TO THE INSTRUCTOR xiii
TO THE STUDENT xix
1 FUNDAMENTALS OF PROBLEM SOLVING 2
1.1 Introduction 4
1.2 Problem-Solving Tools 4
1.3 Understanding Symbols and Context 8
1.4 Decisions and Pattern Recognition 12
1.5 Inductive Reasoning 23
1.6 Problem-Solving Strategies 30
Summary 37
Vocabulary Check 37
Review Exercises for Chapter 1 37
Chapter Quiz 39
2 SETS 40
2.1 Introduction 42
2.2 Notation and Description 42
2.3 Subsets 47
2.4 Set Operations 51
2.5 Pictures of Sets (Venn Diagrams) 55
2.6 An Application of Sets and Venn Diagrams 67
2.7 Cartesian Products 74
Summary 78
Vocabulary Check 79
Review Exercises for Chapter 2 79
Chapter Quiz 80
3 LOGIC 82
3.1 Introduction 84
3.2 Statements and Symbols 84
3.3 Dominance of Connectives 93
3.4 Truth Tables 97
3.5 More Truth Tables--Conditional and Biconditional Statements 101
3.6 De Morgan's Law and Equivalent Statements 108
3.7 The Conditional (Optional) 111
3.8 Valid Arguments 118
3.9 Picturing Statements with Venn Diagrams (Optional) 124
3.10 Valid Arguments with Venn Diagrams (Optional) 131
3.11 Switching Networks (Optional) 136
Summary 145
Vocabulary Check 146
Review Exercises for Chapter 3 146
Chapter Quiz 148
4 PROBABILITY 150
4.1 Introduction 152
4.2 Definition of Probability 152
4.3 Sample Spaces 157
4.4 Tree Diagrams 163
4.5 Odds and Expectation 167
4.6 Compound Probability 174
4.7 Counting, Ordered Arrangements, and Permutations (Optional) 182
4.8 Combinations (Optional) 190
4.9 More Probability (Optional) 194
Summary 198
Vocabulary Check 199
Review Exercises for Chapter 4 199
Chapter Quiz 202
5 STATISTICS 204
5.1 Introduction 206
5.2 Measures of Central Tendency 206
5.3 Measures of Dispersion 218
5.4 Measures of Position (Percentiles) 225
5.5 Pictures of Data 231
5.6 The Normal Curve 244
Summary 255
Vocabulary Check 256
Review Exercises for Chapter 5 256
Chapter Quiz 259
6 MATHEMATICAL SYSTEMS 260
6.1 Introduction 262
6.2 Clock Arithmetic 262
6.3 More New Systems 272
6.4 Modular Systems 276
6.5 Mathematical Systems Without Numbers 284
6.6 Axiomatic Systems 289
Summary 295
Vocabulary Check 295
Review Exercises for Chapter 6 295
Chapter Quiz 297
7 SYSTEMS OF NUMERATION 300
7.1 Introduction 302
7.2 Simple Grouping Systems 303
7.3 Multiplicative Grouping Systems 307
7.4 Place-Value Systems 311
7.5 Numeration in Bases Other Than 10 316
7.6 Base 5 Arithmetic 324
7.7 Binary Notation and Other Bases 333
Summary 341
Vocabulary Check 342
Review Exercises for Chapter 7 342
Chapter Quiz 344
8 SETS OF NUMBERS
AND THEIR STRUCTURE 346
8.1 Introduction 348
8.2 Natural Numbers--Primes and Composites 348
8.3 Greatest Common Divisor and Least Common
Multiple 355
8.4 Integers 362
8.5 Rational Numbers 372
8.6 Rational Numbers and Decimals 380
8.7 Irrational Numbers and the Set of Real Numbers 387
8.8 Scientific Notation (Optional) 391
Summary 396
Vocabulary Check 397
Review Exercises for Chapter 8 397
Chapter Quiz 399
9 AN INTRODUCTION
TO ALGEBRA 400
9.1 Introduction 402
9.2 Open Sentences and Their Graphs 402
9.3 Algebraic Notation 406
9.4 More Open Sentences 409
9.5 Problem Solving 413
9.6 Linear Equations in Two Variables 424
9.7 Graphing Equations 428
9.8 Inequalities in Two Variables 437
Summary 443
Vocabulary Check 444
Review Exercises for Chapter 9 445
Chapter Quiz 446
10 SELECTED TOPICS
IN ALGEBRA 448
10.1 Introduction 450
10.2 The Slope of a Line 450
10.3 The Equation of a Straight Line 457
10.4 Graphing y = ax2 + bx + c 467
10.5 Linear Programming 472
10.6 Quadratic Equations 479
Summary 484
Vocabulary Check 485
Review Exercises for Chapter 10 485
Chapter Quiz 486
11 AN INTRODUCTION
TO GEOMETRY 488
11.1 Introduction 490
11.2 Points and Lines 490
11.3 Planes 495
11.4 Angles 500
11.5 Polygons 509
11.6 Perimeter and Area 520
11.7 Solids 530
11.8 Congruent and Similar Triangles 538
11.9 Networks 543
Summary 547
Vocabulary Check 548
Review Exercises for Chapter 11 548
Chapter Quiz 550
12 CONSUMER MATHEMATICS 552
12.1 Introduction 554
12.2 Ratio and Proportion 554
12.3 Percents, Decimals, and Fractions 560
12.4 Markups and Markdowns 565
12.5 Simple Interest 573
12.6 Compound Interest 578
12.7 Effective Rate of Interest 584
12.8 Life Insurance 587
12.9 Installment Buying 592
12.10 Mortgages 599
Summary 603
Vocabulary Check 604
Review Exercises for Chapter 12 604
Chapter Quiz 606
13 AN INTRODUCTION
TO THE METRIC SYSTEM 608
13.1 Introduction 610
13.2 History of Systems of Measurements 613
13.3 Length and Area 617
13.4 Volume 624
13.5 Mass (Weight) 631
13.6 Temperature 635
Summary 641
Vocabulary Check 642
Review Exercises for Chapter 13 642
Chapter Quiz 644
GLOSSARY 677
APPENDIX A 647
A.1 Introduction to Computers 648
A.2 History of Computers 649
A.3 How a Computer System Works 656
A.4 Using BASIC 662
A.5 More BASIC Statements 669
APPENDIX B
Table 1 Factorials 675
Table 2 Squares, Square Roots, and Prime Factors (1100) 676
ANSWERS TO ODD-NUMBERED
EXERCISES, ALL REVIEW
EXERCISES, AND CHAPTER QUIZZES 685
INDEX 737
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