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Thinking Mathematically / Edition 5

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Overview

Blitzer continues to raise the bar with his engaging applications developed to motivate readers from diverse majors and backgrounds. Thinking Mathematically, Fifth Edition, draws from the author’s unique background in art, psychology, and math to present math in the context of real-world applications. The author understands the needs of nervous readers and provides helpful tools in every chapter to help them master the material. Voice balloons are strategically placed throughout the book, showing what an instructor would say when leading a student through a problem. Study tips, chapter review grids, Chapter Tests, and abundant exercises provide ample review and practice.

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Editorial Reviews

From The Critics
The "less-expanded" version, which is available under ISBN 0-13-065601-1, is about 100 pages shorter. This text is intended for a one- or two-term course in liberal arts mathematics, finite mathematics, and mathematics for education majors, as well as for courses specifically designed to meet state-mandated requirements. Blitzer teaches mathematics at Miami-Dade Community College. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780321645852
  • Publisher: Pearson
  • Publication date: 1/13/2010
  • Series: Pearson Custom Mathematics Series
  • Edition description: Fifth Edition
  • Edition number: 5
  • Pages: 960
  • Sales rank: 141,286
  • Product dimensions: 8.80 (w) x 10.90 (h) x 1.50 (d)

Meet the Author

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written textbooks covering introductory algebra, college algebra, algebra and trigonometry, and precalculus, all published by Prentice Hall. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

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Read an Excerpt

PREFACE:

Preface

To the Student

I've written this book to give you control over the part of your life that involves numbers and mathematical ideas. Gaining an understanding and appreciation of mathematics will help you participate fully in the twenty-first century. In some ways, you cannot get along in life without the mathematics in this book. For example, if you do not understand the basic ideas of investment, you may find it impossible to achieve your financial goals. If you do not have at least a rudimentary understanding of set theory, you may not be able to meaningfully interpret the vast amount of survey data we are presented with almost daily.

This book has been written so that you can learn about the power of mathematics directly from its pages. All concepts are carefully explained, important definitions and procedures are set off in boxes, and worked-out examples that present solutions in a step-by-step manner appear in every section. Study tip boxes offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to show ways to apply mathematics to your life in order to make your learning experience both interesting and relevant.

As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:

1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clearidea of the new material that will be discussed.

2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These worked-out examples provide a model for doing the exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific worked-out examples.

3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.

4. Prepare for chapter exams. After completing a chapter, study the summary, work the exercises in the chapter review, and work the exercises in the chapter test. Answers to all these exercises are given in the back of the book.

5. Use the supplements available with this book. A solutions manual containing worked-out solutions to the book's odd-numbered exercises and all review exercises, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.

It is my hope that you will enjoy the pages of this book, as you empower yourself with the mathematics needed to succeed in college, your career, and in your life.

To the Instructor

Thinking Mathematically provides a general survey of mathematical topics that are useful in our contemporary world. My primary purpose in writing the book was to show students how mathematics can be applied to their lives in interesting, enjoyable, and meaningful ways. The book's variety of topics and flexibility of sequence make it appropriate for a one- or two-term course in liberal arts mathematics, finite mathematics, mathematics for education majors, as well as for courses specifically designed to meet state-mandated requirements in mathematics.

I wrote the book with three major goals: first, to help students acquire knowledge of fundamental mathematics; second, to show students how mathematics can solve authentic problems that apply to their lives; and third, to enable students to develop problem-solving skills, fostering critical thinking, within a varied, interesting, and contemporary setting.

I am avidly interested in psychology, philosophy, and literature, as well as mathematics. I've worked as a musician, psychotherapist, and even attempted book, music, and lyrics to an original musical. (Compared to writing for musical theater, authoring mathematics textbooks is a breeze!) I hope that my love for learning, as well as my respect for the diversity of students I have taught and learned from over the years, is apparent In the hundreds of applications that appear throughout the book. By connecting mathematics to the whole spectrum of learning, it is my intent to show students that their world is profoundly mathematical and, indeed, "pi" is in the sky.

Robert Blitzer
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Table of Contents

1. Problem Solving and Critical Thinking

1.1 Inductive and Deductive Reasoning

1.2 Estimation, Graphs, and Mathematical Models

1.3 Problem Solving

2. Set Theory

2.1 Basic Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Set Operations and Venn Diagrams with Three Sets

2.5 Survey Problems

3. Logic

3.1 Statements, Negations, and Quantified Statements

3.2 Compound Statements and Connectives

3.3 Truth Tables for Negations, Conjunction, and Disjunction

3.4 Truth Tables for the Conditional and the Biconditional

3.5 Equivalent Statements and Variations of Conditional Statements

3.6 Negations of Conditional Statements and De Morgan's Laws

3.7 Arguments and Truth Tables

3.8 Arguments and Euler Diagrams

4. Number Representation and Calculation

4.1 Our Hindu-Arabic System and Early Positional Systems

4.2 Number Bases in Positional Systems

4.3 Computation in Positional Systems

4.4 Looking Back at Early Numeration Systems

5. Number Theory and the Real Number System

5.1 Number Theory, Prime and Composite Numbers

5.2 The Integers; Order of Operations

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties

5.6 Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

6. Algebra: Equations and Inequalities

6.1 Algebraic Expressions and Formulas

6.2 Linear Equations in One Variable and Proportions

6.3 Applications of Linear Equations

6.4 Linear Inequalities in One Variable

6.5 Quadratic Equations

7. Algebra: Graphs, Functions, and Linear Systems

7.1 Graphing and Functions

7.2 Linear Functions and Their Graphs

7.3 Systems of Linear Equations in Two Variables

7.4 Linear Inequalities in Two Variables

7.5 Linear Programming

7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions

8. Consumer Mathematics and Financial Management

8.1 Percent, Sales Tax, and Income Tax

8.2 Simple Interest

8.3 Compound Interest

8.4 Annuities, Stocks, and Bonds

8.5 Installment Loans, Amortization, and Credit Cards

9. Measurement

9.1 Measuring Length; The Metric System

9.2 Measuring Area and Volume

9.3 Measuring Weight and Temperature

10. Geometry

10.1 Points, Lines, Planes, and Angles

10.2 Triangles

10.3 Polygons, Perimeter, and Tessellations

10.4 Area and Circumference

10.5 Volume

10.6 Right Triangle Trigonometry

10.7 Beyond Euclidean Geometry

11. Counting Methods and Probability Theory

11.1 The Fundamental Counting Principle

11.2 Permutations

11.3 Combinations

11.4 Fundamentals of Probability

11.5 Probability with the Fundamental Counting principle, Permutations, and Combinations

11.6 Events Involving Not and Or; Odds

11.7 Events Involving And; Conditional Probability

11.8 Expected Value

12. Statistics

12.1 Sampling, Frequency Distributions, and Graphs

12.2 Measures of Central Tendency

12.3 Measures of Dispersion

12.4 The Normal Distribution

12.5 Problem Solving with the Normal Distribution

12.6 Scatter Plots, Correlation, and Regression Lines

13. Mathematical Systems

13.1 Mathematical Systems

13.2 Rotational Symmetry, Groups, and Clock Arithmetic

14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of Voting Methods

14.3 Apportionment Methods

14.4 Flaws of Apportionment Methods

15. Graph Theory

15.5 Graphs, Paths, and Circuits

15.2 Euler Paths and Euler Circuits

15.3 Hamilton Paths and Hamilton Circuits

15.4 Trees

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Preface

PREFACE:

Preface

To the Student

I've written this book to give you control over the part of your life that involves numbers and mathematical ideas. Gaining an understanding and appreciation of mathematics will help you participate fully in the twenty-first century. In some ways, you cannot get along in life without the mathematics in this book. For example, if you do not understand the basic ideas of investment, you may find it impossible to achieve your financial goals. If you do not have at least a rudimentary understanding of set theory, you may not be able to meaningfully interpret the vast amount of survey data we are presented with almost daily.

This book has been written so that you can learn about the power of mathematics directly from its pages. All concepts are carefully explained, important definitions and procedures are set off in boxes, and worked-out examples that present solutions in a step-by-step manner appear in every section. Study tip boxes offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to show ways to apply mathematics to your life in order to make your learning experience both interesting and relevant.

As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:

1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and prepared, you will find it useful to read the section before it is covered in lecture. This will give you aclearidea of the new material that will be discussed.

2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These worked-out examples provide a model for doing the exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific worked-out examples.

3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.

4. Prepare for chapter exams. After completing a chapter, study the summary, work the exercises in the chapter review, and work the exercises in the chapter test. Answers to all these exercises are given in the back of the book.

5. Use the supplements available with this book. A solutions manual containing worked-out solutions to the book's odd-numbered exercises and all review exercises, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.

It is my hope that you will enjoy the pages of this book, as you empower yourself with the mathematics needed to succeed in college, your career, and in your life.

To the Instructor

Thinking Mathematically provides a general survey of mathematical topics that are useful in our contemporary world. My primary purpose in writing the book was to show students how mathematics can be applied to their lives in interesting, enjoyable, and meaningful ways. The book's variety of topics and flexibility of sequence make it appropriate for a one- or two-term course in liberal arts mathematics, finite mathematics, mathematics for education majors, as well as for courses specifically designed to meet state-mandated requirements in mathematics.

I wrote the book with three major goals: first, to help students acquire knowledge of fundamental mathematics; second, to show students how mathematics can solve authentic problems that apply to their lives; and third, to enable students to develop problem-solving skills, fostering critical thinking, within a varied, interesting, and contemporary setting.

I am avidly interested in psychology, philosophy, and literature, as well as mathematics. I've worked as a musician, psychotherapist, and even attempted book, music, and lyrics to an original musical. (Compared to writing for musical theater, authoring mathematics textbooks is a breeze!) I hope that my love for learning, as well as my respect for the diversity of students I have taught and learned from over the years, is apparent In the hundreds of applications that appear throughout the book. By connecting mathematics to the whole spectrum of learning, it is my intent to show students that their world is profoundly mathematical and, indeed, "pi" is in the sky.

Robert Blitzer
Read More Show Less

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