Thinking Mathematically / Edition 3

by Robert Blitzer

Overview

Take a closer look at the front cover to see how mathematics affects our everyday experience.

• You may have participated in a survey, for example, but do you know how we use mathematics to interpret and present the results? (Chapter 2)
• Do you know a quick way to estimate the size of a large crowd from a photograph? (Chapter 1)
• Look at the architecture in the background. The buildings all around us are based on familiar geometric figures such as triangles, squares, and rectangles. (Chapter 10)
• In some areas, crowds like this are commonplace. However, in order locales, wide-open spaces are the norm. We can describe these differences using the mathematical concept of population density. (Chapter 9)

Thinking Mathematically invites you to navigate life and its challenges with greater ease and enthusiasm.

Product Details

ISBN-13:	9780131920118
Publisher:	Savvas Learning Company Llc
Publication date:	02/01/2004
Edition description:	Older Edition
Product dimensions:	8.80(w) x 10.60(h) x 1.40(d)

About 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 developmental mathematics, algebra & trigonometry, trigonometry, college algebra, and precalculus, all published by Pearson. 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.

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

Table of Contents

	About the Author	x
	Preface	xi
	To the Student	xiii
	Acknowledgments	xv
	Resources	xxii
	Applications Index	xxiii
Chapter 1	Problem Solving and Critical Thinking	3
Chapter 2	Set Theory	41
Chapter 3	Logic	91
Chapter 4	Number Representation and Calculation	169
Chapter 5	Number Theory and the Real Number System	203
Chapter 6	Algebra: Equations and Inequalities	275
Chapter 7	Algebra: Graphs, Functions, and Linear Systems	345
Chapter 8	Consumer Mathematics and Financial Management	419
Chapter 9	Measurement	477
Chapter 10	Geometry	505
Chapter 11	Counting Methods and Probability Theory	579
Chapter 12	Statistics	655
Chapter 13	Mathematical Systems	731
Chapter 14	Voting and Apportionment	757
Chapter 15	Graph Theory	815
	Answers to Selected Exercises	1
	Subject Index	1
	Photo Credits	1

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

Editorial Reviews

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