Thinking Mathematically

by Blitzer, Robert

ISBN13:

9780139488450

ISBN10:

0139488456

Format:

Hardcover

Pub. Date:

1/1/2000

Publisher(s):

Prentice Hall

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Summary

This highly anticipated first edition achieves the difficult balance between coverage and motivation while helping students develop strong problem-solving skills. Blitzer's examples, problems and applications foster both an appreciation and understanding of mathematics encouraging students to take the math a step further into their everyday lives. Blitzer's use of current data and examples drawn from real life are used to develop key mathematical concepts, as well as reduce math anxiety in students.

About the Author

To the Student

To the Instructor

xii

Acknowledgments

xiii

Applications Index

xxi

Problem Solving and Critical Thinking

(30)

Inductive and Deductive Reasoning

(7)

Estimation and Graphs

(8)

Problem Solving

(13)

Summary

(1)

Review Exercises

(2)

Chapter 1 Test

(2)

Set Theory

(42)

Basic Set Concepts

(9)

Venn Diagrams and Subsets

(10)

Venn Diagrams and Set Operations

(5)

Set Operations and Venn Diagrams with Three Sets

(7)

Surveys and Cardinal Numbers

(9)

Summary

(1)

Review Exercises

(1)

Chapter 2 Test

(1)

Logic

(72)

Statements, Negations, and Quantified Statements

(6)

Compound Statements and Connectives

(9)

Truth Tables for Negation, Conjunction, and Disjunction

(12)

Truth Tables for the Conditional and Biconditional

103

(10)

Equivalent Statements, Conditional Statements, and De Morgan's Laws

113

(10)

Arguments and Truth Tables

123

(10)

Arguments and Euler Diagrams

133

(13)

Summary

141

(2)

Review Exercises

143

(1)

Chapter 3 Test

144

(2)

Number Representation and Calculation

146

(30)

Our Hindu-Arabic System and Early Positional Systems

148

(7)

Number Bases in Positional Systems

155

(6)

Computation in Positional Systems

161

(6)

Looking Back at Early Numeration Systems

167

(9)

Summary

172

(1)

Review Exercises

173

(2)

Chapter 4 Test

175

(1)

Number Theory and the Real Number System

176

(66)

Number Theory: Prime and Composite Numbers

178

(9)

The Integers; Order of Operations

187

(10)

The Rational Numbers

197

(9)

The Irrational Numbers

206

(8)

Real Numbers and Their Properties

214

(6)

Exponents and Scientific Notation

220

(9)

Arithmetic and Geometric Sequences

229

(13)

Summary

237

(2)

Review Exercises

239

(2)

Chapter 5 Test

241

(1)

Algebra: Equations and Inequalities

242

(64)

Algebraic Expressions and Formulas

244

(9)

Solving Linear Equations

253

(11)

Applications of Linear Equations

264

(8)

Ratio, Proportion, and Variation

272

(11)

Solving Linear Inequalities

283

(7)

Solving Quadratic Equations

290

(16)

Summary

302

(1)

Review Exercises

303

(2)

Chapter 6 Test

305

(1)

Algebra: Graphs, Functions, and Linear Systems

306

(64)

Graphing and Functions

308

(11)

Linear Functions and Their Graphs

319

(8)

Quadratic Functions and Their Graphs

327

(10)

Exponential Functions

337

(5)

Systems of Linear Equations

342

(13)

Linear Inequalities in Two Variables

355

(5)

Linear Programming

360

(10)

Summary

366

(1)

Review Exercises

367

(2)

Chapter 7 Test

369

(1)

Consumer Mathematics and Financial Management

370

(54)

Percent

372

(9)

Interest

381

(9)

Installment Buying

390

(11)

The Cost of Home Ownership

401

(8)

Investing in Stocks, Bonds, and Mutual Funds

409

(15)

Summary

419

(1)

Review Exercises

420

(3)

Chapter 8 Test

423

(1)

Measurement

424

(28)

Measuring Length; The Metric System

426

(9)

Measuring Area and Volume

435

(8)

Measuring Weight and Temperature

443

(9)

Summary

449

(1)

Review Exercises

450

(1)

Chapter 9 Test

451

(1)

Geometry

452

(70)

Points, Lines, Planes, and Angles

454

(8)

Triangles

462

(9)

Polygons, Quadrilaterals, and Perimeter

471

(6)

Area and Circumference

477

(9)

Volume

486

(7)

Right Triangle Trigonometry

493

(11)

Beyond Euclidean Geometry

504

(18)

Summary

514

(1)

Review Exercises

515

(5)

Chapter 10 Test

520

(2)

Counting Methods and Probability Theory

522

(68)

The Fundamental Counting Principle

524

(6)

Permutations

530

(7)

Combinations

537

(6)

Fundamentals of Probability

543

(8)

Probability with the Fundamental Counting Principle, Permutations, and Combinations

551

(6)

Events Involving Not and Or; Odds

557

(11)

Events Involving And; Conditional Probability

568

(9)

Expected Value

577

(13)

Summary

584

(1)

Review Exercises

585

(4)

Chapter 11 Test

589

(1)

Statistics

590

(72)

Sampling, Frequency Distributions, and Graphs

592

(13)

Measures of Central Tendency

605

(13)

Measures of Dispersion

618

(8)

The Normal Distribution

626

(16)

Scatter Plots, Correlation, and Regression Lines

642

(20)

Summary

655

(1)

Review Exercises

656

(4)

Chapter 12 Test

660

(2)

Mathematical Systems

662

(23)

Mathematical Systems

664

(9)

Rotational Symmetry, Groups, and Clock Arithmetic

673

(12)

Summary

683

(1)

Review Exercises

683

(2)

Chapter 13 Test

685

Answers to Selected Exercises

AA1

Subject Index

I-1

Photo Credits

P-1

Thinking Mathematically

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