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Copyright, iv
Preface, xiii
Acknowledgements, xviii
Part I. Management Science, 1
Chapter 1. Urban Services, 3
1.1. Euler Circuits, 3
1.2. Finding Euler Circuits, 6
SPOTLIGHT 1.1: Leonhard Euler, 7
SPOTLIGHT 1.2: The Human Aspect of Problem Solving, 8
1.3. Beyond Euler Circuits, 11
1.4. Urban Graph Traversal Problems, 16
SPOTLIGHT 1.3: Israel Electric Company Reduces Meter-Reading Task, 17
Review Vocabulary, 19
Skills Check, 20
Exercises, 22
Applet Exercises, 29
Writing Projects, 29
Suggested Readings, 29
Suggested Web Sites, 29
Chapter 2. Business Efficiency, 31
2.1. Hamiltonian Circuits, 32
2.2. Traveling Salesman Problem, 38
2.3. Helping Traveling Salesmen, 39
SPOTLIGHT 2.1: NP-Complete Problems, 41
2.4. Minimum-Cost Spanning Trees, 42
SPOTLIGHT 2.2: AT&T Manager Explains How Long-Distance Calls Run Smoothly, 46
2.5. Critical-Path Analysis, 46
SPOTLIGHT 2.3: Common Ancestors?, 47
SPOTLIGHT 2.4: Every Moment Counts in Rigorous Airline Scheduling, 51
Review Vocabulary, 52
Skills Check, 53
Exercises, 54
Applet Exercises, 64
Writing Projects, 65
Suggested Readings, 65
Suggested Web Sites, 66
Chapter 3. Planning and Scheduling, 67
3.1. Scheduling Tasks, 67
3.2. Critical-Path Schedules, 74
SPOTLIGHT 3.1: Management Science and Disaster Recovery, 75
3.3. Independent Tasks, 78
3.4. Bin Packing, 80
SPOTLIGHT 3.2: Using Mathematical Tools, 83
3.5. Resolving Conflict via Coloring, 84
SPOTLIGHT 3.3: Four Color Problem, 87
SPOTLIGHT 3.4: Scheduling Job Interviews, 88
Review Vocabulary, 88
Skills Check, 89
Exercises, 91
Applet Exercises, 100
Writing Projects, 101
Suggested Readings, 101
Suggested Web Sites, 101
Chapter 4. Linear Programming, 103
SPOTLIGHT 4.1: Case Studies in Linear Programming, 105
4.1. Mixture Problems: Combining Resources to Maximize Profit, 105
4.2. Finding the Optimal Production Policy, 111
4.3. Why the Corner Point Principle Works, 118
4.4. Linear Programming: Life Is Complicated, 121
SPOTLIGHT 4.2: Father of Linear Programming Recalls Its Origins, 123
SPOTLIGHT 4.3: Finding Fast Algorithms Means Better Airline Service, 125
4.5. A Transportation Problem: Delivering Perishables, 125
4.6. Improving on the Current Solution, 134
Review Vocabulary, 136
Skills Check, 137
Exercises, 139
Writing Projects, 145
Suggested Readings, 145
Suggested Web Sites, 146
Part II. Statistics: The Science of Data, 147
Chapter 5. Exploring Data: Distributions, 149
5.1. Displaying Distributions: Histograms, 151
5.2. Interpreting Histograms, 153
5.3. Displaying Distributions: Stemplots, 156
5.4. Describing Center: Mean and Median, 157
SPOTLIGHT 5.1: Think!, 160
5.5. Describing Spread: The Quartiles, 161
5.6. The Five-Number Summary and Boxplots, 162
5.7. Describing Spread: The Standard Deviation, 163
SPOTLIGHT 5.2: Calculating Standard Deviation, 165
5.8. Normal Distributions, 166
SPOTLIGHT 5.3: Density Estimation, 171
5.9. The 68—95—99.7 Rule, 171
Review Vocabulary, 173
Skills Check, 174
Exercises, 175
Applet Exercises, 182
Writing Projects, 183
Suggested Readings, 183
Suggested Web Sites, 183
Chapter 6. Exploring Data: Relationships, 185
6.1. Displaying Relationships: Scatterplot, 186
6.2. Making Predictions: Regression Line, 189
6.3. Correlation, 191
SPOTLIGHT 6.1: Scatterplot Smoothers: Crashtest Dummies, 191
SPOTLIGHT 6.2: Calculating Correlation, 193
6.4. Least-Squares Regression, 194
SPOTLIGHT 6.3: Regression in Action, 194
6.5. Interpreting Correlation and Regression, 196
Review Vocabulary, 200
Skills Check, 200
Exercises, 202
Applet Exercises, 208
Writing Projects, 209
Suggested Readings, 209
Suggested Web Sites, 209
Chapter 7. Data for Decisions, 211
7.1. Sampling, 211
7.2. Bad Sampling Methods, 213
7.3. Simple Random Samples, 214
SPOTLIGHT 7.1: Is It Really Random?, 217
7.4. Cautions About Sample Surveys, 218
7.5. Experiments, 220
7.6. Experiments Versus Observational Studies, 223
7.7. Inference: From Sample to Population, 225
7.8. Confidence Intervals, 229
SPOTLIGHT 7.2: Truth in Polling, 234
Review Vocabulary, 234
Skills Check, 235
Exercises, 237
Applet Exercises, 243
Writing Projects, 244
Suggested Readings, 244
Suggested Web Sites, 244
Chapter 8. Probability: The Mathematics of Chance, 247
8.1. Probability Models and Rules, 248
SPOTLIGHT 8.1: Probability and Psychology, 254
8.2. Discrete Probability Models, 255
8.3. Equally Likely Outcomes, 256
SPOTLIGHT 8.2: Combinatorics Calculations, 261
8.4. Continuous Probability Models, 261
8.5. The Mean and Standard Deviation of a Probability Model, 264
SPOTLIGHT 8.3: Birthday Coincidences, 267
8.6. The Central Limit Theorem, 267
Review Vocabulary, 273
Skills Check, 274
Exercises, 275
Applet Exercises, 281
Writing Projects, 281
Suggested Readings, 282
Suggested Web Sites, 282
Part III. Voting and Social Choice, 283
Chapter 9. Social Choice: The Impossible Dream, 285
9.1. Majority Rule and Condorcet’s Method, 286
9.2. Other Voting Systems for Three or More Candidates, 289
SPOTLIGHT 9.1: The Historical Record, 290
9.3. Insurmountable Difficulties: Arrow’s Impossibility Theorem, 301
SPOTLIGHT 9.2: Kenneth J. Arrow, 303
9.4. A Better Approach? Approval Voting, 305
Review Vocabulary, 306
Skills Check, 307
Exercises, 308
Writing Projects, 312
Suggested Readings, 312
Chapter 10. The Manipulability of Voting Systems, 313
10.1. Majority Rule and Condorcet’s Method, 316
10.2. The Manipulability of Other Voting Systems for Three or More Candidates, 318
10.3. Impossibility, 323
10.4. The Chair’s Paradox, 325
Review Vocabulary, 327
Skills Check, 327
Exercises, 328
Writing Projects, 331
Suggested Readings, 331
Chapter 11. Weighted Voting Systems, 333
11.1. How Weighted Voting Works, 334
SPOTLIGHT 11.1: The Electoral College, 335
SPOTLIGHT 11.2: Power Indices, 336
11.2. The Shapley-Shubik Power Index, 336
SPOTLIGHT 11.3: Battleground States, 339
11.3. The Banzhaf Power Index, 344
SPOTLIGHT 11.4: A Mathematical Quagmire, 345
11.4. Comparing Voting Systems, 355
SPOTLIGHT 11.5: The Electoral College: Presidential Elections of 2004 and 2008, 356
Review Vocabulary, 361
Skills Check, 362
Exercises, 362
Writing Projects, 366
SPOTLIGHT 11.6: What Are Your Chances of Being a Critical Voter, 367
Suggested Readings, 367
Chapter 12. Electing the President, 369
12.1. Spatial Models for Two-Candidate Elections, 371
12.2. Spatial Models for Multicandidate Elections, 379
12.3. Narrowing the Field, 383
12.4. What Drives Candidates Out?, 384
12.5. Election Reform: Approval Voting, 386
12.6. The Electoral College, 389
12.7. Is There a Better Way to Elect a President?, 396
Review Vocabulary, 397
Skills Check, 398
Exercises, 400
Writing Projects, 403
Suggested Readings, 404
Suggested Web Sites, 404
Part IV. Fairness and Game Theory, 405
Chapter 13. Fair Division, 407
13.1. The Adjusted Winner Procedure, 408
13.2. The Knaster Inheritance Procedure, 411
13.3. Fair Division and Organ Transplant Policies, 413
13.4. Taking Turns, 415
13.5. Divide-and-Choose, 417
13.6. Cake-Division Procedures: Proportionality, 419
SPOTLIGHT 13.1: Sixty Years of Cake Cutting, 421
13.7. Cake-Division Procedures: The Problem of Envy, 422
Review Vocabulary, 425
Skills Check, 425
Exercises, 427
Writing Projects, 431
Suggested Readings, 432
Chapter 14. Apportionment, 433
14.1. The Apportionment Problem, 433
14.2. The Hamilton Method, 436
14.3. Divisor Methods, 442
14.4. Which Divisor Method Is Best?, 449
SPOTLIGHT 14.1: A Legal Challenge to Apportionment, 450
SPOTLIGHT 14.2: Mathematics and Politics: A Strange Mixture, 456
Review Vocabulary, 457
Skills Check, 458
Exercises, 459
Applet Exercises, 464
Writing Projects, 464
Suggested Readings, 465
Suggested Web Sites, 465
Chapter 15. Game Theory: The Mathematics of Competition, 467
SPOTLIGHT 15.1: The Early History of Game Theory, 468
15.1. Two-Person Total-Conflict Games: Pure Strategies, 469
15.2. Two-Person Total-Conflict Games: Mixed Strategies, 474
15.3. Partial-Conflict Games, 482
SPOTLIGHT 15.2: The Nobel Prize in Economics, 487
15.4. Larger Games, 488
15.5. Using Game Theory, 495
Review Vocabulary, 499
Skills Check, 500
Exercises, 502
Applet Exercises, 505
Writing Projects, 505
Suggested Readings, 506
Suggested Web Sites, 506
Part V. The Digital Revolution, 507
Chapter 16. Identification Numbers, 509
16.1. Check Digits, 509
SPOTLIGHT 16.1: The VIN System, 515
16.2. The ZIP Code, 515
16.3. Bar Codes, 517
SPOTLIGHT 16.2: New Frontier: Bar Coding DNA, 522
SPOTLIGHT 16.3: History of the Bar Code, 522
16.4. Encoding Personal Data, 523
SPOTLIGHT 16.4: Social Security Numbers, 523
Review Vocabulary, 525
Skills Check, 526
Exercises, 527
Writing Projects, 530
Suggested Readings, 531
Suggested Web Sites, 531
Chapter 17. Information Science, 533
17.1. Binary Codes, 533
SPOTLIGHT 17.1: The Ubiquitous Reed–Solomon Codes, 535
SPOTLIGHT 17.2: Vera Pless, 536
17.2. Encoding with Parity-Check Sums, 536
SPOTLIGHT 17.3: Neil Sloane, 538
SPOTLIGHT 17.4: Morse Code, 541
SPOTLIGHT 17.5: David Huffman, 544
17.3. Cryptography, 546
SPOTLIGHT 17.6: Modeling the Genetic Code, 548
17.4. Web Searches and Mathematical Logic, 553
SPOTLIGHT 17.7: Six Degrees of Kevin Bacon, 554
Review Vocabulary, 562
Skills Check, 563
Exercises, 564
Writing Projects, 567
Suggested Readings, 567
Suggested Web Sites, 567
Part VI. On Size and Growth, 569
Chapter 18. Growth and Form, 571
18.1. Geometric Similarity, 572
18.2. How Much Is That in… ?, 575
18.3. Scaling a Mountain, 579
SPOTLIGHT 18.1: A Mile-High Building?, 581
18.4. Sorry, No King Kongs, 583
SPOTLIGHT 18.2: Galileo and the Problem of Scale, 585
18.5. Dimension Tension, 585
SPOTLIGHT 18.3: Scaled to Fit, 588
18.6. How to Grow, 592
SPOTLIGHT 18.4: Helping to Find Missing Children, 593
Review Vocabulary, 596
Skills Check, 597
Exercises, 598
Writing Projects, 604
Suggested Readings, 606
Suggested Web Sites, 607
Chapter 19. Symmetry and Patterns, 609
19.1. Fibonacci Numbers and the Golden Ratio, 610
SPOTLIGHT 19.1: Leonardo of Pisa (“Fibonacci”), 611
SPOTLIGHT 19.2: How the Greeks Constructed a Golden Rectangle, 612
SPOTLIGHT 19.3: The Consumer Price Index: An Application of the Geometric Mean, 614
19.2. Rosette, Strip, and Wallpaper Patterns, 616
SPOTLIGHT 19.4: “Strive Then to Be Perfect”, 619
SPOTLIGHT 19.5: Patterns Created by the Bakuba People, 621
SPOTLIGHT 19.6: The 17 Wallpaper Patterns, 622
19.3. Notation for Patterns, 624
19.4. Symmetry Groups, 627
19.5. Fractal Patterns and Chaos, 631
SPOTLIGHT 19.7: The Father of Fractals, 635
Review Vocabulary, 635
Skills Check, 636
Exercises, 637
Writing Projects, 645
Suggested Readings, 646
Suggested Web Sites, 646
Chapter 20. Tilings, 647
20.1. Tilings with Regular Polygons, 648
SPOTLIGHT 20.1: Regular Polyhedra and Buckyballs, 649
20.2. Tilings with Irregular Polygons, 652
20.3. Using Translations, 655
SPOTLIGHT 20.2: In Praise of Amateurs, 656
20.4. Using Translations Plus Half-Turns, 659
20.5. Nonperiodic Tilings, 663
SPOTLIGHT 20.3: Sir Roger Penrose, 664
SPOTLIGHT 20.4: Quasicrystals, 669
Review Vocabulary, 670
Skills Check, 670
Exercises, 671
Writing Projects, 676
Suggested Readings, 676
Suggested Web Sites, 676
Part VII. Your Money and Resources, 677
Chapter 21. Savings Models, 679
21.1. Arithmetic Growth and Simple Interest, 679
21.2. Geometric Growth and Compound Interest, 681
SPOTLIGHT 21.1: Thomas Robert Malthus, 688
21.3. A Limit to Compounding, 688
SPOTLIGHT 21.2: The Number e, 689
21.4. A Model for Saving, 690
21.5. Present Value and Inflation, 693
SPOTLIGHT 21.3: Nobel Prize for a Model in Economics, 698
Review Vocabulary, 698
Skills Check, 699
Exercises, 700
Applet Exercises, 707
Writing Projects, 707
Suggested Readings, 708
Suggested Web Sites, 708
Chapter 22. Borrowing Models, 709
22.1. Simple Interest, 709
22.2. Compound Interest, 710
22.3. Conventional Loans, 712
SPOTLIGHT 22.1: What’s the Real Rate?, 713
SPOTLIGHT 22.2: What We Did with Our House, and What Else You Could Do, 719
SPOTLIGHT 22.3: The Mortgage Crisis, 720
22.4. Annuities, 721
SPOTLIGHT 22.4: What Actuaries Do, 723
Review Vocabulary, 723
Skills Check, 724
Exercises, 725
Applet Exercises, 729
Writing Projects, 729
Suggested Readings, 729
Suggested Web Sites, 730
Chapter 23. The Economics of Resources, 731
23.1. Growth Models for Biological Populations, 732
SPOTLIGHT 23.1: 12 Billion by 2050—or Only 9 Billion?, 735
23.2. How Long Can a Nonrenewable Resource Last?, 736
23.3. Sustaining Renewable Resources, 741
23.4. The Economics of Harvesting Resources, 746
SPOTLIGHT 23.2: The Tragedy of Easter Island, 749
23.5. Dynamical Systems and Chaos, 751
Review Vocabulary, 755
Skills Check, 756
Exercises, 757
Writing Projects, 761
Suggested Readings, 761
Suggested Web Sites, 762
Answers to Skills Check Exercises, SC-1
Answers to Odd-Numbered Exercises, A-1
Index, I-1

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