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Fundamentals of College Algebra - With CD - 11th edition
Summary: This latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. The goal of this text is to prepare students for further courses in mathematics. Mathematically sound, FUNDAMEN...show moreTALS OF COLLEGE ALGEBRA effectively prepares students for further courses in mathematics through its excellent, time-tested problem sets. This edition has been improved in many respects including the addition of technology inserts with specific keystrokes for the TI-83 Plus and the TI-86, ideal for students who are working with a calculator for the first time. The design of the text makes the technology inserts easily identifiable, so if a professor prefers to skip these sections it is simple to do so. ...show less
Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More Than Two Variables. The Algebra of Matrices. Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. Chapter 6 Review Exercises. Chapter 6 Discussion Exercises
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The Illusion of Linear related set of flaws in mathematics education and proposes remedies
Integrates and organizes existing literature on mathematics education
Linear or proportional relationships are a major topic in mathematics education. However, recent research has shown that secondary school students have a strong tendency to apply the linear model also in situations wherein it is not applicable. This overgeneralization of linearity is sometimes referred to as the "illusion of linearity" and has a strong negative impact on students' reasoning and problem solving skills.
"The Illusion of Linearity: From Analysis to Improvement" presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. Although the empirical study of students' improper linear reasoning clearly constitutes a new line of research, it owes a great deal to prior work in mathematics education research community such as the work of the scholars of the Freudenthal Institute on realistic mathematics education.
Based on both quantitative and qualitative research, "The Illusion of Linearity: From Analysis to Improvement" discusses the following issues: (1) how the illusion of linearity appears in diverse domains of mathematics and science and how it is conceptually related to other more general misconceptions identified in the research literature, (2) what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon, and (3) how the illusion of linearity can be remedied by appropriate instruction.
"The Illusion of Linearity: From Analysis to Improvement" is essential to those working in mathematics education, particularly teacher educators and curriculum research and development.
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** Participants must hold certification through Algebra I and be seeking Math I Authorization or participants must be working towardan alternative route to certification in Mathematics as a certified special education teacher seeking to beome highly qualified.
Course Syllabus
Overview
By the end of this course, participants will:
understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.
develop a vocabulary of functions.
investigate the learning progression for functions.
interpret key features of graphs and tables given a function that models a relationship between two quantities.
distinguish between situations that can be modeled with linear or exponential functions.
find and interpret the average rate of change of a function.
compare properties of two functions each represented in a different way (algebraically, graphically and numerically in tables).
explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately.
identify the effect on the graph of replacing by and for specific values of (both positive and negative); find the value given the graphs: f(x), f(x) + k, k f(x), f(kx), f(x + k).
experiment with cases and illustrate an explanation of the effects on the graph using technology.
interpret the parameters in a linear or exponential function in terms of a context.
recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
represent arithmetic and geometric sequences using both explicit and recursive formulas.
use functions to find terms of sequences, and represent those terms in tables.
explore limits of sequences by using graphs of discrete functions.
showcase and discuss student work from selected course activities.
create a student assessment for Math I Functions Unit course is designed for High School Math 1 teachers.
High School Mathematics I Course Description (graphic)
The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics 1 uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
Although not a requirement, high speed Internet access definitely enhances the online experience. Participants should be proficient with using email, browsing the Internet and navigating through computer files. Access to Microsoft Office is recommended. Participants who do not have Microsoft Office should click here for some available options.
Prior to Session One course participants at to secure:
1. a WVDE WebTop account.
2. a SAS Curriculum Pathways teacher account.
3. the SAS Curriculum Pathways school account for students.
4. graphing calculators, TI-84 or TI-Inspire, for student and teacher use. Online graphing calculator information is provided within the Session One readings/resource section.
5. a scanner for scanning course assignments to be uploaded to the course drop box.
Format and Requirements
This workshop is divided into six one-week sessions which each include readings, activities, and an online discussion among workshop participants. The time necessary to complete each session is estimated to be six to seven hours.
The outline for the workshop is as follows:
Session One
Introduction to Functions
Session Two
Multiple Representations
Session Three
Building Functions from Existing Functions
Session Four
Building Functions in Context
Session Five
Using Functions to Represent Sequences
Session Six
Connect, Reflect and Assess
Session One: introduction to Functions
Middle school students will have studied functions mostly as input/output machines. This session reviews and extends the concept by developing an understanding of domain and range, the vocabulary of functions, and function notation. The learning progression of functions is also addressed. Course participants will investigate the function standards and explore their importance to student learning.
Session Two: Multiple Representations
Multiple representations aids student understanding of functions. Participants will focus on identifying the key features of functions given a table, a graph or an equation and decide which representation is best to use to solve a problem.
Session Three: Building Functions from Existing Functions
Participants will investigate through different resources the effect of changing the parameters of given functions. They will also explain the effects on the graph of a function using technology.
Session Four: Building Functions from Context
This session will focus on interpreting the parameters in linear and exponential functions. Participants will distinguish between situations the can be modeled with and solved by using linear and exponential functions.
Session Five: Using Functions to Represent Sequences
Participants will investigate the different types of sequences and represent them in the form of a table, a graph and an equation. They will use function notation with subscripts to represent arithmetic and geometric sequences, both explicitly and recursively. Participants will deepen their understanding of sequences by exploring the limits of sequences using the graphs of discrete functions.
Session Six: Connect, Reflect and Assess
Participants will complete the portfolio requirements by completing all session reflections and including the student work samples. Participants will also develop a Math 1 Functions comprehensive student assessment/solution key with work Math I portfolio components throughout the duration of the course. The time for completing each session is estimated to be six to seven hours weekly.
Math 1 Portfolio:
Course participants will choose three activities to use in their classroom from those suggested throughout this Math I Functions course. The activities must be from three different sessions throughout Math I Functions. Portfolio items are to be selected from the following course activities:
Complete the following for each activity to be submitted to your portfolio:
Submit two samples of your students' work that show different levels of understanding.
Explain why you selected each sample of student work and describe the level of understanding demonstrated by each student.
Discuss how this particular lesson or activity has helped develop your students' understanding of the mathematics involved.
A total of six student samples are to be included in your portfolio for Math I Functions.
Culminating Assessment:
Course participants will create a Math 1 Functions culminating assessment for students along with a solution key, complete with all work. This assessment may be used with Math I students to evaluate their conceptual understanding of the Next Generation CSO's that were targeted in this course. Categories and indicators from the Student Assessment Rubric are to be used to guide the development of the Math 1 Functions culminating assessment for students.
Discussion Participation
Participants will be evaluated on the frequency and quality of their participation in the discussion forum. Participants are required to post a minimum of one substantial original posting each session reflecting on the question for that session. They are to read all Math 1 Functions, and the successful panel portfolio review participants will receive a Certificate of Completion documenting successful completion of the course requirements.
Non-Degree Graduate Credit Information
Participants in this course are eligible to receive non-degree graduate credits from either West Virginia University, Marshall University, West Virginia State University or Concord University. Credits will be awarded at the end of the semester in which the course occurs. Additional information is available on the course News/Welcome Page.
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Editorial Reviews
Booknews
A textbook for courses or self-study within an electronics curriculum and designed to be used in conjunction with any of the popular texts on electric circuits. Assuming only a knowledge of mathematical fundamentals, proceeds from pre-algebra through number notation, the fundamentals of algebra, evaluating formulas, and linear equations. Explains scientific calculators at the beginning and requires them henceforth. Complementary educational support material is available from the publisher. No bibliography. Previously published between 1980 and 1988. Annotation c. by Book News, Inc., Portland, Or.
Related Subjects
Read an Excerpt theTable of Contents
1. Selected Prealgebra Topics.
Natural Numbers and Number Systems. Signed Numbers. Numerical Expressions and Equations. Order of Operations. Symbols of Grouping. Double Meaning of + and -. Absolute Value of a Signed Number. Combining Signed Numbers. Relational Operators. Multiplying with Signed Numbers. Dividing with Signed Numbers.
International System of Units. Selected Physical Quantities. Forming Decimal Multiples and Submultiples of the SI Units. Unit Analysis and Conversion between Systems. Applying Unit Analysis to Energy Cost. Units and Exponents.
Multiplying Monomials. Multiplying a Monomial and a Binomial. Multiplying a Monomial and a Polynomial. Subtracting Polynomials. Additional Work with Polynomials. Division of Monomials. Dividing a Polynomial by a Monomial. Factoring Polynomials with a Common Monomial Factor. Evaluating Algebraic Expressions.
Voltage Division in a Series Circuit. Conductance of the Parallel Circuit. Equivalent Resistance of the Parallel Circuit. Current Division in the Parallel Circuit. Solving Parallel Circuit Problems. Using Network Theorems to Form Equivalent Circuits.
11. Special Products, Factoring, and Equations.
Mentally Multiplying Two Binomials. Product of the Sum and Difference of Two Numbers. Square of a Binomial. Factoring the Difference of Two Squares. Factoring a Perfect Trinomial Square. Factoring By Grouping. Combining Several Types of Factoring. Literal Equations.
21. Applications of Logarithmic and Exponential Equations to Electronic Concepts.
The Decibel. System Calculations. RC and RL Transient Behavior. Preferred Number Series.
22. Angles and Triangles.
Points, Lines, and Angles. Special Angles. Triangles. Right Triangles and the Pythagorean Theorem. Similar Triangles; Trigonometric Functions. Using the Trigonometric Functions to Solve Right Triangles. Inverse Trigonometric Functions. Solving Right Triangles When Two Sides Are Known.
23. Circular Functions.
Angles of Any Magnitude. Circular Functions. Graphs of the Circular Functions. Inverse Circular Functions. The Law of Sines and the Law of Cosines. Polar Coordinates. Converting between Rectangular and Polar Coordinates.
Preface the )
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AdvancedBasic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
* Contains chapters about analysis on manifolds and foundations of probability
* Proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
* Includes many examples and nearly two hundred problems, and a separate 45-page section gives hints or complete solutions for most of the problems
* Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds
Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician.
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Basic College Mathematics
wr written with student success as its top priority, now with an emphasis on study skills growth and an expanded instructor supplements package. Whole Numbers, Multiplying and Dividing Fractions, Adding and Subtracting Fractions, Decimals, Ratio and Proportion, Percent, Measurement, Geometry, Basic Algebra, Statistics For all readers interested in basic mathematics....more
Paperback, 848 pages
Published
October 1st 2008
by Pearson
(first published September 1st 1997)
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MTH131 Principles of Calculus
Spring 2015
TEXT:
Brief Applied Calculus, Berressford and Rockett, 6th edition
OBJECTIVE:
This course presents a one-semester study of differential and integral calculus, with emphasis on polynomials, trigonometric functions, exponential functions and logarithmic functions. This course is for individuals with a good high school background in mathematics.
GOALS:
learn the mathematic concepts of the derivative and the integral.
learn the application of these two concepts.
OUTCOMES:
students will be able to explain the concept of a limit and its relationship to the derivative.
students will be able to use the derivative and integral to solve a wider variety of problems.
students will be able to describe the relationship between a function f(x) and it's derivative and integral.
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more familiar with the basic functions of differential calculus, the rules of differentiation, linear combinations of functions, quotient of two functions and much more. You will gain a good knowledge of the applications of differentiation such as maximum, minimum and equations of tangents.
Read More
You will know what the polynomial function is used for and how to factorise polynomials successfully. This course will demonstrate how to use straight line and circular functions on a graph successfully.You will have a good understanding inverse functions, logarithms, index laws and the binomial theorem of Pascal's Triangle. Read Less
This intermediate math course continues our free online maths suite of courses. It covers rules and applications of differentiation, straight line graphs, graphing circular functions, logs and indices, the Binomial theorem, inverse functions, and factors of polynomials. This course is ideal for second-level students, anyone studying for an exam, and those interested in re-igniting their knowledge of mathematics!
License
Release Date
25 February 2011
Content
Course Duration (Avg Learner)
2-3
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Precalculus with Unit-Circle Trigonometry - 3rd edition
Summary: This book introduces trigonometry through the unit circle. Cohen emphasizes graphing to explain complex concepts in an uncomplicated style, and provides supplementary graphing-calculator exercises at the end of most sections for additional perspective and reinforcement.
Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
PART X. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
PART XI. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
PART XII. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations : The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions6.49 +$3.99 s/h
Acceptable
AlphaBookWorks Alpharetta, GA
053435275805343527581960 Houston, TX
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work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed.
Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading.
Most important to this text:
* Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves
* Presents residue theory in the affine plane and its applications to intersection theory
* Methods of proof for the Riemann–Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings
* Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook
From a review of the German edition:
"[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students… The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation…highly enlightening, motivating and entertaining at the same time… One simply cannot do better in writing such a textbook."
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A detailed review of many of the things high school teachers expect their incoming students to know. Includes astronomy, world geography, U.S. geography, Canadian geography, world history, U.S. history, U.S. presidents, Canadian history, math, science, writing & grammar, literature, art & music history, major religions, languages, famous people, and more. Equally important, the book provides a strategy for learning large and complex chunks of ...
Childbirth is one of the most natural and universal experiences in life. Every year, millions of babies are born, and for new parents especially, it's both an exhilarating and frightening milestone.
In July 1985, a young Connecticut couple left their house minutes before midnight and drove to the hospital to have their first child. The husband returned home the next day, his infant daughter a week later. His wife was gone for twenty-seven ...
This book does more than teach you how to solve the problem. It teaches you how to see the problem, how to recognize and avoid the traps, and how to think! Even if you hate geometry, have nightmares about algebraic equations, and can't stand the sight of a percent sign, this book will turn you into a fearless giant-killer. Using SAT-style questions to demonstrate one hundred critical concepts, it delivers plenty of straight talk, solid ...
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A resource written specifically for the Principles of Mathematics 10 (MPM2D) course. Principles of Mathematics 10 will help students learn the mathematics skills and concepts they need to succeed in school and beyond.
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| 677.169 | 1 |
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems.
The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving... more...
Blackline master book designed
to complement a remedial Math program for small groups of students.
Explains
the basic concepts of number, exploring in detail the processes of addition,
subtraction, multiplication and division.
Decimals are investigated in detail as
well as their relationship with percentages. The activities are sequenced in
line... more...
Contains a set of black line masters for interesting math number games that can be reproduced on A3 card for practical use in the classroom, strengthening students? knowledge of times tables and number skills. Activities to suit Grades 1-7 students.
moreThis book is a collection of selected papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE conferences aims at addressing mathematical problems which have a relevance to industry, with an emphasis on modeling and numerical simulation of electronic circuits,... more...
Presents computational issues arising in financial mathematics. This guide to the financial engineering features revisions that concern topics like calibration, Monte Carlo Methods, American options, exotic options and Algorithms for Bermuda Options. It includes various figures, exercises, background material of financial engineering. more...
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites,... more...
Accessible Mathematics is Steven Leinwand?s latest important book for math teachers. He focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts... more...
This book is a collection of 65 selected papers presented at the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Espoo, Finland, in 2008. The aim of the SCEE 2008 conference was to bring together scientists from academia and industry, e.g. mathematicians, electrical engineers, computer scientists, and... more...
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The Student[Calculus1] subpackage is designed to help teachers present and students understand the basic material of a standard first course in single-variable calculus. There are three principal components to the subpackage: interactive, visualization, and single-step computation. These components are described in the following sections. General commands that are not related to visualization, interactive, or single-step computation are described in the Additional Commands section.
•
This subpackage has associated tutors. To access Student[Calculus1] tutors, from the main menu select the Tools>Tutors>Calculus.
•
Note: Throughout the help pages for the Calculus1 subpackage, the terms function and expression are generally used interchangeably, and refer to the mathematical objects that can be manipulated using the operations of calculus. The routines in the subpackage are referred to using the terms routine or command.
•
Each command in the Student[Calculus1] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.
As the underlying implementation of the Student[Calculus1] subpackage is a module, it is also possible to use the form Student[Calculus1]:-command or Student:-Calculus1:-command to access a command. For more information, see Module Members.
•
The Maple Command Completion facility is helpful for entering the names of Student package commands.
•
Many of the commands and tutors in the Student[Calculus1] package can be accessed through the context-menu. These commands are consolidated under the Student[Calculus1] name.
•
Note on boolean options: Many of the commands in the Student[Calculus1] subpackage take boolean options, that is, options of the form option_name = value, where value is true or false. These options are used, for example, to control which components are included in a plot. In all cases, the form option_name =true can be abbreviated as option_name.
Calculus1 in the Maple System
While the focus of the Calculus1 subpackage is single-variable calculus, and in particular, real-variable calculus, it exists as a part of the Maple system, whose normal domain of computation is the field of complex numbers. The routines in the Calculus1 subpackage compute only over the real domain and do not accept input expressions that contain complex numbers. However, it is also a goal to introduce as few conflicts with the main Maple system as possible.
This has resulted in the following consequences.
•
, not . The latter answer, often found in calculus textbooks, is actually a shorthand representation of two different antiderivatives of : if and if . While convenient in the context of single-variable calculus, this form is of questionable value in general. For example, it creates difficulties when studying the integration theory of complex numbers. The Rule routine returns when appropriate for a definite integral.
•
The general power function, where is a given real number, is real-valued only for unless is an integer. This follows from the fact that the power function is multi-valued when is not an integer. Maple implements what is known as the principal branch of this function. For negative and non-integer , this principal branch is complex-valued. This can conflict with your expectations for some common functions, for example, the cube root function . If you plot the cube root function over the interval using the Maple plot command, you see only the part of the graph on the positive interval because the rest of the graph consists of complex numbers. To avoid this situation, Maple has another power function, surd, that returns a real value whenever possible.
•
Certain transformations that are valid for real-variable calculus are not valid for general complex numbers. Therefore, Maple may not perform them. If Maple does not perform an operation (for example, by calling simplify) that is valid for your expression, use the assuming operator.
•
The antiderivative, or indefinite integral, of a function is an entire class of functions, whose members differ by an additive constant. For example, . Maple, in general, does not explicitly include the constant . For consistency, the Calculus1 integration rules also omit the constant.
Visualization
The visualization routines are designed to assist in the understanding of basic calculus concepts, theorems, and computations. These routines normally produce a Maple plot, and most can optionally return one or more symbolic representations of the studied quantity.
You have considerable control over the presentation of plots produced by the visualization routines. The display of each object included in the plot can be adjusted by using a corresponding option in the calling sequence. See the help pages for the individual commands for details.
The interactive routines use the Maple Maplet technology to assist you to work through the standard problems of calculus in a visually directed manner. These commands display one or more dialog boxes allowing you to plot a function and change the various plot options.
The DiffTutor, IntTutor, and LimitTutor display dialog boxes presenting the current state of the problem you are working on and a set of controls which let you move to the next step in the solution of that problem.
To help you study the techniques of computation in single-variable calculus, the Calculus1 subpackage provides facilities to proceed in small steps through calculations. For example, you can request that a differentiation problem be solved one step at a time, where you specify the differentiation rule applied at each step.
The operations that can be stepped through in this manner are: limit, differentiation, and integration.
At any time during a single-step computation, you can ask for a hint about the next step to take, which you can then apply to the problem.
The subpackage maintains a list of all the problems that you have stepped through in this manner in the current session. You can ask for a review of any or all of these problems.
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Inside.IVC (Intranet)
BASIC MATH MODULES (MATH 350 A-H) ORIENTATION
ONLINE STUDENTS ONLY:
Please watch the Overview and the 8-step videos. You do not need to come in to take this class. You do all the work online including the final exam. Please take your final exam before or on the last day of your class duration. You will get credit if you score 70% or higher in the final exam. You have to take the final exam in one sitting and without a calculator.
TRADITIONAL (CLASSROOM) STUDENTS ONLY:
Please watch the 8-step videos. You are required to attend your classes in person. Please take your final exam on the last day of your class. You will get credit if you score 70% or higher in the final exam. You have to take the final exam in one sitting and without a calculator.
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theoretical foundation for analysis of functions of several variables
Motivates the topics with examples, observations, exercises, and illustrations
Includes appendix of mathematicians who made important contributions to analysis
Exciting historical background motivates the subject
Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.
The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.
This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations.
Other books published by the authors – all of which provide the reader with a strong foundation in modern-day analysis – include:
* Mathematical Analysis: Functions of One Variable
* Mathematical Analysis: Approximation and Discrete Processes
* Mathematical Analysis: Linear and Metric Structures and Continuity
* Mathematical Analysis: An Introduction to Functions of Several Variables
Reviews of previous volumes of Mathematical Analysis:
The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties.
—Journal of Analysis and its Applications
The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature ofthis lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations.
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You are here
Visual Linear Algebra: With Maple and Mathematica Tutorials
Publisher:
John Wiley
Number of Pages:
550
Price:
92.30
ISBN:
0-471-68299-3
"Visual Linear Algebra is a new kind of textbook," the authors tell us in the Preface. Actually, the book looks very much like any other linear algebra text, until you notice that inside the front cover is hidden a CD. Reading the Preface, one learns about the tutorials provided in this CD in the format of Maple worksheets and Mathematica notebooks; these are to be the center of the student's learning process. The significance of the CD and the justification of the above comment of the authors in fact become much clearer when one takes a look at the Table of Contents: Out of the forty-seven sections of the text, the thirty that are marked with a blue semidisk are exact text versions of the tutorials provided in the CD. Thus, the computer component of a course using this textbook will not be a mere supplement; rather, it is going to be the core of the whole experience. In fact, the pages corresponding to the tutorial sections have blue margins and the book looks mostly blue from the side! The idea is that the examples that use the computer will be more interesting since they can be selected to be computationally more challenging and hence involve more complex systems.
Linear algebra is undoubtedly very basic and important in the undergraduate mathematics curriculum, and often it follows calculus in the list of courses to be taken by students who will not major in mathematics but will need to have a good mathematical foundation in their own majors. Especially for such students, but definitely also for math majors, a good linear algebra course needs to emphasize numerous examples and has to find an approach that will work for a wide variety of learning styles; a purely axiomatic development will not be sufficient. As one way to deal with this situation, various texts and instructors find it useful to spend a considerable time on vectors in two and three dimensional Euclidean spaces in order to help students visualize various concepts of linear algebra; the axiomatics may or may not follow eventually depending on the needs of the students. Visual Linear Algebra also makes extensive use of two and three dimensional examples. The axiomatics part is not postponed until the last few chapters, however; the concepts developed in any tutorial by the help of the visual tools of two and three dimensions are generalized and given a rigorous foundation always within the same chapter.
The text is intended for a one-semester linear algebra course, and the usual mathematical maturity of a student taking a standard first course in linear algebra will suffice to follow it. The subjects covered are the usual bunch; here is the list of the titles of the eight chapters: Systems of Linear Equations; Vectors; Matrix Algebra; Linear Transformations; Vector Spaces; Determinants; Eigenvalues and Eigenvectors; Orthogonality. All the standard concepts of linear algebra are covered, albeit in a somewhat abstract style, in purely textual sections. The use of the computer algebra systems in the tutorial sections allows the authors to add on colorful examples to the text involving Markov processes and more general discrete dynamical systems. There are several sections included which explore interesting applications of linear algebra like computer graphics, cryptology, loops and spanning trees. I was especially intrigued and excited by the use of movies, animated pictures showing how a particular system evolves as some parameter is changed. There is even an exercise where the student is taken through a step-by-step solution of the problem of creating a realistic animation of a car moving along a curved road, taking into consideration the fact that the car needs to be pointing in the right direction!
Incorporating Maple and Mathematica into the text may have one additional benefit; students who use this text will end up getting quite comfortable with the system that they decide to use. This is clearly not a major goal of the text but may be seen as a pleasant by-product. Clearly not all students will come to their first linear algebra course proficient in either of the two computer algebra systems. However, these are both well-documented and widely available computer algebra systems, and it will not take great expertise in either to be able to use and benefit from the tutorials. The time the student uses to learn the basics of either of Maple and Mathematica will be time well-spent; these programs have wide applications and students will most likely come across their various uses further along their careers.
The philosophy underlying this whole project is emphasized in the Preface: the student will only learn by doing. The student is expected to go through a wide variety of exercises; the tutorials allow modifications as well, and thus encourage further exploration of the topics. This indeed is a new kind of textbook, and it tackles with the difficult task of naturally incorporating computers into the standard linear algebra course in order to enhance student participation and understanding. This reviewer believes that this job has been done very well. The few typos in the tutorials and the somewhat unlucky choice of color scheme (blue, gray and black) for the various tips of vector arrows used in the illustrations throughout the text can hopefully be dealt with in a new edition.
Gizem Karaali teaches at the University of California in Santa Barbara.
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Overview
Mathematical Methods in Chemical Engineering builds on students' knowledge of calculus, linear algebra, and differential equations, employing appropriate examples and applications from chemical engineering to illustrate the techniques. It provides an integrated treatment of linear operator theory from determinants through partial differential equations, featuring an extensive chapter on nonlinear ordinary differential equations as well as strong coverage of first-order partial differential equations and perturbation methods. Numerous high-quality diagrams and graphics support the concepts and solutions. Many examples are included throughout the text, and a large number of well-conceived problems at the end of each chapter reinforce the concepts presented. Also, in some cases the results of the mathematical analysis are compared with experimental data--a unique feature for a mathematical book.
The text offers instructors the flexibility to cover all of the material presented or to select a few methods to teach, so that they may cultivate the specific mathematical skills which are most appropriate for their students. The topical coverage provides a good balance between material which can be taught in a one-year course and the techniques that chemical engineers need to know to effectively model, analyze, and carry out numerical simulations of chemical engineering processes, with an emphasis on developing techniques which can be used in applications. Mathematical Methods in ChemicalEngineering serves as both an ideal text for chemical engineering students in advanced mathematical methods courses and a comprehensive reference in mathematical methods for chemical engineering practitioners in academic institutions and
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Toward the end of a study of equation solving by means of a graphical representation, a seventh grader was asked to solve the equation 7x+4=5x+8 (an equation whose solution is x=2). Rather than graph the two expressions, the student took a "shortcut."
Interviewer: Can you solve 7x+ 4=5x+8?
Jer: Well, you could, see, it would be like start at 4 and 8, this one would go up by 7, hold on, 8, 8 and 7, hold on, no, 4 and 7, 4 and 7 is 11. They'd be equal, like, 2 or 3 or something like that.
Interviewer: How are you getting that 2 or 3?
Jer: I'm just like graphing it in my head.
SOURCE: Kieran and Sfard, 1999, p. 15. Used by permission of the author.
is generalizable, but we will also teach how to use symbol manipulators to solve these and more-complicated equations [emphasis added].62
Thus, most teachers—for the time being, at least—remain insistent that students learn to do by hand the various algebraic transformations of expressions and equations. In 1989 one mathematics educator noted that "the unanswered question standing in the way of reducing the manipulative skills agenda of secondary school algebra is whether students can learn to plan and interpret manipulations of symbolic forms without being themselves proficient in the execution of those transformations."63 Very little research has been conducted since then to help resolve the question; however, the research that has been done is quite telling. A recent study investigated the impact on algebra achievement of a three-year integrated mathematics curriculum in which technology was used to perform symbolic manipulations as well as to link various representations of problem situations.64 In this study, which involved over 300 high school students in 12 schools, some support was found for the notion that learning how to interpret results of algebraic calculations is not highly dependent on the ability to perform the calculations themselves
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Algebra 1
Bring Clarity to Common Core Curriculum
The new topics added by the Common Core Curriculum and the emphasis placed on
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In his masterful teaching style, Leonard Morochnick highlights the important principles
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how these principles are applied. Mr. Morochnik's famous "do not make this
mistake" will prevent students from common pitfalls.The series provides problem solving strategies for all the concepts taught, accompanied
by actual examples and their step by step solutions. Consistent with the approach of
the Common Core Curriculum, the Math Made Easy program helps students build their
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Make Algebra Meaningful
While many algebra teachers focus on rote learning and memorization, Math Made Easy focuses on comprehension. Your child will develop a genuine understanding of algebra concepts as required by the new Common Core Curriculum guidelines. Dynamic lessons and do-it-yourself exercises build upon this foundation of understanding. Watch your child's eyes light up with the "aha" moment of comprehension!
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Math Made Easy empowers students by putting them in control of the learning process. No more struggling to keep up with lightning-fast lessons! Our video-based algebra program will take the stress out of learning. Math Made Easy's Common Core algebra series takes the stress out of learning by enabling students to control the pace of their study. With your child in the driver's seat, he/she will attain a mastery of algebra skills along with the confidence of success.
Series of 5 Algebra Instructional DVDs contains:
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Utilized by thousands of students, Math Made Easy Algebra software provides the extra review that many students need to keep up in school. The program is also ideal for in-classroom and homeschooling use. Its versatile format makes it the perfect resource to supplement an existing algebra course or to provide a comprehensive review.
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Customer Reviews:
shaber7878 (Monday, 12 January 2015)
Rating:
My son always did really well in math until he got to algebra. The core curriculum had him totally lost. This DVD program really helped to clarify the concepts. He took his time and was able to understand what was going on. Now he is getting A's. What a relief!
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Intermediate Algebra (Cloth) - 4th edition
Summary: Get Better Results with high quality content, exercise sets, and step-by-step pedagogy! The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Intermediate Algebra 4e. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students. Throughout the text, the authors communicate to students the very points thei...show morer instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. Also included are Problem Recognition Exercises, designed to help students recognize which solution strategies are most appropriate for a given exercise. These types of exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor, answers, and/or underlining. Used books may have stickers on them. Ships same day or next business day. Free USPS Tracking ...show moreNumber. Excellent Customer Service. Ships from TN ...show less152.38 +$3.99 s/h
Good
BookMob Ottawa, ON
Hardcover Good 00733844153
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This Textbook
Overview
This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.
What People Are SayingEditorial Reviews
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Algebraic text on algebraic combinatorics targeted towards undergraduates
Textbook written by the most well-known algebraic combinatorist world-wide
Covers topics of Walks in graphs, cubes and Radon transform, Matrix-Tree Theorem, the Sperner property, and more
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author's extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models.
The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, de Bruijn sequences, the Erdős-Moser conjecture, electrical networks, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.
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Functions 1.00
Easy to use, intuitive program to visualize and study functions of one variable to find roots, maxima and minima, integral, derivatives, graph. Results, including the graph, can be saved or printed. You can also copy the graph to the clipboard, which you can then paste where you please (Word, Paint, etc.). You have one-click control of the graph with zooming, panning, centering, etc. Includes a help file with instructions, example and methodology
Rt-Plot Rt-Plot is a tool to generate Cartesian X/Y-plots from scientific data. You can enter and calculate tabular data. View the changing graphs, including linear and non linear regression, interpolation, differentiation and integration, during entering. Download Now!
Prime Number Spiral The Prime Number Spiral (a.k.a. the Ulam Spiral) is formed by marking the prime numbers in a spiral arrangement of the natural numbers. This is software is for exploring the Prime Number Spiral. Download Now!
School Calendar School Calendar will help you with assignment organization, project due dates, and scheduling. It can even remind you when your scheduled event is about to happen. Included are two viewing modes, search, auto-backup, iCalendar data exchange. Download Now!
Breaktru Fractions n Decimals Add Download Now!
Archim Archim is a program for drawing the graphs of all kinds of functions. You can define a graph explicitly and parametrically, in polar and spherical coordinates, on a plane and in space (surface). Archim will be useful for teachers and students. Download Now!
Inverse Matrices The program provides detailed, step-by-step solution in a tutorial-like format to the following problem: Given a 2x2 matrix, or a 3x3 matrix, or a 4x4 matrix, or a 5x5 matrix. Find its inverse matrix by using the Gauss-Jordan elimination method. The... Download Now!
HiDigit is a new calculating software with extended capabilities. This is an essential application for math, algebra, calculus, geometry, physics and engineering students. The main advantage of the software is a simple input format even for the most complicated formulas. For example, you can enter 10pi instead of "10*pi". This scientific calculator works with complex numbers, keeps record of previous actions; both mouse and keyboard can be used.
Free math / graphing program - type and graph an equation! Free math / graphing program - type and graph an equation!
AnalyticMath is a FREE, cross-platform math / graphing program with a powerful editor and integrated 'auto-calc' features that will help you develop and visually analyse mathematical...
Vinny Graphics is a novel graphing and data analysis software for science and engineering students. Vinny Graphics is a novel graphing and data analysis software for science and engineering students. It is easy-to-use and accepts and exports data through a variety of sources. The intuitive Windows interface helps produce multi-parameter design...
Explore math with Desmos! Graph functions, create function tables, explore transformations, plot points, animate your graphs, and more for free!At Desmos, we imagine a world of universal math literacy and envision a world where math is ... Explore math with Desmos! Graph functions, create function tables, explore transformations, plot points, animate your graphs, and more for free!
At Desmos, we imagine a world of universal math literacy and envision a world where math is...
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The purpose of this course is twofold. First, to acquaint the student
with several discrete mathematical structures and theories that bear relevance
to Computer Science. These include sets, relations, functions, matrices,
graphs, groups, counting techniques, mathematical logic and boolean algebra.
Second, to equip the student with mathematical tools and analytical
techniques for theorem proving and problem solving.
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Download
Chapter 8: Infinite Series
This chapter introduces the study of sequences and infinite series. In calculus, we are interested in the behavior of sequences and series, including finding whether a sequence approaches a number or whether an infinite series adds up to a number. The tests and properties in this chapter will help you describe the behavior of a sequence or series.
Description
This chapter introduces the study of sequences and infinite series. The properties presented describe the behavior of a sequence or series, including whether a sequence approaches a number or an infinite series adds to a number.
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Algorithms Unlocked - 13 edition
Summary: Have you ever wondered how your GPS can find the fastest way to your destination, selecting one route from seemingly countless possibilities in mere seconds? How your credit card account number is protected when you make a purchase over the Internet? The answer is algorithms. And how do these mathematical formulations translate themselves into your GPS, your laptop, or your smart phone? This book offers an engagingly written guide to the basics of computer algorithms...show more. In Algorithms Unlocked, Thomas Cormen -- coauthor of the leading college textbook on the subject -- provides a general explanation, with limited mathematics, of how algorithms enable computers to solve problems. Readers will learn what computer algorithms are, how to describe them, and how to evaluate them. They will discover simple ways to search for information in a computer; methods for rearranging information in a computer into a prescribed order ("sorting"); how to solve basic problems that can be modeled in a computer with a mathematical structure called a "graph" (useful for modeling road networks, dependencies among tasks, and financial relationships); how to solve problems that ask questions about strings of characters such as DNA structures; the basic principles behind cryptography; fundamentals of data compression; and even that there are some problems that no one has figured out how to solve on a computer in a reasonable amount of time. ...show less
0262518805
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MATH DOESN'T SUCK - 07 edition
Summary: From a well-known actress and math genius-a groundbreaking guide to mathematics for middle school girls, their parents, and educators As the math education crisis in this country continues to make headlines, research continues to prove that it is in middle school when math scores begin to drop-especially for girls-in large part due to the relentless social conditioning that tells girls they can't do math, and that math is "uncool." Young girls today need s...show moretrong female role models to embrace the idea that it's okay to be smart-in fact, it's sexy to be smart! It's Danica McKellar's mission to be this role model, and demonstrate on a large scale that math doesn't suck. In this fun and accessible guide, McKellar-dubbed a "math superstar" by The New York Times-gives girls and their parents the tools they need to master the math concepts that confuse middle-schoolers most, including fractions, percentages, pre-algebra, and more. The book features hip, real-world examples, step-by-step instruction, and engaging stories of Danica's own childhood struggles in math (and stardom). In addition, borrowing from the style of today's teen magazines, it even includes a Math Horoscope section, Math Personality Quizzes, and Real-Life Testimonials?ultimately revealing why math is easier and cooler than readers think. ...show lessRichardson Richardson
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Precalculus Essentials
Browse related Subjects
...Read More Chapter 11 Introduction to Calculus). This text explores math the way it evolved: by describing real problems and how math explains them. It is interesting, lively (with applications you won't see in any other math book), and exceedingly clear. Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly. Students are strongly supported by a consistent pedagogical framework. A See it, Hear it, Try it? format consistently walks students through each and every example in just the same way that an instructor would teach this example in class. Blitzer liberally inserts voice balloons and annotations throughout the text helping clarify the more difficult concepts for
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A student has to be able to solve word problems along with regular exercises, which builds up their skill level. Precalculus builds upon Algebra 2 knowledge and extends it in order to prepare for Calculus. In this subject, it is imperative that the student starts thinking at a higher level and applies the concepts learned in Algebra 2 in order to succeed.
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Calendar
SpringfieldMath Brush Up — Tuesday, January 20, 2015
The workshop includes a brief review of whole numbers, fractions, decimals, ratio, percent, positive and negative numbers and basic arithmetic operations. Free to CCV students enrolled in
credit-bearing courses. Call 885-8360 to enroll in this brushup.
Algebra Brush Up — Thursday, January 22, 2015
This workshop is for students who are ready for Mathematical Concepts or College
Algebra but would benefit from a quick brush-up in basic algebra skills. The
workshop includes a brief review of algebraic laws, polynomials, exponents,
linear equations and factoring. Free to CCV students enrolled in credit-bearing
courses. Call 885-8360 to enroll in this brush up
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A Geometric Approach to Differential Forms
Bachman, David
2nd ed. 2012, XVI, 156p. 43"[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level." —MAA Reviews (Review of First Edition)
"The book certainly has its merits and is very nicely illustrated … . It should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates)." —Mathematical Reviews (Review of First Edition)
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.
Each new concept is presented with a natural picture that students can easily grasp; algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions.
The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. The work is suitable for use as the primary textbook for a sophomore-level class in vector calculus, as well as for more upper-level courses in differential topology and differential geometry.
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Features of all TabletClass Math Courses
This course is designed for the first year community college math student. Completion of high school Algebra 2 is desired but not required.
The first part of the course is an extensive series of sections on basic algebra topics that students should have mastered in Algebra 1. The course also focuses on a student's knowledge and skill to work with quadratic equations/complex numbers, linear systems and matrices/determinants. Functions and relations are studied along with powers and radicals.
The course finishes by introducing many more advance level topics to include exponential and logarithmic functions and concepts and theorems to solve polynomials of n-degree. Also a chapter on rational functions is explored to include a section on graphing rational functions.
When You Complete Our Extremely Comprehensive TabletClass Course You Are More Than Prepared!
Don't just learn...become a master at math and be ready for your future!
College Algebra Course Curriculum
Chapter 1: Basic Algebra (Review)
This chapter reviews many of the fundamental algebra skills that students should have mastered in Algebra 1. Students are encouraged to take the time to go over these sections to ensure they are ready for the more advance concepts later in the course.
Sections:
• Real Numbers (number operations, distributive property, simplifying algebraic expressions)
• Equations (multi-step and formulas)
• Inequalities (linear and compound)
• Absolute Value (equations and inequalities)
Chapter 2: Graphing and Writing Linear Equations
This very important chapter stresses how to graph and write linear equations. Concepts involving the coordinate plane, slope and methods to graph lines are thoroughly reviewed and introduced. The second part of the chapter focuses on the various methods to find and write the equation of a line. Additional related topics are explored to include linear models, regression, absolute value graphs and word problems.
Sections: • Graphing Lines with One Variable
• Graphing Lines with Two Variables
• The Slope of a Line
• Slope Intercept Method
• XY Intercept Method
• Using Slope-Intercept Form
• Using Point-Slope intercept
• Given the Slope and a Point
• Given Two Points
• Standard Form of Linear Equations
• Best Fitting Line
• Linear Models/Word Problems
• Graphing Linear Inequalities in Two Variables
• Graphing Absolute Value Equations
Chapter 3: Quadratic Equations and Complex Numbers
Understanding the properties and methods to solve quadratic equations is essential for to the student to advance in Algebra. This chapter explains each concept in a very specific and focused manner. After students have been introduced to quadratic equations they build up their knowledge by learning various techniques to solve them.
Chapter 4: Functions and Relations
Functions and relations transcend all through mathematics. This chapter explains core concepts at the Algebra level and prepares the student for more advance study of the topic. Time is taken to explain the difference between a function and relation and introduce the student to the language of functions to include the domain, range and linear/nonlinear functions. Students will also learn function operations, composite functions and graphing.
Sections:
• Introduction to Functions and Relations
• Function Operations
• Inverse Functions
• Graphing Functions
• Linear and Nonlinear Functions
• Special Functions
• Composite Functions
Chapter 5: Systems
Understanding systems and the methods to solve them are vital in Algebra. This chapter introduces/reviews techniques to solve linear systems. Students will also explore special systems, word problem s and systems of linear inequalities. Lastly, the topic of Linear Programming will be introduced. This powerful technique uses systems to "optimize" a constrain function. Because Linear Programming is widely used in business and industry this part of the chapter is a nice way to connect concepts of systems to "real world" applications.
Sections:
• Solving Systems by Graphing
• Solving Systems Substitution Method
• Solving Systems by Elimination/Linear Combination
• Solving Linear System Word Problems
• Special Linear Systems
• Solving Systems of Linear Inequalities
• Linear Programming/Word Problems
Chapter 6: Matrices and Determinants
This chapter introduces the core concepts of matrices and determinants to students. Time is taken to teach terminology and common applications of matrices. Students will learn how to perform various matrix operations to include matrix addition, subtraction multiplication and scalar multiplication. Additionally students will learn the steps to find determinants and inverse of a matrix. The chapter also focuses on how matrices can be used to solve linear systems by using an inverse matrix or Cramer's Rule.
Sections: • Introduction to Matrices
• Matrix Operations
• Matrix Multiplication
• Determinants
• Identity and Inverse Matrices
• Solving Systems using Inverse Matrices
• Solving Systems using Cramer's Rule
Chapter 7: Polynomial Functions
The first part of the chapter covers the parts of a polynomial, related terminology and how to perform polynomial operations. A special focus is placed on the extremely important skill of factoring polynomials. Students will understand how to factor out a polynomial GCF and build on this to learn many techniques to factor polynomials.
Chapter 8: Rational Expressions/Equations
The first part of the chapter takes the student through fundamental rational expressions to include ratios, rates, proportions, percent and variation. Special emphasis is placed on learning different methods to solve rational expression problems. The section on simplifying rational algebraic expressions starts by reviewing basic examples using numbers before introducing variable examples.
The second part of the chapter builds from the student's knowledge of polynomials and covers operations with rational expressions. Instruction will focus on learning to multiply, divide, find the LCD and solve rational expressions. Additionally, a section is dedicated to the procedure/ methods to graph rational functions; new terms like vertical and horizontal asymptotes will be explained.
Sections:
• Ratios and Proportions
• Percent
• Direct and Inverse Variation
• Simplifying Rational Expressions
• Multiplying and Dividing Rational Expressions
• Finding the LCD of Rational Expressions
• Solving Rational Equations
• Adding and Subtracting Rational Expressions
• Operations and Equations with Rational Exponents
• Graphing Rational Functions (vertical and horizontal asymptotes)
Chapter 9: Powers and Radicals
This chapter covers all the rules the student will need to work with powers, exponents, radicals and rational exponents. Also, important applications of these rules are coved to include scientific notation, compound interest, Pythagorean Theorem and the Distance and Mid-Point formula. Special emphasis is placed on solving radical and rational root equations.
Sections:
• Product and Power Rules of Exponents
• Negative and Zero Exponents Rules
• Division Rules of Exponents
• Scientific Notation
• Compound Interest
• Simplifying Radicals
• Operations with Radicals
• Solving Radical Equations
• Operations and Equations with Rational Exponents
• The Distance and Mid-Point Formula
• The Pythagorean Theorem
Chapter 10: Logarithmic and Exponential Functions
For most students this chapter will be their first introduction to logarithms. As such the chapter focuses on teaching the basic core concepts of a logarithm and its relationship to an exponential function. Students will learn how to covert between a logarithm/exponential equation.
Additionally, the chapter defines the properties of logarithms and how to condense and expand logarithmic expressions. The Natural Base e and Natural logarithms are explored with explanations of how to use the "log and ln" functions on a scientific calculator. Finally the chapter covers the methods and procedure to solve exponential and logarithmic equations.
Sections:
• Exponential Growth and Decay Functions
• Introduction to Logarithms
• Properties of Logarithms
• The Natural Base e
• Natural Logarithms
• Solving Logarithmic Equations
• Solving Exponential Equations
When You Complete Our Extremely Comprehensive TabletClass Course You Are More Than Prepared!
Don't just learn...become a master at math and be ready for your future!
| 677.169 | 1 |
Extensive coverage of topics provides a welcome prompt for further exploration
A broad range of material that may be applied to a selection of sub-disciplines within science and engineering
The inclusion of exercises enables practical learning throughout the book
Whilst it is a moot point amongst researchers, linear algebra is an important component in the study of graphs. This book illustrates the elegance and power of matrix techniques in the study of graphs by means of several results, both classical and recent. The emphasis on matrix techniques is greater than other standard references on algebraic graph theory, and the important matrices associated with graphs such as incidence, adjacency and Laplacian matrices are treated in detail.
Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph.
Such an extensive coverage of the subject area provides a welcome prompt for further exploration, and the inclusion of exercises enables practical learning throughout the book. It may also be applied to a selection of sub-disciplines within science and engineering.
Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory who want to be acquainted with matrix theoretic ideas used in graph theory, it will also benefit a wider, cross-disciplinary readership.
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PREREQUISITES: Passing the math portion of the THEA test and two
years of high school algebra or completion of the developmental
math sequence as described in the Ranger College Developmental
Education Plan.
EXEMPLARY OBJECTIVES SUPPORTED BY THIS COURSE
The purpose of these objectives is to contribute to your
intellectual and personal growth and assist you in understanding
and appreciating not only your heritage, but also to prepare you
for responsible citizenship and provide you the ability to adapt
to a rapidly changing and highly technological world.
M1. To apply arithmetic, algebraic, geometric, higher-order
thinking, and statistical methods to modeling and solving
real-world problems
M2. To represent and evaluate basic mathematical information
verbally, numerically, graphically, and symbolically
M3. To expand mathematical reasoning skills and formal logic to
develop convincing mathematical arguments
M4. To use appropriate technology to enhance mathematical
thinking and understanding and to solve mathematical problems and
judge the reasonableness of the results
M5. To interpret mathematical models such as formulas, graphs,
tables, and schematics, and draw inferences from them
M6. To recognize the limitations of mathematical and statistical
models
M7. To develop the view that mathematics is an evolving
discipline, interrelated with human culture, and understand its
connections to other disciplines
COURSE CALENDAR (15 weeks plus final) Suggested timetable
(subject to change). The problem set for each section is listed
with the section. Instructions in bold print over-ride and
replace the book's instructions.
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About Math Lab
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The Math Lab seeks to develop each student's ability to understand and apply mathematical
principles and knowledge through tutoring, resources, and programs, which are offered
in a relaxed, friendly atmosphere.
Our Culture of Learning
The UVU Math Lab is a drop-in study space dedicated to helping students develop their
learning skills, mathematical abilities and to reduce mathematics anxiety. The Math
Lab is a great place to work on homework, where tutors can answer questions as they
arise. Additionally, students are welcome to discuss homework exercises with fellow
students.
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Our highly qualified math tutors are required to maintain a 3.0 grade point average
and have completed higher mathematics courses beyond College Algebra. Their mathematics
experience is in pursuit of such fields as Math Education, Engineering, Physics, Business,
Actuarial Science, and even pure Mathematics. Further, each tutor is required to complete
the nationally recognized College Reading and Learning Association (CRLA) Tutor Training
Certification Program. Through this program, our tutors are trained to support student
learning through mentoring, coaching, and modeling effective learning strategies in
addition to using their exceptional knowledge of mathematics.
Our Services
Students check in and out using the self check out service.
Textbooks, solution manuals, calculators, and other tools are available to check out
while in the lab.
The Math Lab has 10 computers available for students to complete computer-based homework
assignments with software such as MyMathLab, WileyPlus, and PHStat.
Appointments for private tutoring available.
Please note that tutors cannot assist students with any take-home exams or make-up assignments which earn test credit.
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More About
This Textbook
Overview
With unusual depth and clarity, it covers the problem of the foundations of geometry, the theory of time, the theory and consequences of Einstein's relativity including: relations between theory and observations, coordinate definitions, relations between topological and metrical properties of space, the psychological problem of the possibility of a visual intuition of non-Euclidean structures, and many other important topics in modern science and philosophy.
While some of the book utilizes mathematics of a somewhat advanced nature, the exposition is so careful and complete that most people familiar with the philosophy of science or some intermediate mathematics will understand the majority of the ideas and problems discussed.
Partial CONTENTS: I. The Problem of Physical Geometry. Universal and Differential Forces. Visualization of Geometries. Spaces with non-Euclidean Topological Properties. Geometry as a Theory of Relations. II. The Difference between Space and Time. Simultaneity. Time Order. Unreal Sequences. Ill. The Problem of a Combined Theory of Space and Time. Construction of the Space-Time Metric. Lorentz and Einstein Contractions. Addition Theorem of Velocities. Principle of Equivalence. Einstein's Concept of the Problems of Rotation and Gravitation. Gravitation and Geometry. Riemannian Spaces. The Singular Nature of Time. Spatial Dimensions. Reality of Space and Time.
Dover Publications, Inc.
In Euclid's work, the geometrical achievements of the ancients reached their final form: geometry was established as a closed and complete system. The basis of the system was given by the geometrical axioms, from which all theorems were derived. The great practical significance of this construction consisted in the fact that it endowed geometry with a certainty never previously attained by any other science. The small number of axioms forming the foundation of the system were so self-evident that their truth was accepted without reservation. The entire construction of geometry was carried through by a skillful combination of the axioms alone, without any addition of further assumptions; the reliability of the logical inferences used in the proofs was so great that the derived theorems, which were sometimes quite involved, could be regarded as certain as the axioms. Geometry thus became the prototype of a demonstrable science, the first instance of a scientific rigor which, since that time, has been the ideal of every science. In particular, the philosophers of all ages have regarded it as their highest aim to prove their conclusions " by the geometrical method."
Euclid's axiomatic construction was also important in another respect. The problem of demonstrability of a science was solved by Euclid in so far as he had reduced the science to a system of axioms. But now arose the epistemological question how to justify the truth of those first assumptions. If the certainty of the axioms was transferred to the derived theorems by means of the system of logical concatenations, the problem of the truth of this involved construction was transferred, conversely, to the axioms. It is precisely the assertion of the truth of the axioms which epitomizes the problem of scientific knowledge, once the connection between axioms and theorems has been carried through. In other words: the implicational character of mathematical demonstrability was recognized, i.e., the undeniable fact that only the implication "if a, then b" is accessible to logical proof. The problem of the categorical assertion "a is true b is true", which is no longer tied to the "if", calls for an independent solution. The truth of the axioms, in fact, represents the intrinsic problem of every science. The axiomatic method has not been able to establish knowledge with absolute certainty; it could only reduce the question of such knowledge to a precise thesis and thus present it for philosophical discussion.
This effect of the axiomatic construction, however, was not recognized until long after Euclid's time. Precise epistemological formulations could not be expected from a naive epoch, in which philosophy was not yet based upon well-developed special sciences, and thinkers concerned themselves with cruder things than the truth of simple and apparently self-evident axioms. Unless one was a skeptic, one was content with the fact that certain assumptions had to be believed axiomatically; analytical philosophy has learned mainly through Kant's critical philosophy to discover genuine problems in questions previously utilized only by skeptics in order to deny the possibility of knowledge. These questions became the central problems of epistemology. For two thousand years the criticism of the axiomatic construction has remained within the frame of mathematical questions, the elaboration of which, however, led to peculiar discoveries, and eventually called for a return to philosophical investigations.
The mathematical question concerned the reducibility of the axiomatic system, i.e., the problem whether Euclid's axioms represented ultimate propositions or whether there was a possibility of reducing them to still simpler and more self-evident statements. Since the individual axioms were quite different in character with respect to their immediacy, the question arose whether some of the more complicated axioms might be conceived as consequences of the simpler ones, i.e., whether they could be included among the theorems. In particular, the demonstrability of the axiom of the parallels was investigated. This axiom states that through a given point there is one and only one parallel to a given straight line (which does not go through the given point), i.e., one straight line which lies in the same plane with the first one and does not intersect it. At first glance this axiom appears to be self-evident. There is, however, something unsatisfactory about it, because it contains a statement about infinity; the assertion that the two lines do not intersect within a finite distance transcends all possible experience. The demonstrability of this axiom would have enhanced the certainty of geometry to a great extent, and the history of mathematics tells us that excellent mathematicians from Proclus to Gauss have tried in vain to solve the problem.
A new turn was given to the question through the discovery that it was possible to do without the axiom of parallels altogether. Instead of proving its truth the opposite method was employed: it was demonstrated that this axiom could be dispensed with. Although the existence of several parallels to a given line through one point contradicts the human power of visualization, this assumption could be introduced as an axiom, and a consistent geometry could be developed in combination with Euclid's other axioms. This discovery was made almost simultaneously in the twenties of the last century by the Hungarian, Bolyai, and the Russian, Lobatschewsky; Gauss is said to have conceived the idea somewhat earlier without publishing it.
But what can we make of a geometry that assumes the opposite of the axiom of the parallels? In order to understand the possibility of a non-Euclidean geometry, it must be remembered that the axiomatic construction furnishes the proof of a statement in terms of logical derivations from the axioms alone. The drawing of a figure is only a means to assist visualization, but is never used as a factor in the proof; we know that a proof is also possible by the help of "badly-drawn" figures in which so-called congruent triangles have sides obviously different in length. It is not the immediate picture of the figure, but a concatenation of logical relations that compels us to accept the proof. This consideration holds equally well for non-Euclidean geometry; although the drawing looks like a " badly- drawn " figure, we can with its help discover whether the logical requirements have been satisfied, just as we can do in Euclidean geometry. This is why non-Euclidean geometry has been developed from its inception in an axiomatic construction; in contradistinction to Euclidean geometry where the theorems were known first and the axiomatic foundation was developed later, the axiomatic construction was the instrument of discovery in non- Euclidean geometry.
With this consideration, which was meant only to make non-Euclidean geometry plausible, we touch upon the problem of the visualization of geometry. Since this question will be treated at greater length in a later section, the remark about "badly-drawn" figures should be taken as a passing comment. What was intended was to stress the fact that the essence of a geometrical proof is contained in the logic of its derivations, not in the proportions of the figures. Non-Euclidean geometry is a logically constructible system—this was the first and most important result established by its inventors.
It is true that a strict proof was still missing. No contradictions were encountered—yet did this mean that none would be encountered in the future? This question constitutes the fundamental problem concerning an axiomatically constructed logical system. It is to be expected that non-Euclidean statements directly contradict those of Euclidean geometry; one must not be surprised if, for instance, the sum of the angles of a triangle is found to be smaller than two right angles. This contradiction follows necessarily from the reformulation of the axiom of the parallels. What is to be required is that the new geometrical system be self-consistent. The possibility can be imagined that a statement a, proved within the non- Euclidean axiomatic system, is not tenable in a later development, i.e., that the statement not-a as well as the statement a is provable in the axiomatic system. It was incumbent upon the early adherents of non-Euclidean geometry, therefore, to prove that such a contradiction could never happen.
The proof was furnished to a certain extent by Klein's Euclidean model of non-Euclidean geometry. Klein succeeded in coordinating the concepts of Euclidean geometry, its points, straight lines, and planes, its concept of congruence, etc., to the corresponding concepts of non-Euclidean geometry, so that every statement of one geometry corresponds to a statement of the other. If in non-Euclidean geometry a statement a and also a statement not-a could be proved, the same would hold for the coordinated statements a' and not-a' of Euclidean geometry; a contradiction in non-Euclidean geometry would entail a corresponding contradiction in Euclidean geometry. The result was a proof of consistency, the first in the history of mathematics : it proceeds by reducing a new system of statements to an earlier one, the consistency of which is regarded as virtually certain.
After these investigations by Klein the mathematical significance of non-Euclidean geometry was recognized. Compared with the natural geometry of Euclid, that of Bolyai and Lobatschewsky appeared strange and artificial; but its mathematical legitimacy was beyond question. It turned out later that another kind of non-Euclidean geometry was possible. The axiom of the parallels in Euclidean geometry asserts that to a given straight line through a given point there exists exactly one parallel; apart from the device used by Bolyai and Lobatschewsky to deny this axiom by assuming the existence of several parallels, there was a third possibility, that of denying the existence of any parallel. However, in order to carry through this assumption consistently, a certain change in a number of Euclid's other axioms referring to the infinity of a straight line was required. By the help of these changes it became possible to carry through this new type of non- Euclidean geometry.
As a result of these developments there exists not one geometry but a plurality of geometries. With this mathematical discovery, the epistemological problem of the axioms was given a new solution. If mathematics is not required to use certain systems of axioms, but is in a position to employ the axiom not-a as well as the axiom a, then the assertion a does not belong in mathematics, and mathematics is solely the science of implication, i.e., of relations of the form "if ... then"; consequently, for geometry as a mathematical science, there is no problem concerning the truth of the axioms. This apparently unsolvable problem turns out to be a pseudo-problem. The axioms are not true or false, but arbitrary statements. It was soon discovered that the other axioms could be treated in the same way as the axiom of the parallels. "Non-Archimedian," "non-Pascalian," etc., geometries were constructed; a more detailed exposition will be found in § 14.
These considerations leave us with the problem into which discipline the question of the truth of the assertion a should be incorporated. Nobody can deny that we regard this statement as meaningful; common sense is convinced that real space, the space in which we live and move around, corresponds to the axioms of Euclid and that with respect to this space a is true, while not-a is false. The discussion of this statement leads away from mathematics; as a question about a property of the physical world, it is a physical question, not a mathematical one. This distinction, which grew out of the discovery of non-Euclidean geometry, has a fundamental significance: it divides the problem of space into two parts; the problem of mathematical space is recognized as different from the problem of physical space.
It will be readily understood that the philosophical insight into the twofold nature of space became possible only after mathematics had made the step from Euclid's geometry to non-Euclidean geometries. Up to that time physics had assumed the axioms of geometry as the self-evident basis of its description of nature. If several kinds of geometries were regarded as mathematically equivalent, the question arose which of these geometries was applicable to physical reality; there is no necessity to single out Euclidean geometry for this purpose. Mathematics shows a variety of possible forms of relations among which physics selects the real one by means of observations and experiments. Mathematics, for instance, teaches how the planets would move if the force of attraction of the sun should decrease with the second or third or nth power of the distance; physics decides that the second power holds in the real world. With respect to geometry there had been a difference; only one kind of geometry had been developed and the problem of choice among geometries had not existed. After the discoveries of non-Euclidean geometries the duality of physical and possible space was recognized. Mathematics reveals the possible spaces; physics decides which among them corresponds to physical space. In contrast to all earlier conceptions, in particular to the philosophy of Kant, it becomes now a task of physics to determine the geometry of physical space, just as physics determines the shape of the earth or the motions of the planets, by means of observations and experiments.
But what methods should physics employ in order to come to a decision? The answer to this question will at the same time supply an answer to the question why we are justified in speaking of a specific physical space. Before this problem can be investigated more closely, another aspect of geometry will have to be discussed. For physics the analytic treatment of geometry became even more fruitful than the axiomatic one.
§ 2. RIEMANNIAN GEOMETRY
Riemann's extension of the concept of space did not start from the axiom of the parallels, but centered around the concept of metric.
Riemann developed further a discovery by Gauss according to which the shape of a curved surface can be characterized by the geometry within the surface. Let us illustrate Gauss' idea as follows. We usually characterize the curvature of the surface of a sphere by its deviation from the plane; if we hold a plane against the sphere it touches only at one point; at all other points the distances between plane and sphere become larger and larger. This description characterizes the curvature of the surface of the sphere "from the outside"; the distances between the plane and the surface of the sphere lie outside the surface and the decision about the curvature has to make use of the third dimension, which alone establishes the difference between curved and straight. Is it possible to determine the curvature of the surface of the sphere without taking outside measurements? Is it meaningful to distinguish the curved surface from the plane within two dimensions? Gauss showed that such a distinction is indeed possible. If we were to pursue "practical geometry" on the sphere, by surveying, for instance, with small measuring rods, we should find out very soon that we were living on a curved surface. For the ratio of circumference u and diameter d of a circle we would obtain a number smaller than π = 3.14 ... as is shown in Fig. 1. Since we stay on the surface all the time, we would not measure the "real diameter" which cuts through the inner part of the sphere, but the "curved diameter" which lies on the surface of the sphere and is longer. This diameter divided into the circumference results in a number smaller than π. Nevertheless, it is meaningful to call the point M "the center of the circle on the surface of the sphere" because it has the same distance from every point of the circle; that we find ourselves on a sphere is noticed by means of the deviation of the ratio from π. In this way we obtain a geometry of a spherical surface which is distinguished from the ordinary geometry by the fact that different metrical relations hold for this kind of geometry. In addition to the change in the ratio between circumference and diameter of a circle, an especially important feature is that the sum of the angles of a triangle on a sphere is greater than 180°.
Table of Contents
Preface
Introduction
Chapter I Space
§ 1. The axiom of the parallels and non-Euclidean geometry
§ 2. Riemannian geometry
§ 3. The problem of physical geometry
§ 4. Coordinative definitions
§ 5. Rigid bodies
§ 6. The distinction between universal and differential forces
§ 7. Technical impossibility and logical impossibility
§ 8. The relativity of geometry
§ 9. The visualization of Euclidean geometry
§ 10. The limits of visualization
§ 11. Visualization of non-Euclidean geometry
§ 12. Spaces with non-Euclidean topological properties
§ 13. Pure visualization
§ 14 Geometry as a theory of relations
§ 15. What is graphical representation?
Chapter II Time
§ 16. The difference between space and time
§ 17. The uniformity of time
§ 18. Clocks used in practice
§ 19. Simultaneity
§ 20. Attempts to determine absolute simultaneity
§ 21. Time order
§ 22. The comparison of time
§ 23. Unreal sequences
Chapter III Space an Time
A. The Space-Time Manifold without Gravitational Fields
§ 24. The problem of a combined theory of space and time
§ 25. The dependence of spatial measurement on the definition of simultaneity
§ 26. Consequences for a centro-symmetrical process of propagation
§ 27. The construction of the space-time metric
§ 28. The indefinite space-type
§ 29. The four-dimensional representation of the space-time geometry
§ 30. The retardation of clocks
§ 31. The Lorentz contraction and the Einstein contraction
§ 32. The principle of the constancy of the velocity of light
§ 33. The addition theorem of velocities
B. Gravitation Filled Space-Time Manifolds
§ 34. The relativity of motion
§ 35. Motion as a problem of a coordinative definition
§ 36. The principle of equivalence
§ 37. Einstein's concept of gravitation
§ 38. The problem of rotation according to Einstein
§ 39. The analytic treatment of Riemannian spaces
§ 40. Gravitation and geometry
§ 41. Space and time in special gravitational fields
§ 42. Space and time in generall gravitational fields
C. The Most General Properties of Space and Time
§ 43. The singular nature of time
§ 44. The number of dimensions of space
§ 45. The reality of space and time
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Elementary Statistics - With CD - 6th edition
Summary: Elementary Statistics is appropriate for a one-semester introductory statistics course, with an algebra prerequisite. ES has a reputation for being thorough and precise, and for using real data extensively. Students find the book readable and clear, and the math level is right for the diverse population that takes the introductory statistics course. The text thoroughly explains and illustrates concepts through an abundance of worked out examples.HPB-Highland-Park Highland ParkBooks-FYI ky cadiz, KY
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Richmond Heights, FL Calculus for your time and consideration, and I look forward to hearing from you soon. Sincerely,
NadeemDiscrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the...
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RiemannianIntended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject.
Important additions to this new edition include:
* A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise;
* An increased number of coordinate calculations of connection and curvature;
* General fomulas for curvature on Lie Groups and submersions;
* Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger;
* Several recent results about manifolds with positive curvature.
From reviews of the first edition:
"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."
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We want to help you succeed on the TABE's mathIf you are one of the millions of people who have already discovered the power of NLP, Neuro-linguistic Programming Workbook For Dummies will allow you to perfect its lessons on how to think more positively and communicate more effectively with others. This workbook is packed with hands-on exercises and practical techniques to help you make the... more...
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Visualizing Functions Summary
Monday - Friday, July 7 - 11, 2008
The afternoon working group looked at the overviews from the work done at PCMI by
previous functions working groups. Some of the members researched ideas on the
Internet.
The group discussed what goals we were interested in and generalized several
objectives. Two general goals emerged. One group decided to work on a project
focusing on quadratic functions which may be used for Algebra One or Algebra Two. The idea is based on (maximized) profit as a function of cost to produce a product. That group envisions students working in small groups on different problems using the same theme.
The other group sees this as an opportunity to teach the basic concept of a function
by photographing an event as it happens and then measuring and graphing the
resulting curve.
This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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This truly unique new title should appeal to both mathematicians and mathematics educators. It should also find a small market among professional and reference book buyers: mathematical professionals with interest in travel, art, architecture. The title is intended for math students who are interested in art, or art students with an interest (or requirement) in mathematics, or professionals with interest in mathematics and art. Geometry concepts are introduced by analyzing well known buildings and works of art. The book is packaged with an access code which allows the reader into a protected site, which will contain most of the fine art from the book in full color as well as teaching resources. The text appeals both to mathematicians and to artists and will generally be used in courses that bridge the two
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The development of Maple 12 was driven by the belief that math software should be instantly accessible and easy to use. Maple 12's "Clickable Math" features eliminate the traditional complex command sets that still encumber other math systems. Necessary operations are now accessible purely through mouse movements, built-in assistants, tutors, embedded components, and button clicks, saving significant time and effort for users.
Maple 12 has also significantly broadened Maple's applicability to Engineering departments. In addition to many new features such as CAD connectivity and MATLAB code import and translation, Maple 12 brings to life the concept of "Clickable Engineering". With the same philosophy as "Clickable Math", which is powerful mathematics delivered through very visual, interactive, point and click methods, "Clickable Engineering" is shifting how engineering faculty approach instruction and research.
Join Dr. Robert Lopez and Dr. Laurent Bernardin at Drexel University on May 29th, 2008. Dr. Robert J. Lopez, Maple Fellow, and Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books. He will be presenting "Redefining Math Education with Clickable Math." Dr. Laurent Bernardin, Chief Scientist at Maplesoft, will present "Innovations in Engineering Analysis, Design and Simulation." Learn more >>
Optimizing the Controller Design to Guide the Motion of a Maglev Train Author: Maple
Magnetically Levitated (Maglev) trains differ from conventional trains in that they are levitated, guided and propelled along a guideway by a changing magnetic field rather than by steam, diesel or electric engine. The absence of direct contact between the train and the rail allows the Maglev to reach record ground transportation speeds, which are on par to that of commercial airplanes.
Maple 12's unique blend of computational power and ease-of-use makes it an essential tool for mathematics and modeling. Its smart document environment provides revolutionary Clickable Calculus™ and Clickable Engineering™ techniques for solving problems from any technical discipline, ensuring that students are instantly productive and engaged. The results can be incorporated in rich, interactive, live documents that are as professional-looking as a textbook.
In this one-hour demonstration and Q&A forum, you will learn how Maple 12 is redefining math education and opening new horizons in technical research. By taking advantage of such features as interactive tutors, context-sensitive menus, expanded mathematical capabilities, and the new Exploration Assistant, see how teachers can bring complex problems to life, students can focus on concepts rather than the mechanics of solutions, and researchers can develop more sophisticated algorithms or models.
Maplesoft's "Clickable Calculus™" introduced an exciting new dimension in calculus education. The idea of powerful mathematics delivered using very visual, interactive, point and click methods, is launching a new generation of teaching and learning techniques in mathematics. "Clickable Engineering Math" carries this philosophy into the applied sciences.
Part I of this two part Webinar will present general engineering problem-solving methods using clickable techniques. Drawing on application areas in mechanics, circuits, control and others, Maple will be shown in a new light. Specific techniques including symbolic equation solving, differential equations and transforms, plotting and visualization, and units, will be covered.
Join Dr. Robert Lopez as he explores Maple 11's remarkable set of user-interface features that makes common mathematical operations as easy as pointing and clicking. By solving a spectrum of standard (and not-so-standard) problems drawn from differential equations, linear algebra, and vector calculus, this session will demonstrate
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Globally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-specialists... more... facilitate children?s mathematical thinking. It looks... more...
In this new text, Steven Givant?the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski?develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as... more...
Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce). Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are... more...
Relation algebras are algebras arising from the study of binary relations. They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is... more...
Tips for simplifying tricky basic math and pre-algebra operations Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math... more...
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problems commonly faced by scientists and engineers.... more...
Developing applications that scale well on massively parallel architectures is quite difficult, due to problems with synchronization and communication time as well as fault tolerance. This book reviews current algorithms and presents new mathematical versions that avoid such problems. It details the implementation and validates the proposed versions... more...
The second edition of this popular text on Maple? programming has been updated to reflect Maple version 15. Suitable for new and advanced users, the guide covers the latest features of Maple and offers a tutorial that extends from high school algebra and graphing to advanced topics of mathematics, such as special functions, multivariable calculus,... more...
Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in "Matrix Computations." The book?s learning outcomes are twofold:... more...
A Thorough Overview of the Next Generation in Computing
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With contributions from some of the most notable experts in the field, Performance Tuning of Scientific Applications presents current research in performance analysis. The book focuses on the following areas.
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The hybrid/heterogeneous nature of future microprocessors and large high-performance computing systems will result in a reliance on two major types of components: multicore/manycore central processing units and special purpose hardware/massively parallel accelerators. While these technologies have numerous benefits, they also pose substantial performance... more...
Known for its versatility, the free programming language R is widely used for statistical computing and graphics, but is also a fully functional programming language well suited to scientific programming.
An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to perform scientific programming while also introducing... more...
The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts... more...
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Instructor Resources
Functional Differential Geometry
Overview
Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.
The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
About the Authors
Gerald Jay Sussman is Panasonic Professor of Electrical Engineering at MIT. He is the coauthor (with Hal Abelson and Julie Sussman) of Structure and Interpretation of Computer Programs (MIT Press). Sussman and Wisdom are also coauthors of Functional Differential Geometry (MIT Press).
Jack Wisdom is Professor of Planetary Science at MIT. Sussman and Wisdom are also coauthors of Functional Differential Geometry (MIT Press).
Endorsements
"Another gem in the tradition of Structure and Interpretation of Computer Programs and Structure and Interpretation of Classical Mechanics, providing for applied mathematics what the previous two books did for computer science and physics." —Piet Hut, Institute for Advanced Study, Princeton, New Jersey"—
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Summary: Financial risk management has become a popular practice amongst financial institutions to protect against the adverse effects of uncertainty caused by fluctuations in interest rates, exchange rates, commodity prices, and equity prices. New financial instruments and mathematical techniques are continuously developed and introduced in financial practice. These techniques are being used by an increasing number of firms, traders and financial risk managers across various...show more industries. Risk and Financial Management: Mathematical and Computational Methods confronts the many issues and controversies, and explains the fundamental concepts that underpin financial risk management.
Provides a comprehensive introduction to the core topics of risk and financial management.
Adopts a pragmatic approach, focused on computational, rather than just theoretical, methods.
Bridges the gap between theory and practice in financial risk management
Includes coverage of utility theory, probability, options and derivatives, stochastic volatility and value at risk.
Suitable for students of risk, mathematical finance, and financial risk management, and finance practitioners.
Includes extensive reference lists, applications and suggestions for further reading.
Risk and Financial Management: Mathematical and Computational Methods is ideally suited to both students of mathematical finance with little background in economics and finance, and students of financial risk management, as well as finance practitioners requiring a clearer understanding of the mathematical and computational methods they use every day. It combines the required level of rigor, to support the theoretical developments, with a practical flavour through many examples and applications. ...show less
2004 Hardcover Good This item may not include any CDs, Infotracs, Access cards or other supplementary material.
$69.71 +$3.99 s/h
Good
Bookbarn International nr Bath,
03/23/2004
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What is Chegg Study?
With Chegg Study, you get step-by-step solutions for odd and even answers at the back of the book Student Solutions Manual, Volume 1 ( Chapters P-11) for Larson/Edwards' Calculus - 9th editionand 2,500 others.
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books.google.com - This is a short, focused introduction to MATLAB, a comprehensive software system for mathematical and technical computing. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, simulation... Guide to MATLAB
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You are here
JOMA Welcome
Author(s):
Tina H. Straley
With this first issue of JOMA, MAA is launching a new and very exciting venture into resources for undergraduate mathematics education. JOMA is a scholarly journal that complements MAA's existing journals, has the same high standards of quality for which the MAA journals are known, and fits the MAA mission to advance mathematics, especially at the undergraduate level. What is new about JOMA is that it is an online journal devoted to online teaching and learning. David Smith, Tom Roby, and the rest of the JOMA team have done a great job in a short time in bringing out this first issue, which is dedicated to calculus mathlets. This is just the beginning of JOMA, and JOMA is just the beginning of the Mathematical Sciences Digital Library, MathDL.
Tina Straley is the Executive Director of the Mathematical Association of America.
You have probably read about MathDL in Focus, but the whole idea is so exciting that I will repeat some of that information here. The National Science Foundation has created a program entitled the Science, Mathematics, Engineering, and Technology Education Digital Library, administered by the Division of Undergraduate Education. The national digital library will be a linked system of sites devoted to online resources in undergraduate education. The NSF is funding umbrella sites and sites with various types of resources. A user will be able to enter any node on the system and access other sites. The content area sites will be primarily discipline-specific. Each site will have its own character and interpretation of a digital library, but search data will be consistent so that a visitor to any part of the library may search the entire library.
In the first round of funding, three disciplinary areas were funded, one of which is the MAA Mathematical Sciences Digital Library. We are partnering with the MathForum, a subsidiary of WebCT, which is designing and hosting our site. The expertise and experiences of MAA and MathForum are a perfect combination to bring to you high quality educational materials on-line. The MAA site is cooperating with the other funded sites to make the overall vision a reality.
The national digital library will address some difficult issues in order to realize the full potential of the World Wide Web as an educational resource. Although there is an enormous amount of material freely available on the web, there is no quality control and no organization. One can do a search and be overwhelmed with sites but have no idea what is on those sites. An advantage of commercial publication is that materials are reviewed, marketed, cataloged, and revised. A work that is not well received is soon pulled off the market. There is no such system for web based materials. Instead the web grows in a chaotic state, materials may or may not function as intended, and materials not intended for anyone else's use may provide no information to rely upon or guide for use.
MathDL has three components. The "holdings" of the library are in the Library Collections, the Library of Online Mathematics and Its Applications. Here, one will find online educational materials ranging from modules to full courses, from tools to curricula. The Library of Commercial Products, LCP, is a bibliography of books, software, and other commercially available resources in undergraduate mathematical sciences available in any medium. All entries in the Library Collections and LCP will be commonly cataloged and searched. All entries will be reviewed and maintained. For each entry, a user may read a description of the materials, a table of contents if appropriate, and reviews provided by the publisher or creator, the MAA, and users. Users will be able to add their own reviews. Each entry will have a discussion site. From the description page you can either access materials available in the collections or the vendor's website for purchases.
Many libraries produce journals. JOMA is the journal of MathDL. Materials in JOMA must meet the high standards of a scholarly publication. Resource materials in JOMA will also appear in Library Collections, marked to indicate that these materials have had a rigorous review. Thus, this issue of JOMA serves several firsts: It is the first issue of a new journal of the MAA; it is the first offering of the Mathematical Sciences Digital Library; and, it contains the first materials to appear eventually in the Library Collections.
I hope that you find these materials interesting and useful. We invite your comments and ideas. The Library Collections and LCP sites will come online next fall, but we have already started to build them. Joining JOMA Editor David Smith, Doug Ensley has been named Editor for the Library Collections. Lang Moore, MathDL Editor-in-Chief and Project PI, and Don Albers, MAA's Director of Publications and Project co-PI, are overseeing LCP. Any and all of us welcome your comments, ideas, suggestions, and submissions. MathDL will be the online place to go for undergraduate mathematics information and materials. But its success depends on you. Please join us by browsing, reviewing, submitting, and discussing. There is room for everybody in our library!
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Hi. I see you''re reading the back of my book. This tells me that you either: A) are hoping to find a brief summary of what to expect from a how-to book by Sterling Archer, the world''s greatest secret agent, or B) don''t know how books work. If your answer was "A," your best bet is probably the…
Hi. I see you're reading the back of my book. This tells me that you either: A) are hoping to find a brief summary of what to expect from a how-to book by Sterling Archer, the world's greatest secret agent, or B) don't know how books work. If your answer was "A," your best bet is probably theTo succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for…
1855: The Industrial Revolution is in full and inexorable swing, powered by steam-driven cybernetic Engines. Charles Babbage perfects his Analytical Engine and the computer age arrives a century ahead of its time. And three extraordinary characters race toward a rendezvous with history—and the…
Now, it is easier than ever before to understand complex mathematical concepts and formulas and how they relate to real-world business situations. All you have to do it apply the handy information you will find in Business Math For Dummies . Featuring practical practice problems to help you expandBesides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and…
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Course Description: This course is a review of arithmetic involving basic operations of whole numbers, fractions, decimals and percents. Additional topics includes an introduction to algebraic concepts such as graphing linear equations in two variables, polynomials and properties of exponents, factoring and other skills need for further study in algebra and general education mathematics. MAT 0022 cannot be used towards an A.A. or A.S. degree requirement. FA, SP, SU
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More About
This Textbook
Overview
This is a revision of an earlier work Means and Their Inequalities by the present author and Professors Mitrinovic and Vasic. Not only does this book bring the earlier version up to date but it enlarges the scope considerably to give a full and in-depth treatment of all aspects of the field. While the mention of means occurs in many books this is the only full treatment of the subject. Outstanding features of the book are the variety of proofs given for many of the basic results, over seventy for the inequality between the arithmetic and geometric means for instance, an exhaustive bibliography and a list of mathematicians who have contributed to this field from the time of Euclid to the present day. The results discussed and the proofs provided are written in a language that not only the expert in the subject will understand but also graduate students worldwide will understand and appreciate. Any person with an interest in means and their inequalities should find this book within their comprehension although to fully appreciate all the topics covered a knowledge of calculus and of elementary real analysis is required.
Editorial Reviews
From the Publisher
"This book is indeed a handbook: it is hard to find a subfield of inequalities related to means that is not described in detail, or at least referred to. It is written in a language that can be understood not only by experts but also by graduate students and others who are interested in the applications: the only requirement on readers is a knowledge of calculus and elementary real analysis."—MATHEMATICAL REVIEWS
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Thinking in Problems
How Mathematicians Find Creative Solutions
Roytvarf, Alexander A.
2013, XXXVII, 405 p. 14This marvelous collection of problems represents an interesting and valuable resource for students who prepare various types of mathematics contests. … very strongly recommends this book to all undergraduate and graduate students curious about elementary mathematics. Teachers would find this book to be a welcome resource, as will contest organizers." (Teodora-Liliana Rădulescu, zbMATH, Vol. 1270, 2013)
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ully evolved teaching text, developed and class tested for over 15 years
Uses original sources to teach the history of mathematics – an original yet fascinating approach
Heavily illustrated with line drawings and half-tones, including many historical photographs
Each chapter is self-contained and could be used independently
Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry, perspective to proposed conceptual solutions, and a glimpse into the direction research has taken. The text is ideal for an undergraduate seminar, independent reading, or a capstone course, and offers a wealth of student exercises with a prerequisite of at most multivariable calculus.
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Search:
Discovering Algebra: An Investigative Approach, 2 edition
2nd edition hardcover student textbook
The Discovering Algebra approach improves learning in many ways:
Investigations at the beginning of each lesson help you give all your students—regardless of their mathematical backgrounds—a shared experience from which to base their learning. The Author of this Book is
You will be able to teach an algebra course that is both rigorous and accessible to your students because the investigations give meaning to mathematics that all students, regardless of their skill level, can understand. Array ISBN .
The investigations will often prompt more advanced students to dig deeper, giving you a natural way to extend the lesson and connect algebra to other topics. Discovering Algebra: An Investigative Approach, 2 edition available in English.
Investigations, visual representations, and opportunities for discussion enable you to integrate multiple teaching modes into your classroom so that visual, auditory, and kinesthetic learners all benefit.
These investigations will also provide you with another tool to use when reviewing and building upon concepts in class. Many teachers tell us that their students find it easier to remember previously taught mathematical concepts and skills when reminded of the classroom activity that helped them learn the concept.
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GED 2014 Math Lessons
The New GED 2014 test will be much more rigorous than the
current 2002 series. The math that will be needed will
require a deeper understanding of basic whole numbers,
fractions, decimals, and percents. It will also require
one to understand a deeper meaning of algebra and geometry.
While it may seem overwhelming for students and teachers alike,
we here at Learningtrends hope that the lessons provided will
give you some of the resources you need to succeed in your
venture. We wish you all the best as you pursue your GED.
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Advanced Mathematical Concepts - 06 edition
Summary: Advanced Mathematical Concepts, 2006 provides comprehensive coverage of all the topics covered in a full-year Pre-calculus course. Its unique unit organization readily allows for semester courses in Trigonometry, Discrete Mathematics, Analytic Geometry, and Algebra and Elementary Functions. Pacing and Chapter Charts for Semester Courses are conveniently located in the Teacher Wraparound Edition.
Advanced Mathematical Concepts lessons develop mathematics us...show moreing numerous examples, real-world applications, and an engaging narrative. Graphs, diagrams, and illustrations are used throughout to help students visualize concepts. Directions clearly indicate which problems may require the use of a graphing calculator.
New Features: " A full-color design, a wide range of exercise sets, relevant special features, and an emphasis on graphing and technology invite your students to experience the excitement of understanding and applying higher-level mathematics skills. " Graphing calculator instructions is provided in the Graphing Calculator Appendix. Each Graphing Calculator Exploration provides a unique problem-solving situation. " SAT/ACT Preparation is a feature of the chapter end matter. The Glencoe Web site offers additional practice: amc.glencoe.com " Applications immediately engage your students; interest. Concepts are reinforced through a variety of examples and exercise sets that encourage students to write, read, practice, think logically, and review. " Calculus concepts and skills are integrated throughout the course. ...show less
2005-01-051979Hardcover Good 00786822
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For most textbooks we explain the odd-numbered problems. We skip group problems, writing problems, chapter tests and problems that are not generally assigned for homework.
What if I need help on an even-numbered problem?
You might be able to see how to do it by looking at our solution to a nearby odd problem. Or, you can sign up for our 24/7 Tutoring and ask our tutors, they will be more than happy to help!
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You are here
Visual Complex Functions: An Introduction with Phase Portraits
Publisher:
Birkhäuser
Number of Pages:
360
Price:
59.95
ISBN:
9783034801799
The graph of an analytic function f(z) naturally lives in two complex dimensions or four real dimensions. Therefore we cannot visualize such graphs directly. There are several ways to work around this limitation.
One way is to use before-and-after plots: here's a region of the complex plane, and here is its image under f. Or we could graph |f|, the absolute value of the function. Another way to visualize analytic functions is to view the range in (r, θ) polar coordinates and encode the value of θ as a position on a color wheel. A pure phase plot would graph the θ component of f(z) as a function of z.
There are several variations on the phase approach that add information regarding the r component of f(z). One would be to create a 3-D plot using height to indicate |f(z)| and color to indicate the phase. If we want to stay in two dimensions, we could add contour lines for |f(z)| or map the θ component to hue and the r component to saturation in a HSV (hue, separation, value) description of color.
All the methods above are used in Visual Complex Functions by Elias Wegert, though pure phase plots are used most often. True to its title, Visual Complex Functions emphasizes visualization. However, it is not simply a book on visualization. It is an introductory complex analysis book with an unusually heavy emphasis on visualization. The standard topics — power series, residues, the Riemann mapping theorem, etc. — are all included.
One drawback to phase plots is that the mapping of phase to color is subjective. However, the qualitative information apparent in a graph does not rely of the specific mapping. You can, for example, spot zeros of a function by the colors rotating one way and poles by the colors moving in the opposite sequence. You can tell the degree of a zero or pole by how many times the colors cycle around the point. And you can spot an essential singularity by a flurry of change.
The emphasis on visualization gives the reader a deeper intuition for the behavior of complex functions. Experienced mathematicians may be surprised by the new insight this approach gives. The author explains his own excitement regarding visualization as follows.
My acquaintance with complex functions dates back almost forty years, but it took a long time until I could begin to see my friends. I love them even more ever since I know their phases. This book has been written to let you share my joy.
Visual Complex Functions contains over 200 images, many of these quite stunning. The image below is a phase plot of one of the functions plotted in the book. However, the book did not specify the scale and so the image below, while equally interesting, does not reproduce the image in the book.
Visual Complex Functions is the first volume of a series. Wegert says that the second volume "will be devoted to selected topics and various applications of complex methods, like integral transforms, boundary value problems, and signal analysis."
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Send the Gift of Lifelong Learning!
Discrete Mathematics interfaces you remedies delete marketing forDiscrete Mathematics24 lectures | 31 minutes per lectureView MoreWhile continuous mathematics resembles an old-fashioned analog clock, whose second hand sweeps continuously across a dial, discrete mathematics is like a digital watch, whose numbers proceed one second at a time. As a result, discrete mathematics achieves fascinating mathematical results using relatively simple means, such as counting.
Explore this modern realm of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and mathemagician who has designed a course that is mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra.
Problems, Proofs, and Applications
Discrete mathematics covers a wide range of subjects, and Professor Benjamin delves into three of its most important fields, presenting a generous selection of problems, proofs, and applications in the following areas:
Combinatorics: How many ways are there to rearrange the letters of Mississippi? What is the probability of being dealt a full house in poker? Central to these and many other problems in combinatorics (the mathematics of counting) is Pascal's triangle, whose numbers contain some amazingly beautiful patterns.
Number theory: The study of the whole numbers (0, 1, 2, 3, ...) leads to some intriguing puzzles: Can every number be factored into prime numbers in exactly one way? Why do the digits of a multiple of 9 always sum to a multiple of 9? Moreover, how do such questions produce a host of useful applications, such as strategies for keeping a password secret?
Graph theory: Dealing with more diverse graphs than those that plot data on x and y axes, graph theory focuses on the relationship between objects in the most abstract sense. By simply connecting dots with lines, graph theorists create networks that model everything from how computers store and communicate information to transportation grids to even potential marriage partners.
Learn to Think Mathematically
Professor Benjamin describes discrete mathematics as "relevant and elegant"—qualities that are evident in the practical power and intellectual beauty of the material that you study in this course. No matter what your mathematical background, Discrete Mathematics will enlighten and entertain you, offering an ideal point of entry for thinking mathematically.
In discrete math, proofs are easier and more intuitive than in continuous math, meaning that you can get a real sense of what mathematicians are doing when they prove something, and why proofs are an immensely satisfying and even aesthetic experience.
The applications featured in this course are no less absorbing and include cases such as these:
Internet security: Financial transactions can take place securely over the Internet, thanks to public key cryptography—a seemingly miraculous technique that relies on the relative ease of generating 1000-digit prime numbers and the near impossibility of factoring a number composed of them. Professor Benjamin walks you through the details and offers a proof for why it works.
Information retrieval: A type of graph called a tree is ideal for organizing a retrieval structure for lists, such as words in a dictionary. As the number of items increases, the tree technique becomes vastly more efficient than a simple sequential search of the list. Trees also provide a model for understanding how cell phone networks function.
ISBN error detection: The International Standard Book Number on the back of every book encodes a wealth of information, but the last digit is very special—a "check digit" designed to guard against errors in transcription. Learn how modular arithmetic, also known as clock arithmetic, lies at the heart of this clever system.
Deepen Your Understanding of Mathematics
Professor Benjamin believes that, too often, mathematics is taught as nothing more than a collection of facts or techniques to be mastered without any real understanding. But instead of relying on formulas and the rote manipulation of symbols to solve problems, he explains the logic behind every step of his reasoning, taking you to a deeper level of understanding that he calls "the real joy and mastery of mathematics."
Dr. Benjamin is unusually well qualified to guide you to this more insightful level, having been honored repeatedly by the Mathematical Association of America for his outstanding teaching. And for those who wish to take their studies even further, he has included additional problems, with solutions, in the guidebook that accompanies the course.
With these rich and rewarding lectures, Professor Benjamin equips you with logical thinking skills that will serve you well in your daily life—as well as in any future math courses you may take.
View Less
24 Lectures
1
What Is Discrete Mathematics?
In this introductory lecture, Professor Benjamin introduces you to the entertaining and accessible field of discrete mathematics. Survey the main topics you'll cover in the upcoming lectures—including combinatorics, number theory, and graph theory—and discover why this subject is off the beaten track of the continuous mathematics you studied in high school. x
2
Basic Concepts of Combinatorics
Combinatorics is the mathematics of counting, which is a more subtle exercise than it may seem, since the question "how many?" has at least four interpretations. Investigate factorials as well as the binomial coefficient, n choose k, which shows the number of ways that k things can be chosen from n objects. x
3
The 12-Fold Way of Combinatorics
As an overview of combinatorial concepts, explore 12 different interpretations of counting by asking how many ways x pieces of candy can be distributed among b bags. The answers depend on such factors as whether the candies and bags are distinguishable, and how many candies are allowed in each bag. x
4
Pascal's Triangle and the Binomial Theorem
Devised to calculate the payout in games of chance, Pascal's triangle is filled with beautiful mathematical patterns, all based on the binomial coefficient, n choose k. Professor Benjamin demonstrates some of the triangle's amazing properties. x
5
Advanced Combinatorics—Multichoosing
How many ways can you choose three scoops of ice cream from 31 flavors, assuming that flavors are allowed to be repeated? Using the method of "stars and bars," you find 5,456 possibilities if the order of flavors does not matter. The technique also works for counting endgame positions in backgammon. x
6
The Principle of Inclusion-Exclusion
Learn how the principle of inclusion-exclusion allows you to solve problems such as these: What is the probability that a five-card poker hand has at least one card in each suit? If homework papers are randomly distributed among students for grading, what are the chances that no student gets his or her own homework back? x
7
Proofs—Inductive, Geometric, Combinatorial
Proofs by induction are a fundamental tool in any discrete mathematician's toolkit. This lecture guides you through several inductive proofs and then introduces geometric proof, also known as proof without words, and combinatorial proof. You see how all three techniques can prove properties of Pascal's triangle and Fibonacci numbers. x
8
Linear Recurrences and Fibonacci Numbers
Investigate some interesting properties of Fibonacci numbers, which are defined using the concept of linear recurrence. In the 13th century, the Italian mathematician Leonardo of Pisa, called Fibonacci, used this sequence to solve a problem of idealized reproduction in rabbits. x
9
Gateway to Number Theory—Divisibility
Starting the section of the course on number theory, explore some key properties of numbers, beginning with what you know intuitively and working toward surprising properties such as Bezout's theorem. You also prove several important theorems relating to divisibility and prime factorization. x
10
The Structure of Numbers
Study the building blocks of integers and how numbers can be created additively or multiplicatively. For example, every integer can be expressed as the sum of distinct powers of 2 in a unique way. Similarly, every integer is the product of a unique set of prime numbers. x
11
Two Principles—Pigeonholes and Parity
Explore fascinating examples of two ideas: the pigeonhole principle, which can be used to prove that a mathematical situation is inevitable, such as that there must be a power of 3 that ends in the digits 001; and the parity principle, which is useful for proving that certain outcomes are impossible. x
12
Modular Arithmetic—The Math of Remainders
Introducing the important tool of modular arithmetic, Professor Benjamin uses the example of a clock to show how practically everyone is already adept with mod 12 arithmetic. Among the technique's many applications are the ISBN codes found on books, which use mod 11 for error detection. x
13
Enormous Exponents and Card Shuffling
Exploring more applications of modular arithmetic, examine the Chinese remainder theorem, used in ancient China as a fast way to count large numbers of troops. Also learn about password protection, the mathematics behind the "perfect shuffle," and the "seed planting" technique for raising big numbers to big powers. x
14
Fermat's "Little" Theorem and Prime Testing
Use modular arithmetic to investigate more properties of prime numbers, leading to a practical way to test if an integer is prime. At the same time, meet two important figures in the history of number theory: Pierre de Fermat and Leonhard Euler. x
15
Open Secrets—Public Key Cryptography
The idea behind public key cryptography sounds impossible: The key for encoding a secret message is publicized for all to know, yet only the recipient can reverse the procedure. Learn how this approach, widely used over the Internet, relies on Euler's theorem in number theory. x
16
The Birth of Graph Theory
This lecture introduces the last major section of the course, graph theory, covering the basic definitions, notations, and theorems. The first theorem of graph theory is yet another contribution by Euler, and you see how it applies to the popular puzzle of drawing a given shape without lifting the pencil or retracing any edge. x
17
Ways to Walk—Matrices and Markov Chains
Use matrices to answer the question, How many ways are there to "walk" from one vertex to another in a given graph? This exercise leads to a discussion of random walks on graphs and the technique used by many search engines to rank web pages. x
18
Social Networks and Stable Marriages
Apply graph theory to social networks, investigating such issues as the handshake theorem, Ramsey's theorem, and the stable marriage theorem, which proves that in any equal collection of eligible men and women, at least one pairing exists for each person so that no extramarital affairs will take place. x
19
Tournaments and King Chickens
Discover some interesting properties of tournaments that arise in sports and other competitions. Represented as a graph, a tournament must contain a Hamiltonian path that visits each vertex once; and at least one "king chicken" competitor who has either beaten every opponent or beaten someone who beat that opponent. x
20
Weighted Graphs and Minimum Spanning Trees
When you call someone on a cell phone, you can think of yourself as a leaf on a giant "tree"—a connected graph with no cycles. Trees have a very simple yet powerful structure that make them useful for organizing all sorts of information. x
21
Planarity—When Can a Graph Be Untangled?
Professor Benjamin introduces the concept of a planar graph, which is a graph that can be drawn on a sheet of paper in such a way that none of its edges cross. Then, encounter the two simplest nonplanar graphs, at least one of which must be contained within any nonplanar graph. x
22
Coloring Graphs and Maps
According to the four-color theorem, any map can be colored in such a way that no adjacent regions are assigned the same color and, at most, four colors suffice. Learn how this problem went unsolved for centuries and has only been proved recently with computer assistance. x
23
Shortest Paths and Algorithm Complexity
Examine more problems in graph theory, including the shortest path problem, the traveling salesman problem, and the Hamiltonian cycle problem. Some problems can be solved efficiently, while others are so hard that no simple solution has yet been found. x
24
The Magic of Discrete Mathematics
In his final lecture, Professor Benjamin reviews areas where combinatorics, number theory, and graph theory overlap. Then he looks ahead at topics that build on the course's solid foundation in discrete mathematics. He closes with a flourish of mathematical magic, including the "four-ace surprise." x
Lecture Titles
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Your professor
Ph.D. Arthur T. Benjamin
Harvey Mudd College
Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989. Professor Benjamin's teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. The MAA also named Professor Benjamin the 2006-2008 George Pólya Lecturer. In 2012, Princeton Review profiled him in The Best 300 Professors. He is a professional magician, whose techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. Professor Benjamin also served for five years as coeditor of Math Horizons magazine. An avid games player, Dr. Benjamin is a past winner of the American Backgammon Tour and has written more than 15 papers on the mathematics of games and puzzles. Professor Benjamin has appeared on dozens of television and radio programs and has been featured in publications, including Scientific American, People, and The New York Times. In 2005, Reader's Digest called him America's Best Math Whiz.
Reviews
Rated 4.8 out of 5 by 33
reviewers.
Rated 1 out of 5 by Ari0 Simpler and clearer explanations elsewhere
Simpler and clearer explanations (in my opinion,) for some of the formulas given in the first lectures can be found elsewhere. I returned the course before completing it.
I received a refund from The Great Courses on the same day that I requested it. I was dissatisfied with this particular course, but very satisfied with the customer service of The Great Courses and how they handled my refund request.
November 9, 2014
Rated 5 out of 5 by Milo Great prof, hard course
Professor Benjamin is as bright as a button and a pleasure to spend time with, which is a good thing, because the course was way over my head, and more often than not it seemed as though he was speaking in tongues. Discrete Mathematics is not for the math-phobic or algebra-deficient. But Professor Benjamin is so buoyant and charming, with such mirth in his eyes, that he seduces you into staying the course even if you realize, as I did, that you will not be acquiring Discrete Mathematics in this lifetime. For those who are truly comfortable with algebra, and willing to stop each lesson multiple times to work through the proofs, I think it would be possible to learn this material. For the rest of us, we can marvel at his cheerful brilliance and maybe, if we are diligent, pick up a magic trick or two.
September 28, 2014
Rated 5 out of 5 by Polymath Excellent, but intense!
This is certainly not one of those overview courses that you can watch and absorb with little effort. It's the real deal, discrete maths for people who want to explore and use the techniques.
I had to watch some of the videos more than once to follow some of the proofs.
The presenter is a joy to watch, his enthusiasm is contagious!
Great course for those with a reasonably strong math background.
April 20, 2014
Rated 5 out of 5 by RicS Great lecturer
A great job of lecturing. I will have to listen to it several times to take it all in but Prof. Benjamin is a joy to listen to. I wish I had had math teachers half as good.
January 21, 2014
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Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty...
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Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages.The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional.International Trade: Theory and Policy is built on Steve Suranovic's belief that to understand the international economy,...
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International Trade: Theory and Policy is built on Steve Suranovic's belief that to understand the international economy, students need to learn how economic models are applied to real world problems. It is true what they say, that "economists do it with models." That's because economic models provide insights about the world that are simply not obtainable solely by discussion of the issues. International Trade: Theory and Policy presents a variety of international trade models including the Ricardian model, the Heckscher-Ohlin model, and the monopolistic competition model. It includes trade policy analysis in both perfectly competitive and imperfectly competitive markets. The text also addresses current issues such as free trade area formation and administered protection policies. The models are developed, not by employing advanced mathematics, but rather by walking students through a detailed description of how a model's assumptions influence its conclusions. But more importantly, each model and theory is connected to real world policy issues. The main purpose of the text is to provide a thorough grounding in the arguments concerning the age-old debate about free trade versus protectionism. This text has the following unique features: o The text begins with an historical overview of trade policy issues to provide context for the theory. o The text concludes with a detailed economic argument supporting free trade. o The welfare analysis in the Ricardian, Heckscher-Ohlin and specific factors models emphasize the redistributive effects of free trade by calculating changes in real incomes. o The trade policy chapter provides a comprehensive look at many more trade policies than are found in a printed textbook. o A chapter about domestic policies contains an evaluation of domestic taxes and subsidies that are often ignored in traditional trade textbooks but are increasingly important as large countries complain more about each other's domestic agriculture policies and labor and environmental policies. o The text uses the theory of the second-best to explain why protection can improve national welfare. This well-known theoretical result is rarely presented as methodically and consistently as it is in this text
This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first...
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This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Students are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces. For recommended 10-week and 15-week syllabuses, read the preface.
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High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
High school math for grade 10, 11 and 12 math questions and problems to test deep understanding of math concepts and computational procedures are presented. Answers to the questions are provided and located at the end of each page.
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Overview
This book exposes nursing students to the mathematics required for success in their profession. In the teaching arithmetic, the text also presents a survey of the various types of mathematical problems encountered in clinical surroundings. This book is suitable for use in traditional lecture
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Linear Algebra for EconomistsBased on mathematical explanations in combination with economic applications
This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics.
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This undergraduate textbook on Linear Algebra and n-Dimensional Geometry, in a self-teaching style, is invaluable for sophomore level undergraduates in mathematics, engineering, business, and the sciences. These...
$ 35.49
John Holland is one of the few scientists, who all by themselves and by their pursuits, helped change the course of science and the wealth of human knowledge. There is hardly a field of science or problems,...
$ 104This book aims to make the subject of geometry and its applications easy and comfortable to understand by students majoring in mathematics or the liberal arts, architecture and design. It can be used to teach...
$ 8.29
This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed...
$ 9.99
How many people achieve a cult following because of their writing in mathematics? Only a handful, and Martin Gardner is among the most well known and well loved. Not only did he present a notoriously difficult...
$ 4.99
Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications...
$ 15.29
This book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of...
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Algebra and Trigonometry - 4th edition
Beecher, Penna, and Bittinger'sAlgebra and Trigonometryis known for enabling students to see the math through its focus on visualization and early introduction to functions. With theFourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively. Mid-chapter Review exercise sets have been added to give students practice in synthesizing the conc...show moreepts, and new Study Summaries provide built-in tools to help them prepare for tests. The MyMathLab course (access kit required) has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Review exercises from the text as well as example-based videos created by the authors16939148.651881-24-11 Hardback 4
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Algebra and Trigonometry - 2nd edition
Summary: Often, algebra & trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors commun...show moreicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics
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Calculator: A calculator is not required in this course, but a
graphing calculator such as the TI-83 will certainly help. It is easy to
become too dependent on a calculator. You should think of the calculator
as a tool to be used in computationally challenging problems, in approximating
solutions, and in verifying results, not as a primary tool for problem
solving. I will give specific rules for using or not using calculators on
tests.
Homework: Problems will be assigned regularly, and everyone is
expected to do them. They will not be collected without warning, and it
is your responsibility to do all of the assigned problems. Feel free to
work with others on the homework problems, and ask me about problems that you
cannot solve.
Quizzes: There will be frequent daily quizzes. Quizzes
are always at the beginning of the period, take about ten minutes, and are open
book and notes. Often they consist of a homework problem or two. No
excuses will be accepted for missing quizzes, and there will be no makeups. You will receive a grade of 0 for missed
quizzes, regardless of the reason for absence. However, you may drop one
quiz grade. The remaining quiz grades will be counted equally to compute
your composite quiz grade.
Class participation: Often you will be asked to work in groups
in class. Working in small groups of three or four, you will be asked to
solve a problem and present your results to the class. Each group will
receive a grade on that day's work. Each member of the group will receive
the same grade, except a member who is absent, who will receive a grade of
0. Missed class participation sessions cannot be made up, but you will be
allowed one absence from a class participation session without penalty.
All remaining group grades will be counted equally to determine your composite
group grade.
Writing
assignment:As a general education
course, MATH 164 will require more writing than some non-general education
mathematics courses.There will be at
least one writing assignment in this course.It will be graded both for factual correctness and for writing
style.More details and a grading rubric
will be provided with the assignment.
Attendance: Your attendance is expected at all classes.
Makeup tests will be given reluctantly, and then only upon presentation of a
doctor's excuse. Makeup tests are always more difficult than regular
tests, regardless of the reason for absence. You may not make up missed
class participation sessions or quizzes.
You need to be on time for each class. Coming into class late is
disruptive to other students and to the teacher. In addition, quizzes are
given at the start of the period, and no extension is given for
tardiness. Similarly, you should not leave during class, even
temporarily. Get your drink of water before class starts. Leaving
briefly and then returning is rude and disconcerting to others in the class and
to the teacher.
Honor code: I subscribe to the Longwood honor system, which,
among other things, assumes you do not cheat and that you take responsibility
to see that others do not. Infractions will be dealt with harshly.
A student who is convicted of an Honor Code offense involving this class will
receive a course grade of F, in addition to any penalties imposed by the Honor
Board.
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Abstract
A pedagogical application-oriented introduction to the calculus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear connections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their traditional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional machinery, are stressed throughout the article.
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978-0-17-438476-2 / 9780174384762
Shipping prices may be approximate. Please verify cost before checkout.
About the book:
The "MSM Mathematics" series offers an integrated and comprehensive assessment for GCSE mathematics. It provides a one-book-per-year mathematics course. There are worked examples and numerous graded exercises. The maths is set in the context of everyday life, involving investigations and project work, to provide approaches to all kinds of mathematical problem solving. The writing team has organized the mathematics covered by the National Curriculum into a series of topic-based sections within each book. Mathematical knowledge and skills are developed in line with current practice in maths teaching. The "MSM" series comprises course books at all levels. Books 1 and 2 provide maths for all abilities at Key Stage 3. Students of average ability can continue with the "x" series - books 3x, 4x and 5x. The "w" series provides support for students having difficulty with the maths covered in the books 1, 2, 3x-5x. The material in the "w" books is organized in the same sequence as the main course, but concentrates on the development of basic concepts for those students experiencing difficulties. The "y" series caters for more able students, providing maths for top grades of GCSE and preparation for Sixth-Form work leading up to Levels 9-10 at Key Stage 4.
Softcover, ISBN 0174384769 Publisher: Nelson Thornes Ltd, 199174384769 Publisher: Nelson Thornes Ltd, Oxford, 1991 New edition. New edition.. Spiralbound. Used - Fair Fair . A readable copy of the book which may include some defects such as highlighting and notes. Cover and pages may be creased and show discolouration. MSM assessment. . New edition. New edition.
Softcover, ISBN 0174384769 Publisher: Nelson Thornes Ltd, 1991 Used - Acceptable. A readable copy of the book which may include some defects such as highlighting and notes. Cover and pages may be creased and show discolouration.
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Algebra 1
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THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! Glencoe Pre-Algebra is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scTHE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! Glencoe Pre-Algebra is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics sc 97800782508352508
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The Prentice-Hall mathematics series is designed to help students develop a deeper understanding of math through an emphasis on thinking, reasoning, and problem-solving. A mix of print and digital materials helps engage students with visual and dynamic activities alongside textbook instruction. Course 2 (Grade 7) presents a structured approach to a variety of topics such as ratios, percents, equations, inequalities, geometry, graphing, and probability.In the Getting Ready to Learn portion of the textbook lesson, Check your readiness exercises help students see where they might need to review before the lesson. Check skills you'll need list out the skills used in the lesson, and new vocabulary is listed before it's introduced. Sidebar helps tell students where to go for help in the Prentice Hall Chemistry: Small Scale Chemistry Laboratory Manual [Paperback] PRENTICE HALL (Author)Prentice Hall Chemis
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Synopses & Reviews
Publisher Comments:
This brief book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. Its organization draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in approach, it is written with an assumption that the student reader may have computing facilities for two- and three-dimensional graphics, and for doing symbolic algebra. Chapter topics include coordinate and vector geometry, differentiation, applications of differentiation, integration, and fundamental theorems. For those with knowledge of introductory calculus in a wide range of disciplines includingbut not limited tomathematics, engineering, physics, chemistry, and economics
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Elements ofScience used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.
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Number Properties Guide provides a comprehensive analysis of the properties and rules of integers tested on the GRE to help you learn, practice, and master everything from prime products to perfect squares.
Each chapter builds comprehensive content understanding by providing rules, strategies and in-depth examples of how the GRE tests a given topic and how you can respond accurately and quickly. The Guide contains 150+ questions: \"Check Your Skills\" questions in the chapters that test your understanding as you go and \"In-Action\" problems of increasing difficulty, all with detailed answer explanations.
Purchase of this book includes one year of access to 6 of Manhattan GRE\'s online practice exams.
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...
Show More While this supplement suggests ways in which to use Mathcad to enhance your understanding of statics and teach you efficient computational skills, you may also browse through the Mathcad Student manual and think of your own usage of Mathcad to solve statics problems and applications in other courses. The manual consists of 11 chapters. The first chapter is a general introduction to Mathcad that concludes with a sample application of Mathcad to a statics problem and can be studied while reading Chapter 1 of the accompanying Statics text. The following 10 chapters present appropriate Mathcad solutions for some of the sample problems given in the text. Chapter 1 - Using Mathcad Computational Software Numerical Calculation Working with Functions Symbolic Calculations Solving Algebraic Equations Graphs and Plots Application of Mathcad to a Statics Problem Along with solutions to sample problems, other topics covered within this manual include: Mathcad as a Vector Calculator; Solution of Simultaneous Linear Equations; Using Mathcad for Other Matrix Calculations; Scalar of Dot Product; Vector or Cross Product Between Two Vectors; Parametric Solutions; Solution of Nonlinear Algebraic Equations; Vector or Cross Product Between Two Vectors; Numerical and Symbolic Integration; Three-Dimensional Scatter Plots; Symbolic Generation of Equilibrium Equations; Discontinuity Functions; Cables; Wedges; Belt Friction; Principle Second Moments of Area; Eigenvalue Problems
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More About
This Textbook
Overview
Elementary Algebra offers a practical approach to the study of beginning algebra concepts, consistent with the needs of today's student. The author puts special emphasis on the worked examples in each section, treating them as the primary means of instruction, since students rely so heavily on examples to complete assignments. The applications are also uniquely designed so that students have an experience that is more true to life—students must read information as it appears in a "live" media source and extract only the relevant information needed to solve a stated problem. The unique pedagogy in the text focuses on promoting better study habits and critical thinking skills along with orienting students to think and reason mathematically. Through Elementary Algebra, students will not only be better prepared for future math courses, they will be better prepared to solve problems and answer questions they encounter in their own lives.
Meet the Author
Laura Bracken, co-author of Investigating Prealgebra and Investigating Basic College Mathematics, teaches developmental mathematics at Lewis-Clark State College. As developmental math coordinator, Laura led the process of developing objectives, standardizing assessments, and enforcing placement including a mastery skill quiz program. She has worked collaboratively with science faculty to make connections between developmental math and introductory science courses. Laura has presented at numerous national and regional conferences and currently serves as the regional representative for the AMATYC Placement and Assessment Committee. Her blog, Dev Math Diary, is at
Ed Miller is a professor of mathematics at Lewis-Clark State College. He earned his PhD in general topology at Ohio University in 1989. He teaches a wide range of courses, including elementary and intermediate algebra. His terms as chair of the General Education Committee, the Curriculum Committee, and the Division of Natural Sciences and Mathematics have spurred him to look at courses as part of an integrated whole rather than discrete units. A regular presenter at national and regional meetings, Ed is exploring the use of multiple choice questions as a teaching tool as well as an assessment
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Overview
This is a survey, accessible to advanced undergraduates, of some parts of abstract algebra that are of use in many other areas of discrete mathematics. The treatment is mathematical, but the authors have made great efforts to address the needs of those who will be using the techniques that are being discussed. The presentation assumes knowledge of the material covered in a course on linear algebra and some acquaintance with the basics of groups, rings, and fields. More than 500 exercises accompany the text; fully worked out computational examples are especially emphasized. This new edition has been substantially revised. It includes corrections and improvements to the first four chapters; an enlarged chapter on applications of groups; and two new chapters, one on cryptology and the other an extensive survey of mostly recent applications, many of which are not commonly found in undergraduate texts. A complete solutions manual
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Numerical Methods for Ordinary the analysis of numerical methods without losing sight of the practical nature of the subject
Covers topics traditionally treated in a first course, but also highlights new and emerging themes
Features chapters broken down into lecture-sized pieces, motivated and illustrated by numerous theoretical and computational examples
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.
It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.
Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.
The book covers key foundation topics:
o Taylor series methods
o Runge-Kutta methods
o Linear multistep methods
o Convergence
o Stability
and a range of modern themes:
o Adaptive stepsize selection
o Long term dynamics
o Modified equations
o Geometric integration
o Stochastic differential equations
The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via
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. Calculator can solve three simultaneous equations and delivers fast calculation speed and smooth operation. The Playback feature allows you to edit and make changes to formulas easily. The hard slide cover protects the calculator so it can withstand frequent use. Calculator is recommended for general math, pre-algebra, algebra, trigonometry and biology. PTA approved tests include AP Chemistry, AP Physics, PSAT/NMSQT, SAT I, SAT II, Math IC, and Math IIC. Twin power calculator runs on solar power and battery power.
"The EL-W535XBSL performs over 330 advanced scientific functions and utilizes WriteView Technology 4-line display and Multi-Line Playback to make scientific equations easier for students to solve. It is ideal for students studying general math algebra ge
| 677.169 | 1 |
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Overview
Intended for the undergraduate student majoring in mathematics, physics or engineering, the Sixth Edition of Complex Analysis for Mathematics and Engineering continues to provide a comprehensive, student-friendly presentation of complex analysis. The authors strike a balance between the pure and applied aspects of the subject, and present concepts in a clear writing style that is appropriate for students at the junior/senior level. Through its thorough, accessible presentation and numerous applications, the sixth edition of this classic text allows students to work through even the most difficult proofs with ease. Believing that mathematicians, engineers, and scientists should be exposed to a careful presentation of mathematics, the authors devote attention to important topics such as ensuring that required assumptions are met before using a theorem, confirming that algebraic operations are valid, and checking that formulas are not blindly applied
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Comment
This was a great introduction to both the unit circle (if students have not seen it before) and the graph of a sine function. The review in the beginning and the practice problems helped prepare students to solve for the y values at points along the unit circle eventually leading to the sine graph. I think there was some room for improvement at the review at the beginning only covered the ratios for the different functions and did not include a review example of how to set up an equation to solve for an unknown side. I have found that setting up these equations is more of a struggle for students compared to just writing trig ratios.
I think that the flow of the lesson was great. It incorporated a lot of appealing visual elements and the flow of it made sense and was easy to follow. I enjoyed the tip on how to change the mode of the calculator from radians to degrees.
I enjoyed how students "built" a table by solving a series of problems. Initially I wondered why decimal values were used instead of exact, but this later made the graph much easier to interpret. Overall, I think this stand-alone lesson presented a difficult concept in a very understandable way.
Technical Remarks:
The powerpoint worked well, all the navigational buttons were fuctional.
However, most of the correct answers said "correct" which would need to be changed before using this with students. Likewise answers where a student needed to change the angle mode said "rad", the answer for using cosine instead of sine said "cos", etc.
Additionally some of the animations seemed a bit too long, especially the appearance of the forward button. I understand this instructionally as you want to make sure students take adequate time on the lesson, but I found myself reading the slide and then having to wait to move forward.
Time spent reviewing site:
40
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MoreA quick, easy-to-follow guide to mathematical topics required for important concept development in physics
More than 1,500 fully-solved problems presented from both the physics and mathematics point-of-view
Hundreds more practice problems
Product Attributes
eBooks:
Kobo
Book Format:
Paperback
Number of Pages:
0409
Publisher:
McGraw-Hill
View all buying options for Schaum's Outlines Mathematics for Physics Students
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Mathematics is fun, challenging, and rewarding. It is logical yet creative.
It is important for applications yet enjoyable in its own right. As you
learn more about mathematics, you will see that the logical structure
of theorems, proofs, and classifications has a certain aesthetic appeal.
And mathematics seeks ultimate and eternal truths. Once we know something
is true, it can never be false.
The adventure of mathematics is thrilling, yet it is difficult to find the starting place on your own.
In the Pepperdine University Math major, we serve as guides to start you
on your way to discovering more and more mathematics. Once you start on
this journey, your life may never be the same.
What can I do after I graduate?
You can continue to pursue mathematics formally, by enrolling in
graduate school, and becoming a mathematician. You might teach at a
college or university, or become a part of a private think tank, or
work for one of many engineering and cryptographic companies and
government agencies. At any rate, you can be one of many people
making new and amazing discoveries every year. Read more about
preparing for graduate school.
You can go into industry. Mathematics majors are hot commodities
in the workplace, because employers know that the mathematics degree
is a degree in critical, creative, and logical thinking. Many
engineering, biotech, actuarial, and computer companies need employees
with mathematical knowledge, and many more of the same want employees
who know how to think and solve problems. Some math majors become
very successful management consultants, doctors, and lawyers for this
reason. Read more about careers in mathematics.
You can teach mathematics at the secondary school level. At Pepperdine,
we require prospective teachers to be mathematics majors because we feel
it is the only way to ensure the continued high level of excellence of
mathematics teachers graduating from Pepperdine. Mathematics teachers are
in very high demand around the world, but especially in California. Many
high school students graduate without basic mathematical skills, and without
an appreciation for mathematics. A major reason for this is the lack of
good math teachers. You can make a difference to many
children and teens in a society that demands more and more mathematics of
our students, while preparing them less and less. Read more about
secondary school teacher education.
Mathematics is also a good background for many other fields. Some
mathematics majors end up becoming physicists, chemists, biologists,
engineers, computer scientists, linguists, lawyers, doctors, managers, and
so on. A background in mathematics is often viewed extremely highly in all
of these fields, and math graduates often do very well in these fields.
Mathematics is a good
Pre-med major, and math majors enjoy higher acceptance rates to medical
school than many more traditional majors like biology.
How much can I expect to make?
Of course, it all depends on what career you choose, but
the National Association of Colleges and Employers reported in 1999 that
the average starting salary for a mathematics major with a bachelor's degree
was $37,300 a year, for those with a masters degree, $42,000, and for
those with a Ph.D., $58,900.
In addition, USA Today
reported that the average mathematician over the age of 30 earns
$52,316, which is second only to engineers, who earn on average
$52,998.
While you are a student at Pepperdine, you will learn a broad range of
ideas and experience the world through many ways. Mathematics can help
you think clearly and critically about ideas you encounter. In fact,
mathematics is in many ways a branch of philosophy. Plato required it
of those who would study under him. Descartes used it as a foundation
in his quest to know what is real and what we know is real. In the
20th century Godel's work sent shock waves through the philosophical
community. Many of our students took some time to explore the implications
of mathematics in theology, cosmology, and epistemology. Many students
have also mentioned its importance in learning truth and avoiding error
in their religious pursuits.
Why should I major in math?
Because it's challenging. Because it's beautiful. Because it's important.
Because it's there.
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Computing the Continuous Discrete much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community.
We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant, and the authors' engaging style encourages such participation. The many compelling pictures that accompany the proofs and examples add to the inviting style.
For teachers, this text is ideally suited as a capstone course for undergraduate students or as a compelling text in discrete mathematical topics for beginning graduate students. For scientists, this text can be utilized as a quick tooling device, especially for those who want a self-contained, easy-to-read introduction to these topics.
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So you are about to write the end-of-year examinations!
Some of you are about to write the most important examination of your life, the Grade 12 final examinations.
This is a "high-stakes" examination since the results will determine the course of your life. A good result may open up doors which a poor result will not. And among the subjects, it is Mathemtics and Mathematical Literacy are those which are valued highly for entrance to university and other tertiary studies, and also for entrance to a wide range of further studies. For example, Engineering, Sciences, and Computer Sciences are not available if you do not ave a reaonsable pass in Mathematics.
This article provides a simple approach to answering the questions presented in the mathematical papers to help you improve your marks. By now there is little time left to increase your mathematical knowledge, and so I am focussing rather on how you can present your knowledge to the marker of the examination to show that you know and that you do not lose marks by presenting your knowledge in the wrong way.
In reality there are few right or wrong ways, but for every question in the exam paper there is also a memorandum which helps the markers to provide the marks to you. If a question provides 3 marks, than you are expected to show 3 things, not 2 and not 4, just 3. I will now help you in how to answer, using a method I use with all of my students, and which I call "APEX".
APEX
I have developed the APEX method based upon the well-known work of Polya ("How to Solve It") which is one of the most widely used mathematical books of all time. Polya's work was directed at more complex problem situations, and I have applied this to the most simple of mathematical problems, since all such mathematical problems can be solved in this way.
Polya did not give a name to his 4-step method, and I have restructured this and called is the "APEX" approach, which consists of the following 4 steps.
A : Analyse
P : Plan
E : Execute
X : Crosscheck
ANALYSE
For this step you will do the following:
Read the Question: do not assume that you know the question by just looking at it quickly. Read it in detail.
See what you are given:
See what you have to produce:
See how many marks there are for this question: For every mark you are expected to do something specific. There will not be a situation in which you get two marks for doing one thing, or one mark for two things. Every question / problem is structured
Determine what the marks are for: Knowing how many marks you can get for this question, and also what you are expected to produce as outputs from the inputs which you are given, you need to start to consider what you should be providing in your written answer to be able to get the full marks. However, to continue with this you need to move to step : PLAN.
PLAN
Some questions are presented in a way that you know what type of mathematics you are to use, but in others this is not specified and you need to use your knowledge of mathematics to match the question to the right mathematical approach.
Once you have identified the mathematics you will be using, you can then plan what you will be doing.
In many cases you are also given the formulas, and thus you are not required to remember each and every formula, but you are required to know how to use the right formula and how to apply these to the problem.
For the PLAN step you will do the following:
What Mathematics?: select the type of mathematics which you think you will need. If this is not clear then consider a shortlist and see which may be more applicable than another.
Plan the attack: determine how you will use the mathematics and what specific actions you will do.
Map to the marks: you need to see what you will get marks for, since this may not be clear initially. You need to ensure that you provide enough information to get full marks, and also that you reduce the amount of work which will not contribute to the marks.
Predict the Answer: given the nature of the problem, you may be able to predict the nature of the answer expected. This is important in step 4, CROSSCHECK, in which you will check whether your answer is reasonable or not. For this you will check back to the initial question.
If the question has a mark of one (1), then you only need to provide the mark.
If there are two marks (2), then you need to provide two things, generally a first element of your workings / actions, and the answer.
If there are three marks (3), then you need to provide some workings, and one or more answers.
However, you will NEVER get marks from repeating the question! If you do repeat this it may help to provide the solution and will also help if it is not evident which question it is in case you wrote the wrong question number onto your paper.
You now have the following:
The actions you will undertake, which may be clear or may not be depending on how much still had to be worked out.
Which of these actions you are likely to get marks for, and which should be emphasised.
The sequence in which you will carry out the actions to arrive at teh solution.
Now you have to actually do the work, and we move onto the EXECUTE step of the APEX method.
EXECUTE
In this step you must carry out the actions you identified in the PLAN step. In most cases the PLAN is not written down, but will be structured in your head, but for larger problems it may be better to at least write the steps as an aide for your work.
You will now perform the actions, and at this time will write these down as part of your response and answer.
The following must be considered:
When writing the workings and the answers, be sure to highlight those for which you expect to get marks.
This could be done by positioning them differently on the page, such as in the centre of the page.
All other workings should be positioned elsewhere, such as on the left of the page.
However, some of these workings may also contribute to marks, so do not put them elsewhere.
CROSSCHECK
You now must check your answer to see if it reasonable to what was expected, which you may have already identified in step 1, ANALYSE.
The CROSSCHECK step is perhaps the most difficult for learners, since it is not always obvious what a correct answer should look like, and may learners create answers which are wrong, but for which they cannot see that they are wrong.
In many cases, mathematics exists in a real-world setting, and for these cases it is important to understand the nature of the real world from your own experience.
Practice, practice, practice!
There is a quote attributed to the famous golfer Tiger Woods when someone remarked how lucky he was to always get his low scores, with good drives down the fairway, and good putts to get the golf ball into the hole. His response "yes, but the more I practice, the luckier I get!".
You need to practice how to write examination questions, and I would like to deal with this in my next blog.
Good luck for the examinations, and be sure to write to me by email about your experiences and whether this is useful to you.
I encounter many students who struggle with the concept and practice of rounding.
The general procedure taught in school is that if the last digit is 0-4 we round down, and if it is 5-9 we round up, but what does "rounding up" and "rounding down" mean, and why is this important?
The word "rounding" can be quite confusing, since it sounds like you are doing something round, like a circle, but this is not what this term is concerned with. So let us dispel any notion that rounding has something to do with circles. Rather, the term "round" when used as a verb (to round) is concerned with find a round number, which is the closest number to another number, rather than as an adjective (round) which is used to describe circular objects.
Thus the term "rounding" means to find the closest number of a particular form. If we are asked to round to the nearest 10, then the outcome should be a number like 10, 20, 30, etc… and if we are asked to round to the nearest 2 decimal places, then we are expected to provide a number like 243.23 or 0.17, but not 243.2 or 243.22785.
In some cases we have to found to the nearest 5, and for this the outcome will be a number which is divisble by 5 such as 0, 5, 10, 15, 20, 25, ….
Why do we round?
It is important in all mathematics to understand why we do things and what the different mathematical structures are for. Putting mathematics into context makes it more meaningful and less abstract.
Rounding is used for us to determine an approximate amount since this is often easier to communicate. For example, if I am describing to somehow how far it is for me to drive to work every day I will say "about 20km", rather than saying "exactly 18.6km". No-one expects me to tell them exactly how far it is to my work, and to get an idea of a close amount is sufficient. This is rounding to the nearest 5km, since I could have also said 15km or 25km, but neither of these are that good and are not that close. I could have said 18km or 19km and this would also have been informative, but when asked a request such as how far it is to drive to work people do not expect a detailed answer and only an approximation.
I am sure that almost every day you are engaged in conversations in which you are discussion measures and numbers in a way in you use the work "about" to approximate the number when you do not know the exact number or if it is not necessary to be so exact.
For example, if I ask you how much per week do you spend on airtime you will probably not say "exactly R20.45″, but will rather say "about R20″.
Rounding is the mathematical operation which allows us to find the number which is closest according fo a simple set of rules, and which is also appropriate to the context.
Rounding to the nearest unit
The simplest case of rounding is where we have to round to the nearest unit.
As an example, we have a number 452.35 and we want the nearest whole number to this. This can be achieved by simply dropping the decimal fraction .35 leaving us with 453. But what if the the numebr is 452.93. This is clearly closer to 453 than to 452 and this it is better to round UP to 453.
The rule mentioned above will apply. If the first digit is 0-4 we round down and if it is 5-9 we round up. In this case we do not need to look at any other digits in the decimal fraction.
For example, all of the numbers 3.4, 3.49, 3.495, 3.4957 will ALL round down to 4, since the first digit of the decimal fraction is 4, and this indicates we should round down.
This example may be confusing to some, since if we take 3.49 to one decimal place this will become 3.5 and if we then round this it will become 4, but rounding up since the digit 5 will cause a round up. However, this means that when we round we do this in a single operation and not in multiple operations, and in all cases we only need to look at a single digit to make the decision.
Rounding to Two Decimal Places
It is very common in examinations that answers are required to be entered to two decimal places if this is not specified elsewhere. This means that you need to know how to round to two decimal places since this may be used many times on every examination which you write. If you fail to round the answer you are likely to lose a mark, even if this was not specified in the question.
In this case and answer of 2.456 must be rounded UP to 2.46, since the last digit is 6 which causes you to round up.
So what about 2.45633?
In this case you must look at the first decimal digit AFTER the point you are to stop. In this case, since your rounding to TWO decimal places you must look at the digit after the second decimal position, which is the 6 after the .45 and is not the additional 33 at the end, which are not needed for determining how to round.
Try these
Original number
Rounded number
2.45
0.6
0.798
23.1999
452.5
Rounding to nearest 5
In most cases you are asked to round to a number which is a power of ten, such as to the nearest hundred (100), ten (10), unit (1), tenth (0.1 – one decimal place), or hundredth (0.01 – 2 decimal places).
If you are asked to round to a number other than a power of ten, then you cannot use the rule about that 0-4 rounds down and 5-9 rounds up.
For example consider the problem of rounding 372 to the nearest 5. For this you will need to find the lowest and hight numbers around 372 which are multiple of 5, and then to select which is the closest. You should be able to this by inspection, but to help you understand this better you can find these numbers youself. In this case the numbers are 370, which is the multiple of 5 which is lower than 372 and 375, which is the multipel of 5 larger than 372. It is clear that 372 is closer to 370, which is a difference of 2 (372-370), rather than 375 which is a difference of 3 (375-372).
Try these
Original number
Rounded to nearest 5
245
343
798
2319
452
Rounding to nearest 10, 100, 1000
These are essentially the same process as rounding to the nearest unit. But the answer will be a multipe of 10, 100, or 1000.
For example, rounding 2459 to the nearest 10 is 2460, because the last digit is 9, which means we round up. Rounding this to the nearest 100 give 2500, since the last digit is now 5, being the digit after the 100 position. Rounding to the nearest 1000, then gives us 2000, since the last digit when considering 1000s is 4 which means round down.
I have noticed that a number of relatively senior learners, in Grades 10-12, still struggle with types of integer addition.
For example, consider the following three simple arithmetic integer sums:
Whereas the first and second have the same value they often yield different answers. All I have done is to move the to the start of the sum.
I am hoping that you did understand that both of these will produce the answer of .
For the third sum, the situation is different, and I have also found some confusion with this, in which learners tend to misunderstand whether this means or , and struggle to understand how to subtract a number from a negative numbers. It appears that they see the minus (-) signs used as having different meaning depending upon whether this is at the start of the sum or if this is between two other numbers.
The 2012 Annual National Assessments for Grade 9 include a question to select a particular type of number from a list. Each of these carries one mark only, and thus not much is expected from the learner except to circle their choice on their answer paper. This blog article will talk you through two worked examples.
LaTeX is a language developed from the TeX computer typesetting language which was originally created by the computer scientists Donald Knuth in the 1970s.
LaTeX is generally represented by the logo , which you will only see if your browser can render LaTeX correctly. If this logo does not display, then you should look at the Getting Started page of this web site, which will indicate what browsers support LateX and which do not. Using LaTeX we can easily enter mathematical expressions such as which are in the language of mathematics itself.
This site is dedicated to helping to improve the standards of mathematics in South Africa. It is primarily aimed at school-level learners and teachers but will be a useful resource for those interested in the more advanced aspects of mathematics, as well as those who are simply interested in mathematics or work with mathematics in their daily lives (as do most of us today!).
At present this sites is being started, and thus does not have much content, but over time more and more mathematics will be added to ensure that this becomes a useful reference for all. Continue reading →
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Accuracy and Precision Home Page
Accuracy and Precision Home Page
A series of tutorials on basic measurement theory, including such topics as experimental errors, measurement, accuracy and precision, exact numbers, and significant figures (digits). Applet calculators included, along with quizzes.
A series of tutorials on basic measurement theory, including such topics as experimental errors, measurement, accuracy and precision, exact numbers, and significant figures (digits). Applet calculators included, along with quizzes.
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An independent book written and self-published by former math teacher and private math tutor Larry Zafran. Students are justified in proclaiming that "math is hard," but there is a specific reason why they feel this way. The author maintains that the struggle can be lessened by following the roadmap presented, but it will take time and effort on the part of the student.
Since math is often not properly taught, it is often not properly learned. Anything that hasn't truly been learned, regardless of subject, is "hard." Once the various concepts are more secure, and the student's gaps in understanding have been addressed, math will have been made "a bit easier" as promised by the book's title. However, the book does not imply that learning math is fast, fun, or easy.
Most of the book's content is comprised of the roadmap of topics for a student to work through at his/her own pace. Like all paths, it begins at the beginning, in this case starting with a review of basic arithmetic, followed by basic operations, negative numbers, fractions, decimals, percents, and basic probability and statistics. This is the foundation of all math. The space devoted to each topic is proportional to how difficult most students find the topic, as well as how important the topic is in preparation for later math studies. The material is explained conversationally and "in plain English" as promised by the book's subtitle, without talking down to the reader, and without the use of contrived examples or cartoonish illustrations.
The book concludes with a chapter on how to effectively study math and improve scores on exams. Like the rest of the book, the chapter takes a unique standpoint on the matter, and offers suggestions which include how to get oneself into the proper mental and emotional mindset for being successful with math.
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Lomita GeometryLinear Algebra works great for modeling static situations, but more interesting phenomena in the real world include changing variables such as temperature, volume, population, etc. To understand these more interesting physical situations, one needs to find the differential equation describing th
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This is a free, online textbook offered by Bookboon.com. Topics include: 1. Tangents to curves2. Tangent plane to a surface3. Simple integrals in several variables 4. Extremum (two variables)5. Extrema (three or more variables)
This is a free, online textbook offered by Bookboon.com. Topics include:
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Stewart's clear, direct writing style in SINGLE VARIABLE CALCULUS guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution. iLrn Homework helps you identify where you need additional help, and Personal Tutor with SMARTHINKING gives you live, one-on-one online help from an experienced calculus tutor. In addition, the Interactive Video Skillbuilder CD-ROM takes you step-by-step through examples from the book.
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Functions and Graphs [NOOK Book] ...
More About
This BookEditorial Reviews
From the Publisher
"All through both volumes [Functions & Graphs and The Methods of Coordinates], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated by n ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done 30, 2004
An insightful introduction to analytic geometry.
This brief text gives a lucid introduction to analytic geometry that is notable for the extent to which the authors go to explain why the graphs of the functions they discuss have the properties they do and the many challenging problems the authors include. The authors discuss the properties and graphs of linear functions, absolute value functions, quadratic functions, linear fractional functions, power functions, and rational functions. The text concludes with a chapter length problem set full of challenging problems that will test whether the reader has fully understood the material. While the exercises do not require calculus, the reader may wish to revisit these problems once she or he has had calculus in order to more fully understand the graphs. Answers and hints to a few of the exercises are given in the back of the text.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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Find a League CityThomas and received an A in the course. Linear Algebra is the study of matrices and their properties. The applications for linear algebra are far reaching whether you want to continue studying advanced algebra or computer science
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This webinar offers educators a quick and easy way to learn some of the fundamental concepts of Maple. Learn a few simple techniques that will allow you to use Clickable Math™ features to compose, visualize, and solve a wide variety of mathematical problems without commands. This webinar will also provide an introduction to some of the technical documentation features in Maple, including the use of interactive components such as buttons and sliders.
We'll also explore some of the new features in our latest release, Maple 18, including new embedded videos, advancements in a variety of branches of mathematics, new interactive math apps, and more!
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InstaCalc is a customizable calculator designed with the user in mind. Users can specify operations and relationships between...
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InstaCalc is a customizable calculator designed with the user in mind. Users can specify operations and relationships between entry and output cells and format their own custom designs such as unit converters, loan interest calculators, etc.The platform allows users to save each custom calculator and to copy and embed the code elsewhere so that the calculator can appear on the user's own website site hosts two pages of dynamic geometric animations of common functions.The first page, Derivatives, features...
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This site hosts two pages of dynamic geometric animations of common functions.The first page, Derivatives, features functions such as the natural logarithm, the exponential function, f(x)=sin(x), etc, and displays graphs of their first and second derivatives. As the user traces along each graph, a tangent line is displayed at that x value for each of the three graphs. The second page, Trigonometry, displays side-by-side, unit circle and rectangular coordinate graphs, complete with all six trigonometric functions. Each function is displayed on both graphs, is color coded, and can be toggled on and off to better show specific relationships between functions. The user can also click to freeze tracer points at any angle 0 ≤ θ ≤ 2π.These visualizations give insight into the dynamic nature of various common functions and help users to percieve their fundamental geometric properties and relationships.
'The following mathlets are designed for the students in my geometry classes to review basic algebra skills in such a way...
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'The following mathlets are designed for the students in my geometry classes to review basic algebra skills in such a way that they can check their answers and/or get hints as to how to proceed.The idea behind these "procedure-based" dynamic worksheets is to provide students the opportunity to review and practice algebra skills with problems they create, while at the same time providing a means for students to check their answers and to get a hint if needed. The hints will walk the student through the problem in a step by step manner.'
'This module consists of three units:Unit 1: Descriptive Statistics and Probability DistributionsDescriptive statistics in...
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'This module consists of three units:Unit 1: Descriptive Statistics and Probability DistributionsDescriptive statistics in unit one is developed either as an extension of secondary mathematics or as an introduction to first time learners of statistics. It introduces the measures of dispersion in statistics. The unit also introduces the concept of probability and the theoretical treatment of probability.Unit 2: Random variables and Test DistributionsThis unit requires Unit 1 as a prerequisite. It develops from the moment and moment generating functions, Markov and Chebychev inequalities, special univariate distributions, bivariate probability distributions and analyses conditional probabilities. The unit gives insights into the analysis of correlation coefficients and distribution functions of random variables such as the Chi-square, t and F.Unit 3: Probability TheoryThis unit builds up from unit 2. It analyses probability using indicator functions. It introduces Bonferoni inequality random vectors,, generating functions, characteristic functions and statistical independence random samples. It develops further the concepts of functions of several random variables and independence of X and S2 in normal samples order statistics. The unit summarises with the treatment of convergence and limit theorems
'This module consists of three units which are as follows:Unit 1: (i) Sets and Functions (ii) Composite FunctionsThis unit...
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'This module consists of three units which are as follows:Unit 1: (i) Sets and Functions (ii) Composite FunctionsThis unit starts with the concept of a set. It then intoroduces logic which gives the learner techniques for distinguishing between correct and incorrect arguments using propositions and their connectives. A grasp of sets of real numbers on which we define elementary functions is essential. The need to have pictorial representations of a function necessitates the study of its graph. Note that the concept of a function can also be viewed as an instruction to be carried out on a set of objects. This necessitates the study of arrangements of objects in a certain order, called permutations and combinations.Unit 2: Binary OperationsIn this unit we look at the concept of binary operations. This leads to the study of elementary properties of integers such as congruence. The introduction to algebraic structures is simply what we require to pave the way for unit 3.Unit 3: Groups, Subgroups and HomomorphismThis unit is devoted to the study of groups and rings. These are essentially sets of numbers or objects which satisfy some given axioms. The concepts of subgroup and subring are also important to study here. For the sake of looking at cases of fewer axiomatic demands we will also study the concepts of homomorphisms and isomorphisms. Here we will be reflecting on the concept of a mapping or a function from either one group to the other or from one ring to the other in order to find out what properties such a function has.'
'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all...
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'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems.''The focus is.'
'This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of...
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'This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of functions of a single variable. The third unit is devoted to sequences of real numbers and infinite series of both real numbers and of some special functions. The fourth unit is on the differential and integral calculus of functions of several variables.Starting with the definitions of the basic concepts of limit and continuity of functions of a single variable the module proceeds to introduce the notions of differentiation and integration, covering both methods and applications.Definitions of convergence for sequences and infinite series are given. Tests for convergence of infinite series are presented, including the concepts of interval and radius of convergence of a power series.Partial derivatives of functions of several variables are introduced and used in formulating Taylor's theorem and finding relative extreme values.'
'This module consisst of two units, namely Introduction to Ordinary differential equations and higher order differential...
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'This module consisst of two units, namely Introduction to Ordinary differential equations and higher order differential equations respectively. In unit one both homogeneous and non-homogeneous ordinary differential equations are discussed and their solutions obtained with a variety of techniques.Some of these techniques include the variation of parameters, the method of undetermined coefficients and the inverse operators. In unit two series solutions of differential equations are discussed .Also discussed are partial differential equations and their solution by separation of variables. Other topics discussed are Laplace transforms, Fourier series, Fourier transforms and their applications.Outline: SyllabusUnit 1: Introduction to Ordinary Differential EquationsLevel 2. Priority A. Calculus 3 is prerequisite.First order differential equations and applications. Second order differential equations. Homogeneous equations with constant coefficients. Equations with variable coefficients. Non-homogeneous equations. Undetermined coefficients. Variations of parameters. Inverse differential operators.Unit 2: Higher Order Differential Equations and ApplicationsLevel 2. Priority B. Differential Equations 1 is prerequisite.Series solution of second order linear ordinary differential equations. Special functions. Methods of separation of variables applied to second order partial differential equations. Spherical harmonics. Laplace transform and applications. Fourier series, Fourier transform and applications'
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About The Course
The course has been taught at Brown University since 2008,
and is being taught in Fall
2013. Slides will be made available here.
A shortened version has been taught through Coursera.
The aim of this course is to provide students interested in
computer science an introduction to vectors and matrices and
their use in CS applications.
The course is driven by applications from areas chosen from
among: computer vision, cryptography, game theory, graphics,
information retrieval and web search, and machine learning.
Course Resources
Data and support code required for carrying out the
assignments are provided here.
Auto-grading will be made available (beta version) for the programming
assignments.
Here are the first and second
labs from Edition One. These have nothing to do with linear algebra. They are
provided to bring the reader up to speed in the part of Python
we use in the book. You can use Python Tutor to debug, visualize,
and check your solutions to the tasks in this lab.
Sign up for updates
To receive messages when new material is available, e.g.
blog posts about applications of linear algebra to CS, news of
a follow-on course, or corrections to the book, join the
mailing list. I promise that mailings will be rare and that I
will not share your email address with anybody, ever.
Factoring an integer is a hard computational problem (and
the RSA cryptosystem depends on it being hard). At the
core of the most sophisticated integer-factoring algorithms
is a simple problem in linear algebra.
Image blurring
Blurring an image is a simple linear transformation.
Searching within an audio clip
Searching for one audio clip within another can be formulated
as a convolution. A convolution can be computed very
quickly using the Fast Fourier Transform.
Searching within an image
Convolution can also be done in two dimensions, enabling one
to quickly search for a subimage within an image.
Audio and image compression
Compression of audio and images aids efficient storage and
transmission. Lossy compression techniques such as
those used in MP3 (audio) and JPEG (images) are based in
part on linear algebra,
e.g. wavelet transform and Fourier transform.
100% original
size
40% original
size
10% original
size
Face detection
A "classical" approach to face detection is eigenfaces, a
technique related to principal component analysis.
2d graphics transformations
Simple transformations that arise in graphics such as
rotation, translation, and scaling can be expressed using
matrices.
Lights Out
Lights Out is a puzzle in which you must select the
correct buttons to push in order for all the lights to go
out. Finding a solution can be expressed as a problem in
linear algebra.
Minimum-weight spanning forest
Finding the minimum-weight spanning tree of a graph can be
interpreted as the problem of finding a minimum-weight basis
for a vector space
derived from the graph.
Graph layout
A nice drawing of a graph can be obtained from eigenvectors of
a related matrix.
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More About
This Textbook
Overview
When the answer at the back of the book is simply not enough, then you need the Student Solutions Manual. With fully worked-out solutions to all odd-numbered text problems, the Student Solutions Manual lets you "learn by example" and see the mathematical steps required to reach a solution. Worked-out problems included in the Solutions Manual are carefully selected from the textbook as representative of each section's exercise sets so you can follow-along and study more effectively. The Student Solutions Manual is simply the fastest way to see your mistakes, improve learning, and get better grades
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