knowledge of basic concepts, which you mentally organize so you can recall and apply them
* Computational skill, at a good speed
* Habit of vocalizing or "thinking aloud": you talk yourself through all thoughts
i. how to start the problem
ii. steps to break problems into parts
iii. decisions
iv. analyses
v. conclusions
* Awareness of your own thought processes: What did I do or learn? How did I do or learn this? How effective was my process?
Typical Characteristics of Novice Problem Solvers
1. You don't believe that persistent analysis is essential, therefore your effort and motivation to persist is weak.
2. You are careless in their reasoning.
3. You don't break problem into component parts and go step-by-step, therefore there are errors in logic and computation.
4. You focus on individual details, and don't see how details relate to concepts. Therefore, every problem feels new…how overwhelming!
5. Formula-memorizing is the main strategy.
6. You get behind in your learning, and then sequential learning is hampered.
7. You lose confidence in your ability to solve problems, due to lack of success.
Strategies to Improve Problem Solving Skills
1. Use Time and Resources Effectively
* Work on courses regularly: keep up so you can build on past knowledge (sequential learning), and get help quickly for difficulties.
* Do all the questions assigned, rather than dividing questions among group members, as you will get more practice with the concepts your Professor expects you to know. Aim for accuracy, then speed. Start assignments at least a week ahead of the due date, so you have time for help if needed.
* Use study groups to compare completed solutions to assigned problems. Teaching someone is a very effective learning and study technique.
* Choose problems wisely: learn to apply a specific concept to solve a variety of related problems. Start with simpler ones, and work up. Identify the relevant concept and practice until you know when and how to apply it, i.e. you may not need to do all questions.
* Set a time limit: attempt a new problem every @ 15-20 minutes. If you can't complete a problem, check your "thinking strategies" and change to a new problem. Get help with the problems you couldn't complete, at tutorial, etc.
* Do some uncalculated solutions: If you are confident in your calculations-set up the solution but don't finish the calculation.
* Learn the necessary background and skills: find out from professor, course outline, etc. what the course involves and upgrade before the course begins if you don't feel confident about the prerequisites.
* Find and use help resources: use tutors, professors, TAs, friends, text, internet. For example: in accounting, economics, and finance texts, it is common to find examples that are quite similar to the problems at the end of the chapter. Work through the logic of the examples to develop a better understanding of how best to start the homework problems, if you run into trouble.
2. Develop Strategies to Organize Your Thinking
* Quantitative Concept Summary Strategy
Concepts are general organizing ideas, are there are often very few of them taught in a course, along with their many applications (ie. the spiral of learning). Key concepts may be identified by:
* reading the learning objectives on the course outline or the course description,
* referring to the lecture outline to identify recurring themes,
* thinking about the common aspects of problems you are solving.
Learn and understand the small amount of information essential to each concept.
If in doubt, ask the professor what is important for you to "get".
For more information, click here for the Quantitative Concept Summary Strategy description, Concept Summary form, and an example of a Concept Summary for Ordinary simple Annuities.
View the video at (click Online Resources, scroll to "Math", select desired topic and format)
* General Problem Solving Method
Use a methodical, thorough approach to solve problems logically from first principles. Refer to the self-assessment questionnaire by Woods et al. (2000) in this guide to remind yourself of target activities you need to focus on.
Steps involve:
* Engage with the problem
* Define and understand the problem- what is being asked? Express your thinking in several ways, such as verbally, graphically or pictorially, and finally mathematically
* Explore links between the current problem and related ones you have previously solved.
* Plan how you will solve the problem
* Do it ?
* Evaluate your method and result, and revise as needed
Click here for more information on the General Problem Solving Strategy.
* Decision Steps Strategy
This strategy is a specific application of the General Problem Solving Strategy described above, and is suitable for use in statistics, accounting and other applied problem solving situations.
During the lecture or when reading course notes, focus on the process of solving the problem, instead of on the computation. When your professor is lecturing, listen to their comments on how steps are inked from one to another. This helps you identify the "decision steps" that lead to correct application of a concept. Ask yourself "Why did I move from this step to this step?"
Click here for more information on the Decisions Steps Strategy, and examples of Decision Steps in Calculus and Decision Steps for Rational Expressions.
View the video at (click Online Resources, scroll to "Math", select topic and format)
* Problem Solving Homework Strategy
Use homework as a learning tool. Effective learning of the concepts and general methods will reduce the number of problems you may need to solve to feel confident in your knowledge and computations.
Click here for details on the Problem Solving Homework Strategy.
* Range of Problems Strategy
Exams will challenge you to apply your knowledge to new situations, so prepare by creating questions or problems that are slightly different in some variable from your homework problems.
Actively think about the range of problems that are associated with a concept. Think in terms of both
i. level of difficulty of the problems and
ii. common kinds of difficult problems.
Use this to anticipate different kinds of difficult problems for exam preparation, and solve some practice problems to test yourself. This is an excellent activity for a study group.
Click here for common examples of difficult problems using the Range of Problems Strategy.
View the video at (click Online Resources, scroll to "Math", select topic and format)
.
Some Evidence-Based Components of Expert Problem-Solving1a
Observe yourself as you solve problems, and rate how frequently you DO any of the following. Progress toward internalizing these targets, aiming for doing these activities 80-100% of the time.
Targets for expert problem-solving
20%
40%
60%
80%
100%
1. I describe my thoughts aloud as I solve the problem.
2. I occasionally pause and reflect about the process and what I have done.
3. I don't expect my methods for solving problems to work equally well for others.b
4. I write things down to help overcome the storage limitations of short-term memory (where problem-solving takes place).
5. I focus on accuracy and not on speed.
6. I interact with others. b
7. I spend time reading the problem.c
8. I spend up to half the available time defining the problem.d
9. When defining problems, I patiently build up a clear picture in my mind of the different parts of the problem and the significance of each part.e
10. I use different tactics when solving exercises and problems.f
11. I use an evidence-based systematic strategy (such as read, define the stated problem, explore to identify the real problem, plan, do it, and look back). I am flexible in my application of the strategy.
12. I monitor my thought processes about once per minute while solving problems.
Endnotes
a Problem-solving contrasts with exercise-solving. In exercise-solving, the solution methods are quickly apparent because similar problems have been solved in the past.
bAn important target for team problem solving.
c Successful problem solvers may spend up to three times longer than unsuccessful ones in reading problem statements.
d Most mistakes are made in the definition stage!
e The problem that is solved is not the problem written in the textbook. Instead, it is your mental interpretation of that problem.
f Some tactics that are ineffective in solving problems include:
1. trying to find an equation that includes precisely all the variables given in the problem statement, instead of trying to understand the fundaments needed to solve the problem;
2. trying to use solutions from past problems even when they don't apply;
3. trial and error
Quantitative Concept Summary Strategy
Taken from: Fleet, J., Goodchild, F. and Zajchowski, R., "Learning for Success", 2006
See for several completed examples. Click on SFU Q Conference, used with permission.
Purpose: to provide a structure for organizing fundamental, general ideas. The mental work involved in constructing the summary helps clarify the basic ideas and shift the information from working memory to long-term memory. This is an excellent study tool, for quick review.
Method:
The organizational elements are
i. Concept Title
You can identify key ideas by referring to the course outline, chapter headings in the text, lecture outline. Sometimes concepts are thought of individually, other times they are meaningfully grouped for better recall. Eg. Depreciation, Capital Cost Allowance, and Half-Year Rule;
acid, base and PH..
ii. Use general categories to organize material, and then add specific details as appropriate. Sample general categories may include:
* Allowable key formula- check summary page of text or ask professor
* Definitions- define every term, unit and symbol
* Additional important information- sign conventions, reference values, meaning of zero values, situations in which formula do not work, etc
* Simple examples or explanations- use your own words, diagrams, or analogies to deepen your thinking and check your understanding
* List of relevant knowns and unknowns- to help you know which concepts are associated with which problems, use crucial knowns to help distinguish among problems.
QUANTITATIVE CONCEPT SUMMARY
Concept Title:
Allowable Key Formula:
Definitions of each symbol, and its units;
Additional important information: (eg. sign conventions, special characteristics, when concept doesn't work, special cases, etc)
Simple examples, explanations, cases:
Relevant knowns, and unknowns: (and words or phrases from word problems that signal these)
By permission from website of R. Zajchowki <>
Concept Summary for Ordinary simple Annuities
Used with permission
General Problem Solving Strategy
based on D.R. Woods, "Problem–based Learning", 1994
A systematic approach to problem solving helps the learner gain confidence, and is used consistently as a "blue print" by expert problem solvers as a way to be methodical, thorough and self-monitoring. This model is used in life generally, as well as in the sciences.
The steps are not linear, and multiple processes are happening in your brain simultaneously, but the basic template hinges on effective questioning as you carry out various steps
1. Engage
* Invest in the problem through reading about it and listening to the explanation of what is to be resolved. Your goal is to learn as much as you can about the problem before you begin to actually solve it, and to develop your curiosity (which is very motivating). Successful problem solvers spend two to three times longer doing this than unsuccessful problem solvers. Say "I want to solve this, and I can".
2. Define the stated problem…a challenging and time consuming task
* Understand the problem as it is given you, ie. "What am I asked to do?"
* Ask "What are the givens? the situation? the context? the inputs? the knowns? etc.
* Determine the constraints on the inputs, the solution and the process you can use. For example, "you have until the end of class to hand this solution in" is a time constraint.
* Represent your thinking conceptually first, by reading the problem, drawing a pictorial or graphic representation or mind map (see example attached), and then a relational representation.
* Then represent your thinking computationally, using a mathematical statement
3. Explore and search for important links between what you have just defined as a problem, and your past experience with similar problems. You will create a personal mental image, trying to discover the "real" problem. Ultimately, you solve your "best mental representation" of the problem.
* Guestimate an answer or solution, and share your ideas of the problem with others for added perspective.
* Self-monitoring questions include: What is the simplest view? Have I included the pertinent issues? What am I trying to accomplish? Is there more I need to know for an appropriate understanding?
4. Plan in an organized and systematic way
* Map the sub-problems
* List the data to be collected
* Note the hypotheses to be tested
* Self-monitoring questions include: What is the overall plan? Is it well structured? Why have I chosen those steps? Is there anything I don't understand? How can I tell if I'm on the right track?
5. Do it
* Self-monitoring questions include: Am I following my plan, or jumping to conclusions? Is this making sense?
6. Look back and revise the plan as needed. Significant learning can occur in this stage, by identifying other problems that use the same concepts (remember the spiral of learning?) and by evaluating your own thinking processes. This builds confidence in your problem solving abilities.
* Self-monitoring questions include: Is the solution reasonable? Is it accurate? (you will need to check your work to know this!) Does the solution answer the problem? How might I do this differently next time? How would I explain this to someone else? What other kinds of problems can I solve now, because of my success? If I was unsuccessful, what did I learn? Where did I go off track?
Decision Step Strategy:
Applying the General Method to a Specific Problem
Taken from: J. Fleet, F. Goodchild, R. Zajchowski, "Learning for Success", 2006
See for a completed example. Click on SFU Q Conference
Purpose: to help learners focus on the process of solving problems, rather than on the mechanics of formula and calculations.
The focus is on correct application of concepts to specific situations. This strategy helps you to increase your awareness of the mental steps you make in problem solving, by "forcing" you to articulate your inner dialogue regarding procedure.
Method:
Identify the key decisions that determine what calculations to perform. In lecture, try to record the decision steps the professor uses but may not write down or post.
i. Analyze solved examples, using brief statements focusing on steps you find difficult:
* What was done in this step?
* How was it done; what formula or guideline was followed?
* Why was it done?
* Any spots or traps to watch out for?
ii. Test run the decision steps on a similar problem, and revise until the steps are complete and accurate.
Decision Steps in Calculus
Used with permission
Decision Steps for Rational Expressions
Used with permission
Problem Solving Homework Strategy
This strategy encourages a deep understanding of concepts and procedures in calculation. The time you spend on this will reduce the amount of time you may spend in "plug and chug" attempts to do the homework, and reduce the amount of time you will need for studying later on.
1. Prepare for the homework questions..
* review class notes and understand the concepts in the examples. This might take 30 - 45 minutes.
* write the first line of a sample problem, close the book, and work as far as you can without looking.
* refer back to notes, and then again attempt sample
* repeat over again until you can solve the sample problem both accurately and quickly. You will have memorized the rules in the process. This might take 1 hour.
2. Start the homework questions.
Interrogate your problem solutions: ask questions about the problem and your method of solving it. E.g.
1. What are the givens? Can the givens be classified as Assets, Liabilities, Owner's Equity, Income, Expenses, etc? Is there any Depreciation?
2. What is required?
3. Can I diagram this?
4. What concepts are referred to? Theorems? Operations?
5. Is the problem similar to others I solved/How?
6. What more do I need to understand this?
7. Are there any "tricks" to the question? If so, how do I deal with them?
3. Keep track of problems you have trouble solving, isolate the particular difficulty, and get help to figure it out. Drill these problems until you are both accurate and fast in solving them.
Range of Problems Strategy:
Common Types of Difficult Problems
Taken from: J. Fleet, F. Goodchild, R. Zajchowski, Learning for Success, 2006
Expand your thinking in preparation for exams, where problems are not exactly the same as you have previously solved.
Work from an existing problem, and make it more challenging by adding or changing:
Hidden knowns: needed information is hidden in a phrase or diagram Eg. "at rest" means initial v = 0 in physics.
Multipart-same concept: a problem may comprise 2 or more sub-problems, each involving the same concept. This type of problem can be solved only by identifying the given information in light of these sub-problems
Mulitpart-different concepts: same idea as above, but the sub-problems involve the use of different concepts
Multipart-simultaneous equations: same idea as above, but no single sub-problem can be solved by itself. You may have 2 unknowns and 2 equations or 3 unknowns and 3 equations, and you will need to solve them simultaneously, eg. using substitution, comparison, addition and subtraction, matrices, etc.
Work backwards: some problems look different because to solve them you have to work in reverse order from problems you have previously solved
Letters only: when known quantities are expressed in letters, problems can look different. If you follow the decision steps, they are not usually as difficult.
"Dummy variables": sometimes a quantity that you think should be a known is not specified because it is not really needed- that is, it cancels out. Eg. mass in work-energy problems, temperature in gas-law problems.
Red herrings, unnecessary information: a problem may give you more information than is needed, which is confusing if you think you should use everything provided.
Resources
Online:
last accessed May 2010. Use this free inventory, the Index of Learning Styles, to assess preferred learning styles, and get additional information on interpretation of your profile
, last accessed May 2010. click "Online Resources", scroll to "Math", select topic and format
There are 3 videos on Problem Solving illustrating general ideas (Problem Solver I), differences in applying concepts vs. formula chasing (Problem Solver II), and applying the Decision Steps strategy (Problem Solver III).
, last accessed May 2010. Click on SFU Q Conference. The personal web site for Richard Zajchowski, with examples of completed Concept Summaries, Decision Steps and other strategies
Books:
Fleet, J, Goodchild, F, Zajchowski, R Learning for Success: Effective strategies for students, Thomson Nelson, 4th ed, 2006
Whimbey, A, Lockhead, J, Problem Solving & Comprehension, New Jersey: Lawrence Erlaum Associates, 5th ed., 1991
Woods, DR, Problem-based Learning: How to gain the most from PBL, Waterdown, ON: DR Woods, 1994
Mar. 2009
1 Woods, D.R., Felder, R.M., Rugarcia, A., Stice, J.E. (2000). The Future of Engineering Education III: Developing Critical Skills. Chemical Engineering Education, 34 (2), 108-117.
---------------
------------------------------------------------------------
---------------
------------------------------------------------------------
Learning Strategies Development
Queen's University | 677.169 | 1 |
MA 201 College
Algebra
Instructor:
Ann Ostberg
Semester: Spring
Course Description
This course is designed to explore the concepts of college
algebra. It will include a study of linear, quadratic, rational, polynomial,
and radical equations; relations and functions; rectangular coordinate system
and graphs; systems of equations and inequalities; exponential and logarithmic
functions; and matrices.
Course Schedule
Unit
Topic
Learning Objectives
1
Welcome
·This section reviews the different sets of
numbers such as natural numbers, whole numbers, integers, and rational
numbers and their properties.It
continues with graphing on a number line and associated topics such as intervals,
inequality symbols, absolute value, and distance.
·This section reviews exponents and the rules
of exponents along with order of operations, evaluating expressions, and
scientific notation.
2
rational exponents, radicals, and polynomials
·This section reviews rational exponents.Rational exponent is another name for
fractional exponents.Radical
expressions such as square roots, cube roots, etc. are presented along with
the methods to simplify and combine (addition and multiplication).Remember rationalizing the
denominator?We will also rationalize
the numerator in this section.
·This section covers polynomials.We will define, add, subtract, multiply,
and divide. Remember the term FOIL?A
new term might be conjugate binomials.
3
factoring of the polynomials and
algebraic fractions
·This section lays the foundation of a key
process in algebra:factoring
polynomials.Many factoring techniques
will be presented.Practice as much as
possible to become proficient!
·This section reviews the basic concepts of
fractions; however, it extends it to algebraic fractions.The techniques to simplifying, multiplying,
dividing, adding, and subtracting algebraic fractions are based on simple
fractions that you learned in grade school.To make things more interesting, we will also work with complex
fractions.
4
equations and their applications
·In this section, you'll learn about properties
of equality, linear equations, rational equations, and formulas.All of these concepts are vital to your
ability to work with equations.
·This section extends the concepts of linear
equations to the practical application of linear equations.You may be familiar to these as 'story
problems.'Pay close attention to the
Strategy for Modeling with Equations in your text.
5
quadratic equations and their
applications and complex numbers
·This section introduces quadratic equations.
These are second-degree equations (they have an exponent of 2 on the
variable).The key topics are solving
the quadratic equation, i.e., finding the values that make the equation a
true statement.In order to solve, the
methods of zero-product, completing the square, square root property, and the
quadratic formula will be used.
·This section looks at some applications of
quadratic equations.We will place
emphasis on the geometric problems, uniform motion problems, and flying
object problems.
·This section investigates complex
numbers.Complex numbers developed as
solutions to certain quadratic equations.There are two types of complex numbers: real and imaginary.We will be looking at the definition and
simplification of imaginary numbers and complex numbers.The techniques of FOIL will prove useful as
you do arithmetic with complex numbers.
6
polynomial and radical equations and inequalities
·This section teaches solving polynomial
equations by factoring and the methods used in solving radical
equations.So your factoring skills
will be put to the test in this section.Radical equations aren't trying to protest anything but they are
equations that involve square roots and cube roots.
·This section looks at the properties of
inequalities.You will utilize those
properties to solve linear inequalities and compound inequalities.Of particular emphasis will be solving
quadratic and rational inequalities. Of these types, you must make a separate
chart to actually find the solution.
7
absolute value
·This section on absolute value concludes the
chapter.Emphasis will be placed on
the definition of absolute value and solving equations and inequalities
involving absolute value.We will look
at equations with two absolute values – these are actually easier than they sound.
8
rectangular coordinate system
·In this section, you will be able to graph
linear equations on the Rectangular Coordinate Plane.On this plane, one may also find the
distance and/or the midpoint between two points.Some basic applications will be presented.Be sure to understand these formulas and
the terminology associated with this topic.
·This section focuses on the slope of
lines.This will include horizontal,
vertical, perpendicular, and parallel lines.An emphasis will be placed on the nonvertical lines (simply all lines
that are not vertical).You will want
to memorize the formula for slope.
·This section focuses on the methods of taking
graphical information (points, slope, etc) and translating that into an
algebraic equation.This was actually
a very revolutionary development in the history of mathematics!Key formulas are the point-slope form and
the slope-intercept form.
9
graphs of equations and ends with
proportions and variations
·This section covers the graphing of other types
of equations.Emphasis will be placed
on the symmetries of graphs, miscellaneous graphs such as absolute value,
square root, quadratic (parabolas), and circles.The formula for a circle will be presented.
·This section presents the topics of proportion
and variation.You have undoubtedly
worked proportion problems in earlier math classes.You will use the process of 'cross-multiplication.'Variation problems might be a bit new,
however, they are practical problems.Direct variation implies that as one element (x) increases so does the
other (y).Think of as you eat more
calories, you will gain more weight.Indirect or inverse variation implies that as one element increases
(x) the other (y) decreases.
10
functions and function notation and quadratic functions
·This section begins the discussion on
functions.The variables, x and y,
will be given new ideas:independent
variable and dependent variable for x and y, respectively.The x values will also be referred to as
the domain. The y values will be considered the range of the function.Understand the notation that is used to
denote a function.We will conclude
with drawing the graphs of functions:actually you have already done this.Using the 'vertical line test' will allow you to tell whether a graph
is the graph of a function.
·This section looks specifically at the
quadratic function.You are already
familiar with this function as its graph is a parabola.The quadratic equation is very important as
it has many practical applications. Besides knowing how to graph the
parabola, finding the vertex is very useful.The vertex will tell the maximum or minimum value of a situation.
11
polynomials and other functions. Translating
graphs and rational functions
·This section focuses on graphing polynomial
functions.Did you know that there
were 'even' and 'odd' functions? We will also look at increasing and
decreasing function.Think of going up
a hill versus going down a hill.Finally, we will graph piecewise-defined functions.These functions often frustrate students
until they realize that it is just like taking a piece from two or more pies
(graphs), say apple and cherry, and placing them on your plate (coordinate
plane), side by side.
·This section will demonstrate how one can move
graphs of equations to the right, left, up, down, and flip!These are called translations.The 'flip' is called a reflection about the
x- or y-axes.For all of these translations,
they will start with the basic graph of the equation.
·This section will provide a brief introduction
to rational functions. The definitions of asymptotes, rational function, and
their related domain will be discussed. We will not focus on the graphing of
rational equations.
12
functions and inverse functions
·This section focuses on special functions
called inverse functions.Only
one–to-one functions can have inverse functions.Visually, this can be determined from the graph
of the function using The Horizontal Line Test. You will also learn to write
the 'inverse' of an equation.
13
exponential functions and their graphs,
applications of exponential functions, and logarithmic functions
·This section will look at a special type of
function, called an exponential function.You will always be able to recognize an exponential function as the
variable (x) is the exponent.For
example, ,
where b is a constant.The graphs of
all exponential functions are similar in shape and go through the point (0,
1).A practical application of
exponential functions is finding the value of compound interest.If the interest is compounded continuously,
a special number, e, is used. The value of e is 2.7182818....
·This section discusses some of the
applications of exponential functions.We will focus only on radioactive decay and Malthusian population
growth.
·This section covers logarithmic functions and
their graphs.A logarithmic function
is simply the inverse of an exponential function.The inverse is more commonly written
as.If the base (b) is 10, it is
called a common logarithm. If the base (b) is e, it is called a natural
logarithm.The shape of the graph is
similar to the exponential function, except it passes through the point (1,
0) instead of (0, 1).These graphs can
also be written so that they have horizontal and vertical movement.
14
logarithmic functions, properties of logarithms, and
exponential and logarithms equations
·This section focuses on the applications of
logarithmic functions.We will only
look at those applications from electrical engineering, geology, and
population growth.
·This section investigates the properties of
logarithms.The key thing to remember
is that a logarithm IS an exponent!Remember the properties associated with exponents and you will see how
they become applicable to the properties of logarithms.The Change-of-Base Formula allows one to
calculate the value of any logarithm.
·This section shows how one may solve
exponential and logarithmic equations.The steps are straightforward. Be sure to be able to write equations
in exponential form to logarithmic form and vice versa.Carbon-14 dating is an important
application that involves logarithmic equations.
15
linear equations, determinants, and
graphs of linear inequalities
·This section covers the various methods that
one can use to solve systems of linear equations in two variables:the graphing method, the substitution method,
and the addition method.We will also
look at the characteristics of a system with either infinitely many solutions
or no solutions (inconsistent).Finally, the techniques will be utilized to solve a system of linear
equations in three variables.Systems
of linear equations are crucial in solving linear programming problems.
·This section investigates another method of
solving a system of linear equations.It involves the use of matrices.Through the use of determinants (which are found from a matrix), one
can find the solution to systems.Techniques involving determinants can also be used to find the
equation of a line and the area of a triangle.
·The final section of this semester will
discuss graphing linear inequalities.You will utilize the techniques of graphing equations and then
determining which sections of the graph represent the solution area.Graphing a system of linear inequalities is
also used in linear programming. | 677.169 | 1 |
Offering a helpful introduction to basic algebraic concepts, this guide is useful for any student in pre-algebra and beyond as a reference tool at any level of algebra. The 6-page guide covers all the major topics included in a pre-algebra class. This guide is laminated and is three-hole punched for easy use. | 677.169 | 1 |
Essentials Of Basic College Mathematics - With Cd - 2nd edition
Summary: TheTobey/Slater seriesbuilds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical ''building block'' organization makes it easy for readers to understand each topic and gain confidence as they move through each section. The authors provide a ''How am I Doing?'' guide to give readers constant reinforcement and to ensure that they understand each concept before moving on to the next. With Tobey/Slater, readers have a tutor and study com...show morepanion with them every step of the way. Whole Numbers, Fractions, Decimals, Ratio and Proportion, Percent. For all readers interested in basic college mathematics. ...show less
All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU:9780321570659-5-0
$19.8721 | 677.169 | 1 |
Imagine Deerfield
Give/Volunteer for Deerfield
Share this page
Function with Confidence
Calculators
The Mathematics Department requires that ALL students own a TI-84 graphics calculator. Students may purchase a graphics calculator at Hitchcock House or in most department stores.
In the Mathematics Department, the faculty encourages students to develop the ideas, skills, and attitudes that will enable them to function with confidence and intelligence in a swiftly changing world. In pursuing this goal, teachers strive to instill a sense of excitement for the concepts and aesthetic qualities of mathematics. Deerfield students learn how to solve mathematical problems with a variety of strategies, how to communicate their solutions clearly, how to work effectively on projects with their peers, and how to use technology. The department offers a variety of courses, and places students into a level of mathematics that will provide appropriate challenges and successes. For example, the department teaches three levels of Algebra II, and at the higher end of the spectrum, outstanding students may study college-level mathematics in one-on-one tutorial classes.
For entering freshmen who have been advised to take Algebra I (Math 101 or Math 102), the usual sequence of mathematics courses consists of Math 102 (or Math 101), Math 202 (or Math 201), Math 302 (or Math 301) and Math 402 (or Math 401). For entering freshmen who place out of Algebra I (Math 101 or Math 102), the usual sequence is Math 202 (or Math 201), Math 302 (or Math 301), Math 402 (or Math 401), and Math 602 (or Math 503). The department will annually guide students in the selection of a program that is appropriate in both content and pace. Accelerated and enriched courses (Math 203, 303 and 403) provide an alternative to the usual sequence and permit advancement towards AP Calculus courses (either Math 602 or 603) and beyond. Students who are very successful in Math 401 or Math 402 or higher courses are eligible to take AP Statistics. | 677.169 | 1 |
Cairine Wilson Secondary School
Course Outline
Principles of Mathematics
MPM1D (9)
Academic
Prerequisite: None
Description: This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Overall Expectations:
• demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;
• manipulate numerical and polynomial expressions, and solve first-degree equations.
• apply data-management techniques to investigate relationships between two variables;
• demonstrate an understanding of the characteristics of a linear relation;
• connect various representations of a linear relation.
• determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;
• determine, through investigation, the properties of the slope and y-intercept of a linear relation;
• solve problems involving linear relations.
• determine, through investigation, the optimal values of various measurements;
• solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures;
• verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.
Resources: Principles of Mathematics 9 (Nelson) $75.95
Learning Skills: The separate evaluation and reporting of the learning skills in the following five areas reflects their critical role in students' achievement of the curriculum expectations. Students will be assessed continually on the following learning skills:
Works Independently
Teamwork
Organization
Work Habits/Homework
Initiative
Self-Regulation
accepts responsibility for completing tasks, follows instructions, completes assignments on time and with care, uses time effectively
works willingly and cooperatively with others, is sensitive to the needs of others, takes responsibility in sharing the work, shows respect for others ideas and opinions
sets own individual goals and monitors progress towards achieving them
Assessment and Evaluation Policy
Insufficient
Evident
Response
Late, Missed or
Skipped Tasks
(Parents are
reminded to
contact the school for all absences)
· The student will be consulted regarding the reason
· The parent/guardian will be contacted
· A second due date will be negotiated.
· If the task is not submitted according to the negotiated second due date
deductions of 10% per day up to and including "0" may be awarded in
consultation with the School Success team which may include Department Head, Administration, and Guidance.
· Students who miss assessment tasks have presented zero evidence of learning. Based on the professional judgment of the teacher, students may be required to complete the assignment in order to meet the overall expectations of the curriculum.
· A final mark of " I " or "insufficient evidence" is acceptable for grade 9 and 10 course
Academic Integrity
· Fraudulent work is of no value and provides zero evident of learning.
· Intentional academic fraud is a disciplinary issue and will incur consequences which may include suspension and mark reduction.
· Teachers will take into account mitigating circumstances when dealing with academic fraud.
· Students will be given an additional opportunity to demonstrate achievement when in the teacher's professional judgment there is not sufficient evidence that the student has met overall course expectations.
· Fraudulent material will be documented and archived.
· The parent/guardian will be contacted.
· Students who commit intentional academic fraud will forfeit the possibility of winning subject awards.
· All students in grade 9 will be required to attend academic integrity workshops at the beginning of each school year.
Extra Help:The staff of CW is committed to the success of all students. Students are strongly encouraged to seek extra help from the teacher both in and out of the classroom. The Green room is available after school Tuesday, Wednesday and Thursday.
Communication: Please feel free to contact me at the school ,613-824-4411, if you have any questions or concerns. My Voicemail extension is ________ and my email address is _______________________ | 677.169 | 1 |
Math 366 - Numerical Analysis
Spring Semester, 1997-98
One of the best definitions of numerical analysis appeared several years
ago in SIAM News. In a commentary, Lloyd N. Trefethen defined
numerical analysis as "the study of algorithms for the problems of
continuous mathematics." Thus, in view of this definition, a
numerical analyst is a mathematician who develops, analyzes, and
evaluates algorithms for obtaining (approximate) solutions to
mathematical problems.
Numerical analysis has evolved to the point where it is regarded as a
branch of mathematics in its own right, but it has strong roots and ties
to the applications of mathematics and the development of computer science
and technology. It involves applying the power of mathematics and the
power of the computer to solving quantitative problems in science and
engineering.
class attendance and participation; attendance at three or more department colloquia and other designated special events (10%).
***There will be no make-up exams, and late work will not be accepted.***
DAILY READINGS:
Read the textbook! Assigned readings should be done before class so that you will have some familiarity with the new material when it is discussed in class.
Working problems is essential for an understanding of the material, and there is an adequate supply of problems in the textbook.
TEAM HOMEWORK:
Homework will be assigned, collected, and graded. It is due at the beginning of class. As noted under GRADING POLICY, late homework will not be accepted.
Assignments may include material that will not be discussed in class. You are expected to learn this material on your own and to make use of the resources available to you to complete the assignments.
Homework will be completed by teams of three people with each team producing a single write-up.
Homework must be written neatly in standard English with complete sentences using standard 8-1/2 by 11 paper (no ragged edges) in a style appropriate to the subject. Express yourself clearly and concisely. Do not write to me. Assume instead that you are writing to other students in the class.
Grading will be based both on mathematical content and on the quality of your write-up. NEATNESS COUNTS! Show all work necessary to justify your solutions. Answers alone are not sufficient. | 677.169 | 1 |
Algebra
posted on: 10 Dec, 2011 | updated on: 22 Sep, 2012
Algebra is an important branch of mathematics in which we deal with several types of problems. These problems may either related to constants or variables. It is an interesting part of Math, and in this we mainly concentrate on "how to solve Numbers"? When we solve any algebra problem we solve numbers only. There are several games using which you can easily learn the concept of algebra like kids have a great fun when they solve the puzzles, play some computer games by running, finding secret doors, etc.
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. Equations are mathematical statements, which show the equality of two different numbers or expressions. Using algebra we solve the equation problems. Algebra is much broader than elementary algebra, in algebra we use different type of rules and operations, and perform all operations. In this, the variable symbol that represents numbers and expressions are mathematical termed as variables, numbers or both. On the different side, expressions are the, mathematical phrases, which don't use equal to symbol as it doesn't show any equality.
Apart from algebra, there are several different branches of mathematics like Geometry, trigonometry, calculus, etc. To understand all these branches properly your base must be strong, which can only develop with help of algebra. So, learn algebra properly and become master of math. | 677.169 | 1 |
Sharpen your skills and prepare for your precalculus exam with a wealth of essential facts in a quick-and-easy Q&A format! Get the question-and-answer practice you need with McGraw-Hill's 500 College Precalculus Questions. Organized for easy reference and intensive practice, the questions cover all essential precalculus topics and include detailed answer explanations. The 500 practice questions are similar to course exam questions so you will know what to expect on test day. Each question includes a fully detailed answer that puts the subject i... MOREn context. This additional practice helps you build your knowledge, strengthen test-taking skills, and build confidence. From ethical theory to epistemology, this book covers the key topics in precalculus. Prepare for exam day with: 500 essential precalculus questions and answers organized by subject Detailed answers that provide important context for studying Content that follows the current college 101 course curriculum | 677.169 | 1 |
AcademicsCalculus
Course Outline: The course will follow
chapters 1 - 5 and 8 of Himonas and Howard's "Calculus:
Ideas and Applications" (Wiley). After this we
will briefly consider two more advanced topics depending on
the interests of the class (possibilities include multivariable
calculus, differential equations and power series) The
program will follow a strict schedule that includes drill
and practice routines for developing a familiarity with the
common tools of calculus alongside discussions surrounding
the concepts behind the subject. Thus assignments from the
text will prompt class discussion surrounding the concepts,
while daily problem sets will reinforce a command of the material.
This is a four-credit course and there is much to learn. Please
keep in mind that this course requires a daily commitment.
The best way to successfully learn the material is to stay
ahead of the game and work through the assignments before
final class discussion.
Homeworks: Bold numbered problems in the homework
assignment section below are to be handed in for grading.
Plaintext numbered problems are more drill and practice material
that should be worked through to keep up with course material.
By 4pm each Friday you are expected to hand in your solutions
to the appropriate bold numbered questions (exactly which
questions these are will be announced on the Wednesday beforehand).
You may wish to discuss any assignments that you find difficult. | 677.169 | 1 |
Precalculus: Mathematics for Calculus Book Description
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader.
Popular Searches
The book Precalculus: Mathematics for Calculus by James Stewart, Lothar Redlin, Saleem Watson
(author) is published or distributed by Brooks Cole [0495109975, 9780495109976].
This particular edition was published on or around 2005-10-27 date.
Precalculus: Mathematics for Calculus has Paperback binding and this format has 397 | 677.169 | 1 |
CARY, NC (Aug. 08, 2012) – SAS Curriculum Pathways has launched a free Algebra 1 course that provides teachers and students with all the required content to address the Common Core State Standards for Algebra. Available online, the course engages students through real-world examples, images, animations, videos and targeted feedback. Teachers can integrate individual components or use the entire course as the foundation for their Algebra 1 curriculum.
"Success in Algebra 1 opens the door to STEM opportunities in high school and beyond, and can set students on the path to some of the most lucrative careers," said Scott McQuiggan, Director of SAS Curriculum Pathways. "This course gives teachers engaging content to support instruction, and will help them meet Common Core requirements."
SAS developed the Algebra 1 course in collaboration with the North Carolina Virtual Public School, the North Carolina Department of Public Instruction and the Triangle High Five Algebra Readiness Initiative, an organization that promotes the important role mathematics teachers play in preparing students for college and careers.
The course maps to publisher requirements recently established by the lead writers of the Common Core State Standards for Mathematics. More specifically, the course addresses the authors' concerns for greater emphasis on mathematical reasoning, rigor and balance. In addition, the course takes a balanced approach to three elements the writers see as central to course rigor: conceptual understanding, procedural skill, and opportunities to apply key concepts. It incorporates 21st-century themes like global awareness and financial literacy while weaving assessment opportunities throughout the content.
While Algebra 1 is the first full course developed, SAS Curriculum Pathways provides interactive resources in every core subject for grades six through 12 in traditional, virtual and home schools at no cost to all US educators. SAS Curriculum Pathways has registered more than 70,000 teachers and 18,000 schools in the US.
SAS Curriculum Pathways aligns to state and Common Core standards (a framework to prepare students for college and for work, and adopted by 45 states), and engages students with differentiated, quality content that targets higher-order thinking skills. It focuses on topics where doing, seeing and listening provide information and encourage insights in ways conventional methods cannot. SAS Curriculum Pathways features over 200 Interactive Tools, 200 Inquiries (guided investigations, organized around a focus question), 600 Web Lessons and 70 Audio Tutorials.
SAS IN EDUCATION
In addition to SAS Curriculum Pathways online resources, SAS analytics and business intelligence software is used at more than 3,000 educational institutions worldwide for teaching, research and administration. SAS has more than three decades of experience working witheducational institutions.® .
Many new homeschoolers are often driven to stick to rigid school hours. Admittedly, when our family began, that was exactly what we believed. It took some time, observation, and the sound advice of some seasoned homeschoolers that helped us see the light. I had to ask myself why I was so resistant to changing in the first place. The answer was clear. Institutionalized thinking.
Institutionalized thinking is the idea that something cannot be done because it has never done before within a given set of parameters (i.e. classroom, industry,etc.). Most of us that are products of the public school system, universities, corporate America, etc. are victims. The side effects can linger long after we have been exposed and indoctrinated. Here are just a few of the symptoms:
Following rules, black and white thinking (not flexible, unable to perceive the value in gray areas).
Making assumptions – about others, about the world, about ideas, about the expectations you feel weighing on you, about your own abilities.
Over-reliance onlogic, along with assuming you have an accurate grasp of what is logical.
I realized that just because" it" had always been that way, didn't mean that "it" had to continue to be that way. I began my quest to be more flexible by alternating our school hours. I introduced more field trips and unique ways to approach lessons. I began to embrace every teachable moment that I could.
So what is a teachable moment? A teachable moment is that moment when a unique, high interest situation arises that lends itself to discussion of a particular topic. For example, you are teaching a lesson about the seven continents and your child expresses a particular interest in the Panama Canal. You can embrace this teachable moment and delve deeper into the area of interest. You begin to talk about imports and exports and so on. Is it a tangent? Sort of, but your child is more likely to retain what he/she learns because of their interest in the subject~Steve Jobs, 2005
Teachable moments can occur at any moment, any place, anytime, so embrace them! They help restore the zeal for teaching your child and affirm you as a capable educator.
Blogroll
Disclaimer
All postings and emails are not intended to be legal advice and are distributed for information purposes only. Additionally, they are not intended to be and do not constitute the giving of legal advice. | 677.169 | 1 |
Categories
Get Newsletter
Algebra 2 with Trigonometry
The AskDrCallahan Algebra II with Trig (sometimes called Pre-calculus) will develop your son's or daughter's skill in math and prepare them future courses in math, the ACT and SAT, and specifically college or high school calculus.
This course is taught like we would teach it in the college setting, so the student will not only be getting a taste of the content, but also the pace and treatment of such a math course at the college level.
Algebra II with Trig DVD Set Videos of course content - Approximately 14 hours of video following the textbook. Includes the tests, the test grading guide, and the Syllabus.
Disk 1 - Contains the Teachers Guide and the Solutions to Selected Problems. The Solutions to Selected Problems provides solutions to all the problems we have assigned on our syllabus which are not clearly answered in the back of the textbook. Both documents are PDF files to be used on your computer. They can be printed as needed. The same files can be downloaded at the links below. | 677.169 | 1 |
Print, save or share
Maths
Maths at Derby
What's next?
Degree level mathematics at Derby uses the skills you've developed at A level, particularly algebra and calculus, as the building blocks for learning new concepts and mathematical techniques. You'll learn how to use these effectively to model and solve problems relevant to industry and organisations.
Maths for the real world
First year modules cover the essential fundamental techniques and methods of maths, including differential and integral calculus, solution of differential equations, complex numbers, matrices, and the use of mathematical software.
Second year modules include mathematical methods and modelling, and you'll be involved in the Maths group project for a local company. You'll apply your knowledge in innovative ways to solve a real business problem for them.
In your final year you'll complete a dissertation. You'll also study more advanced maths, statistics and operational research. Topics include genetic algorithms, tabu search, game theory, fractals, number theory and cryptography.
Professional accreditation
Our Mathematics courses are approved by the Institute of Mathematics and its Applications (IMA), which means you'll be accepted for associate membership upon graduation. This is the first step to becoming a Chartered Mathematician (C.Math).
International students
If you're an international student, see more information on how we help and support you. | 677.169 | 1 |
Contains information on the following subjects: straight
lines, conic sections, tangents, normals, slopes; introduction todifferential and integral calculus; combinations and permutations;
and introduction to probability. This course is general innature and is not directed toward any specific specialty.
Assists enlisted and officer personnel of the United
States Navy and Naval Reserve in acquiring the knowledge requisite to thecomputation of time. It uses two-dimensional charts and expanded
narratives to explain both the global division anddesignation, and the processes and mathematical formulas used in
the conversion of time. | 677.169 | 1 |
Number Theory and Its Mathematical Structures Editions
Chegg carries several editions of the Number Theory and Its Mathematical Structures textbook.
Below you'll find a list of all the Number Theory and Its Mathematical Structures editions available to rent or buy. | 677.169 | 1 |
The Aftermath of Calculator Use in College Classrooms
13.11.2012
Students may rely on calculators to bypass a more holistic understanding of mathematics, says Pitt researcher
Anzeige
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center.
King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics | 677.169 | 1 |
Clear, lively style covers all basics of theory and application, including mathematical models, elementary concepts of graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, graphs and social psychology, planar graphs and coloring problems, and graphs and other mathematics.
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book is intended to be an introductory text for mathematics and computer science students at the second and third year level in universities. It gives an introduction to the subject with sufficient theory for that level of student, with emphasis on algorithms and applicationsThis book written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. The book focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineeringIn this substantial revision of a much-quoted monograph first published in 1974, Dr. Biggs aims to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first section, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth.
This is a highly self-contained book about algebraic graph theory which iswritten with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvaluesReviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring.
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. | 677.169 | 1 |
Quantitative Reasoning
QR 100 Basic Quantitative Reasoning 3 Prereq.: Permission of instructor or department chair. Designed to improve student's ability to succeed in mathematics courses and other disciplines requiring quantitative reasoning, problem-solving skills and overcoming math anxiety. Students will be given diagnostic tests to identify areas requiring remediation and will take the mathematics placement examination at the end of the course. This does not meet the prerequisite for any mathematics course and may not be used to meet the general education requirement or any major or minor in mathematics. | 677.169 | 1 |
, intended for a graphing calculator optional college algebra and trigonometry course, offers students the content and tools they will need to successfully master college algebra and trigonometry. The authors have addressed the needs of students who will continue their study of mathematics, as well as those who are taking college algebra and trigonometry as their final mathematics course. Emphasis is placed on exploring mathematical concepts by using real data, current applications and optional technology.
Oblique Triangles and the Law of Sines. The Law of Cosines. Vectors and Their Applications. Products and Quotients of Complex Numbers. Powers and Roots of Complex Numbers. Polar Equations. Parametric Equations. | 677.169 | 1 |
Designed for use by those in Years 7/8, "So You Really Want to Learn Maths 3" is the ideal resource for Key Stage 3 mathematics pupils as well as those working towards papers 2 and 4 of the 13+ Common Entrance examination or scholarship. The So you really want to learn Maths course is a rigorous, thorough mathematical course for those who really want to learn. Clear explanations are followed by an impressive amount of practice exercises which will ensure that even the fastest mathematicians will never run out of exercises! This course is ideal for use at school or by parents and home schoolers looking for a textbook which takes a rigorous approach to mathematics whilst also providing clear explanations of current mathematical methods and plenty of exercises for consolidation. An accompanying Answer Book is also available to purchase separately. | 677.169 | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.