1 SET THEORY: Using Mathematics
to Classify Objects 1
l.l Problem Solving 2
l.2 The Language of Sets 16
1.3 Comparing Sets 23
l.4 Set Operations 30
l.5 Survey Problems 42
Chapter Sununary 51
ChaPterTest 53
Of Further Interest: Fuzzy Sets 55
2 LOGIC: The Study of What'S TFue or False
or Somewhere in Between 62
2.l Statements, Connectives, and Quanhfiers 63
2.2 TruthTables 75
2.3 The Conditional and Biconditional 88
2.4 VerifyingArguments 97
2.5 Using Euler Diagrams to Verify Syllogisms 108
ChaPter Summary 116
ChaPterTest 119
Of Further Interest: Fuzzy Logic I21
3 GRAPH THEORY: The Mathematics
of Relationships 130
3.l Graphs, Puzzles, and Map Coloring 131
3.2 The Traveling Salesperson Problem 152
3.3 Directed Graphs 166
3.4 Scheduling Projects Using PERT 177
Chapter Summary 189
ChapterTest 192
Of Further Interest: Finite State Machines 196
4 LEGISLATIVE APPORTIONMENT: How Do
We Measure Fairness? 202
4.1 Understandin g Apportionment 203
4.2 Inequalities 212
4.3 The Huntington-Hill Apportionment Principle 216
4.4 Apponioning a Representative Board 224
4.5 Other Applicahons of Apponionment 232
Chapter Sununary 239
ChapterTest 240
Of Further Interest: Fair Division 242
5 VOTING: Using Mathematics
to Make Choices 2S3
5.l Voting Methods 254
5.2 Defects in Voting Methods 267
5.3 WeightedVoting Systems 283
Chapter Sununary 293
Chapter Test 295
Of Further Interest: The Shapley-Shubik Index 298
6 CONSUMER MATHEMATlCS: The Mathematic:
of Everyday Life 306
6.1 Interest 307
6.2 ConsumerLoans 321
6.3 Annuities 331
6.4 Amortization 340
Chapter Summary 351
ChapterTest 353
Of Further Interest: The Annual Percentage Rate 355
7 DATA: How Do We Know What Is TFue? 362
7.l Surveys and Survey Biases 363
7.2 Detendning the Accuracy of Surveys 373
Chapter Sununary 388
ChapterTest 389
Of Further Interest: Experiments 391
8 DESCRIPTIVE STATISTICS: What a Data
Set Tells Us
8.l Organizing and Visualizing Data 399
8.2 Measures of Central Tendency 412
8.3 Measures of Dispersion 427
8.4 The Normal Distribution 441
Chapter Sununary 455
Chapter Test 4S7
Of Further Interest: Linear Correlation 459
9 COUNTING: Just How Many Are There?
9.1 Introduction to Counting Methods 468
9.2 The Fundamental Counting Principle 477
9.3 Permutations and Combinations 485
9.4 Pascal's Triangle 495
Chapter Sununary 502
Chapter Test 503
Of Further Interest: Counting and Gambling 504
10 PROBABILITY: What Are the Chances?
l0.l The Basics of Probability Theory 510
l0.2 Complements and Unions of Events 527
10.3 Conditional Probability and Intersechons of Events 535
10.4 ExpectedValue 547
Chapter Surnmary S55
ChapterTest 556
Of Further Interest. Binomial Experiments 558
11 ALGEBRAIC MODELS: How Do we
Approximate Reality?
ll.1 Linear Equations 566
l1.2 Modeling with Linear Equations 579
1l.3 Modeling with Quadratic Equations 590
11.4 Exponential Equations and Growth 599
Chapter Summary 613
Chapter Test 6I4
Of Further Interest: Dynamical Systems 6I6
12 GEOMETRY Ancient and Modern
Mathematics Embrace
12.l Lines, Angles, and Circles 625
l2.2 Polygons 636
l2.3 Perimeter and Area 648
l2.4 Volume and Sdse Area 664
l2.5 Geometric Synunetry and Tessellations 675
Chapter Summary 694
Chapter Test co7
Of Further Interet: Fractals 701
13 MATRICES: Calculating with Tables of
Numerical Information
l3.l Matrix Terminology and Operations 712
13.2 MatrixMultiPlication 722
13.3 Transformational Geometry 732
l3.4 More Transformahons and Homogeneous Coordinates
Chapter Sunnnmp 755
Chapter Test 757
Of Fuhaer Interest. Matrices and Directed Graphs
Answers to QuizYourself 769
Answers to Exercises 779
Index I-1
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