Table of Contents


PART 1--MATHEMATICS IN LIFE 1

1. CRITICAL THINKING, LOGICAL REASONING, AND
PROBLEM SOLVING 2

1.1 Statements and Logical Connectives 5

1.2 Deduction 15

1.3 Categorical Syllogisms 24

1.4 Problem Solving 33

2. NUMBERS AND NUMERACY 54

2.1 Numeration Systems 57

2.2 Mental Math and Estimation 66

2.3 Integers and Rational Numbers 75

2.4 Decimals and Real Numbers 85

2.5 Solving Percent Problems 94

2.6 Integer Exponents 102

2.7 General Exponents 110

3. DESCRIPTIVE STATISTICS--DATA AND PATTERNS 120

3.1 Organizing and Picturing Data 123

3.2 Comparisons 138

3.3 Enhancement, Distraction, and Distortion 152

3.4 Means, Medians, and Percentiles 173

4. INFERENTIAL STATISTICS--DISTRIBUTIONS, SURVEYS,
SAMPLES, AND CONFIDENT PREDICTIONS 186

4.1 Normal Distributions 189

4.2 Samples and Bias 198

4.3 Confidence Intervals and Reliable Estimation 208

4.4 Scatterplots 219

5. PROBABILITY 234

5.1 Computing Probabilities in Simple Experiments 237

5.2 Computing Probabilities in Complex Experiments 249

5.3 Conditional Probability, Independence, and Expected Value 261

6. CONSUMER MATHEMATICS--BUYING AND SAVING 276

6.1 Interest 279

6.2 Loans 287

6.3 Amortized Loans 294

6.4 Buying a House 301

6.5 Annuities and Sinking Funds 308

PART 2--MATHEMATICS IN SOCIETY 319

7. GAME THEORY 320

7.1 The Description of a Game 323

7.2 Determined Games 337

7.3 Mixed Strategies 349

8. MANAGEMENT MATHEMATICS 360

8.1 Linear Constraints 363

8.2 Linear Programming 375

8.3 Routing Problems 386

8.4 Network Problems 403

9. VOTING AND APPORTIONMENT 420

9.1 Voting Systems 423

9.2 Flaws of Voting Systems 434

9.3 Apportionment Methods 447

9.4 Flaws of Apportionment Methods 456

PART 3--MATHEMATICS IN THE WORLD 469

10. GEOMETRY 470

10.1 Tilings 473

10.2 Symmetry, Motions, and Escher Patterns 490

10.3 Conic Sections: Parabolas 507

10.4 Conic Sections: Ellipses and Hyperbolas 518

11. GROWTH AND SCALING 536

11.1 Scaling of Length and Area 539

11.2 Similarity and Scaling 553

11.3 Applications to Population Growth and Radioactive Decay 560

11.4 Scaling Physical Objects 573

12. RECURSION AND FRACTALS 586

12.1 Fibonacci Numbers, the Golden Ratio, and Recursion 589

12.2 Geometric Recursion 601

12.3 Fractals 613

REVIEW TOPICS 626

1. Sets 626

2. Calculators 633

3. The Metric System 637

4. Systems of Linear Equations 646

5. Perimeter and Area 652

6. Surface Area and Volume 660

APPENDIXES 672

A Random Digits 672

B Amortization Tables 672

ANSWERS TO ODD-NUMBERED PROBLEMS A1

PHOTOGRAPH CREDITS A64

INDEX I1


 
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