Front Matter

Prefacexv
Part I MANAGEMENT SCIENCE / 2
Chapter 1Urban Services5
1.1 Euler Circuits 6
- SPOTLIGHT 1.1
  Leonhard Euler 9
- SPOTLIGHT 1.2
  The Human Aspect of Problem Solving 10
1.2 Finding Euler Circuits 10
1.3 Beyond Euler Circuits 14
1.4 Urban Graph Traversal Problems 20
- SPOTLIGHT 1.3
  Israel Electric Company Reduces Meter-Reading Task 21
- Review Vocabulary 23
- Self Check Answers 23
- Skills Check 23
- Chapter Exercises 27
- Applet Exercises 37
- Writing Projects 37
- Suggested Readings 38
- Suggested Websites 38
Chapter 2Business efficiency39
2.1 Hamiltonian Circuits 40
2.2 Traveling Salesman Problem 47
2.3 Helping Traveling Salesmen 48
- SPOTLIGHT 2.1
  NP-Complete Problems 51
2.4 Minimum-Cost Spanning Trees 52
- SPOTLIGHT 2.2
  AT&T Manager Explains How Long-Distance Calls Run Smoothly 56
- SPOTLIGHT 2.3
  Common Ancestors? 57
2.5 Critical-Path Analysis 58
- SPOTLIGHT 2.4
  Every Moment Counts in Rigorous Airline Scheduling 61
- Review Vocabulary 62
- Self Check Answers 63
- Skills Check 63
- Chapter Exercises 66
- Applet Exercises 79
- Writing Projects 79
- Suggested Readings 79
- Suggested Websites 80
Chapter 3Planning and Scheduling81
3.1 Scheduling Tasks 82
3.2 Critical-Path Schedules 89
- SPOTLIGHT 3.1
  Management Science and Disaster Recovery 90
3.3 Independent Tasks 93
3.4 Bin Packing 96
- SPOTLIGHT 3.2
  Using Mathematical Tools 99
3.5 Resolving Conflict via Coloring 100
- SPOTLIGHT 3.3
  Scheduling Job Interviews 103
- SPOTLIGHT 3.4
  Four Color Problem 104
- Review Vocabulary 105
- Self Check Answers 106
  
  vii
- Skills Check 106
- Chapter Exercises 109
- Applet Exercises 122
- Writing Projects 123
- Suggested Readings 123
- Suggested Websites 124
Chapter 4Linear Programming and the Transportation Problem125
4.1 Linear Programming and Mixture Problems: Combining Resources to Maximize Profit 126
- SPOTLIGHT 4.1
  Case Studies in Linear Programming 128
4.2 Finding the Optimal Production Policy 134
4.3 Why the Corner Point Principle Works 141
4.4 Linear Programming: Life Is Complicated 144
- SPOTLIGHT 4.2
  The Father of Linear Programming Recalls Its Origins 146
- SPOTLIGHT 4.3
  Finding Fast Algorithms Means Better Airline Service 147
4.5 A Transportation Problem: Delivering Perishables 148
4.6 Improving on the Current Solution 157
- Review Vocabulary 160
- Self Check Answers 161
- Skills Check 161
- Chapter Exercises 164
- Writing Projects 172
- Suggested Readings 173
- Suggested Websites 173
- CASE STUDY
  Improving Medical Care Using Mathematics 174
Part II STATISTICS: THE SGIENGE GF DATA / 178
Chapter 5Exploring Data:
Distributions181
5.1 Displaying Distributions: Histograms 182
- SPOTLIGHT 5.1
  John Wilder Tukey, Champion of Exploratory Data Analysis 184
5.2 Interpreting Histograms 188
5.3 Displaying Distributions: Stemplots 194
5.4 Describing Center: Mean and Median 196
- SPOTLIGHT 5.2
  Which Mean Do You Mean? 199
5.5 Describing Variability: Range and Quartiles 200
5.6 The Five-Number Summary and Boxplots 201
5.7 Describing Variability: The Standard Deviation 203
- SPOTLIGHT 5.3
  Using Technology to Calculate Standard Deviation 206
5.8 Normal Distributions 209
- SPOTLIGHT 5.4
  Density Estimation 215
5.9 The 68-95-99.7 Rule for Normal Distributions 216
- Review Vocabulary 219
- Self Check Answers 220
- Skills Check 221
- Chapter Exercises 223
- Applet Exercises 239
- Writing Projects 239
- Suggested Readings 240
- Suggested Websites 240
viii
Chapter 6Exploring Data:
Relationships241
6.1 Displaying Relationships: Scatterplot 242
- SPOTLIGHT 6.1
  Creating Scatterplots Using Technology 249
6.2 Making Predictions: Regression Line 251
6.3 Correlation 254
- SPOTLIGHT 6.2
  Correlation Calculation 259
- SPOTLIGHT 6.3
  Regression Toward the Mean 260
6.4 Least-Squares Regression 260
- SPOTLIGHT 6.4
  Regression and Correlation in Action: College Success 265
- SPOTLIGHT 6.5
  Calculating the Equation of the Least-Squares Regression Line 265
6.5 Interpreting Correlation and Regression 268
- Review Vocabulary 274
- Self Check Answers 274
- Skills Check 275
- Chapter Exercises 277
- Applet Exercises 288
- Writing Projects 289
- Suggested Readings 290
- Suggested Websites 290
Chapter 7Data for Decisions291
7.1 Sampling 292
7.2 Bad Sampling Methods 294
7.3 Simple Random Samples 297
- SPOTLIGHT 7.1
  Using Technology to Select an SRS 300
7.4 Cautions About Sample Surveys 302
- SPOTLIGHT 7.2
  Pew Research Center 303
7.5 Experiments 305
- SPOTLIGHT 7.3
  Ethics in Experiments 309
7.6 Experiments Versus Observational Studies 309
7.7 Inference: From Sample to Population 314
- SPOTLIGHT 7.4
  Truth in Polling 324
- Review Vocabulary 324
- Self Check Answers 326
- Skills Check 327
- Chapter Exercises 328
- Applet Exercises 338
- Writing Projects 339
- Suggested Readings 340
- Suggested Websites 340
Chapter 8Probability: The
Mathematics of chance341
8.1 Random Phenomena and Probability 343
- SPOTLIGHT 8.1
  The Problem of Points 345
8.2 Basic Rules of Probability 348
- SPOTLIGHT 8.2
  Probability and Psychology 349
8.3 Rules of Probability: Independent and Dependent Events 354
8.4 Discrete Probability Models 360
8.5 Equally Likely Outcomes 363
- SPOTLIGHT 8.3
  Using Technology to Compute Permutations, Factorials, and Combinations 369
- SPOTLIGHT 8.4
  Birthday Coincidences 370
8.6 Continuous Probability Models 371
8.7 The Mean and Standard Deviation of a Probability Model 375
8.8 The Central Limit Theorem 380
- Review Vocabulary 385
- Self Check Answers 386
- Skills Check 387
- Chapter Exercises 389
- Applet Exercises 399
- Writing Projects 400
- Suggested Readings 400
- Suggested Websites 400
ix
Part III VOTING AND SOCIAL CHOICE / 402
Chapter 9Social Choice:
The Impossible Dream405
9.1 An Introduction to Social Choice 406
9.2 Majority Rule and Condorcet’s Method 407
- SPOTLIGHT 9.1
  The Historical Record 409
9.3 Other Voting Systems for Three or More Candidates 412
9.4 Insurmountable Difficulties: Arrow’s Impossibility Theorem 424
- SPOTLIGHT 9.2
  Kenneth J. Arrow 425
9.5 A Better Approach? Approval Voting 428
- Review Vocabulary 430
- Self Check Answers 431
- Skills Check 431
- Chapter Exercises 433
- Writing Projects 438
- Suggested Readings 438
Chapter 10The Manipulability
of Voting Systems439
10.1 An Introduction to Manipulability 440
10.2 Majority Rule and Condorcet’s Method 443
10.3 The Manipulability of Other Voting Systems for Three or More Candidates 445
10.4 Impossibility 450
10.5 The Chair’s Paradox 452
- Review Vocabulary 454
- Self Check Answers 454
- Skills Check 455
- Chapter Exercises 456
- Writing Projects 459
- Suggested Readings 460
Chapter 11Weighted Voting
Systems461
11.1 How Weighted Voting Works 462
- SPOTLIGHT 11.1
  The Electoral College 465
11.2 The Shapley-Shubik Model 466
- SPOTLIGHT 11.2
  Power Indices 466
11.3 The Banzhaf Model 474
- SPOTLIGHT 11.3
  Should Blocking Coalitions Be Counted? 476
- SPOTLIGHT 11.4
  A Real Mathematical Quagmire 480
- SPOTLIGHT 11.5
  The Electoral College: Presidential Elections of 2012, 2016, and 2020 484
- SPOTLIGHT 11.6
  Can the Banzhaf and Shapley-Shubik Models Disagree? 487
11.4 Voting Systems—Without Weights 487
- Review Vocabulary 492
- Self Check Answers 493
- Skills Check 494
- Chapter Exercises 496
- Writing Projects 501
- Suggested Readings 501
- Suggested Websites 502
Chapter 12Electing the President503
12.1 Narrowing the Field through the Primary Process 504
12.2 Spatial Models for Two-Candidate Elections: Discrete Distributions 508
12.3 Spatial Models for Two-Candidate Elections: Continuous Distributions 515
12.4 Spatial Models for Multicandidate Elections 518
x

12.5 Spatial Models and the Electoral College 524
- Review Vocabulary 527
- Self Check Answers 528
- Skills Check 529
- Chapter Exercises 530
- Writing Projects 535
- Suggested Readings 535
- Suggested Websites 535
Part IV FAIRNESS AND GAME THEORY / 536
Chapter 13Fair Division539
13.1 The Adjusted Winner Procedure 540
13.2 The Knaster Inheritance Procedure 544
13.3 Fair Division and Organ Transplant Policies 546
13.4 Taking Turns 548
13.5 Divide-and-Choose 551
13.6 Cake-Division Procedures: Proportionality 552
- SPOTLIGHT 13.1
  Seventy Years of Cake Cutting 553
13.7 Cake-Division Procedures: The Problem of Envy 555
13.8 Vickrey Auctions 558
- Review Vocabulary 560
- Self Check Answers 561
- Skills Check 561
- Chapter Exercises 563
- Writing Projects 570
- Suggested Readings 570
Chapter 14Apportionment571
14.1 The Apportionment Problem 572
14.2 The Hamilton Method 578
- SPOTLIGHT 14.1
  Apportionment in the U.S. House of Representatives Before 1900 580
14.3 Divisor Methods 585
- SPOTLIGHT 14.2
  A Puzzling Apportionment of the U.S. House of Representatives 597
14.4 Which Divisor Method Is Best? 598
- SPOTLIGHT 14.3
  Legal Challenges to Apportionment 599
- SPOTLIGHT 14.4
  Mathematics and Politics: A Strange Mixture 607
- Review Vocabulary 608
- Self Check Answers 609
- Skills Check 611
- Chapter Exercises 613
- Writing Projects 619
- Suggested Readings 620
- Suggested Websites 620
Chapter 15Game Theory: The
Mathematics of
competition621
- SPOTLIGHT 15.1
  The Early History of Game Theory 622
15.1 Two-Person Total-Conflict Games: Pure Strategies 623
15.2 Two-Person Total-Conflict Games: Mixed Strategies 628
15.3 Partial-Conflict Games 637
15.4 Mechanism Design and Larger Games 643
- SPOTLIGHT 15.2
  The Nobel Prize in Economics 646
xi
15.5 Using Game Theory 651
- Review Vocabulary 654
- Self Check Answers 655
- Skills Check 656
- Chapter Exercises 659
- Applet Exercise 663
- Writing Projects 664
- Suggested Readings 664
- Suggested Websites 665
Part V THE DIGITAL REVOLUTION / 666
Chapter 16Identification Numbers669
16.1 Check Digits 669
- SPOTLIGHT 16.1
  The VIN System 678
16.2 The ZIP Code 679
16.3 Bar Codes 680
- SPOTLIGHT 16.2
  New Frontier: Bar Coding DNA 686
- SPOTLIGHT 16.3
  History of Bar Codes 687
16.4 Encoding Personal Data 687
- SPOTLIGHT 16.4
  Ten Fun Facts about Social Security Numbers 688
- SPOTLIGHT 16.5
  Census Records at the National Archives 690
- Review Vocabulary 691
- Self Check Answers 691
- Skills Check 691
- Chapter Exercises 693
- Writing Projects 697
- Suggested Readings 697
- Suggested Website 698
Chapter 17Encoding Information699
17.1 Binary Codes 699
- SPOTLIGHT 17.1
  The Ubiquitous Reed-Solomon Codes 701
17.2 Encoding with Parity-Check Sums 702
- SPOTLIGHT 17.2
  Neil Sloane 703
17.3 Data Compression 707
- SPOTLIGHT 17.3
  Morse Code 708
- SPOTLIGHT 17.4
  David Huffman 711
17.4 Cryptography 714
- SPOTLIGHT 17.5
  Modeling the Genetic Code 716
- SPOTLIGHT 17.6
  Enigma Machines 724
- SPOTLIGHT 17.7
  Mavis Batey 725
- SPOTLIGHT 17.8
  Alan Turing 726
- SPOTLIGHT 17.9
  Smart Cards 727
- Review Vocabulary 728
- Self Check Answers 728
- Skills Check 729
- Chapter Exercises 730
- Suggested Websites and Videos 733
xii
Part VI ON SIZE AND GROWTH / 734
Chapter 18Growth and Form737
18.1 Geometric Similarity 738
18.2 How Much Is That in ? 743
18.3 Big Stuff 747
- SPOTLIGHT 18.1
  A Mile-High Building? 749
- SPOTLIGHT 18.2
  Why Would You Want to Be Big? 753
18.4 Dimension Tension 754
- SPOTLIGHT 18.3
  Scaled to Fit 757
18.5 How We Grow 760
- SPOTLIGHT 18.4
  Helping to Find Missing Children 761
- Review Vocabulary 765
- Self-Check Answers 765
- Skills Check 765
- Chapter Exercises 767
- Writing Projects 775
- Suggested Readings 778
- Suggested Websites 778
Chapter 19Symmetry and Pattern779
19.1 Fibonacci Numbers and the Golden Ratio 780
- SPOTLIGHT 19.1
  Leonardo of Pisa (“Fibonacci”) 781
- SPOTLIGHT 19.2
  Fibonacci Solar Power 782
- SPOTLIGHT 19.3
  Drumming Up Mathematics 783
- SPOTLIGHT 19.4
  How the Greeks Constructed a Golden Rectangle 784
- SPOTLIGHT 19.5
  The Consumer Price Index: An Application of the Geometric Mean 785
- SPOTLIGHT 19.6
  Are We Trying to Reclaim the “Glory That Was Greece"? 788
19.2 Rosette and Strip Patterns 790
- SPOTLIGHT 19.7
  “Strive Then to Be Perfect” 793
- SPOTLIGHT 19.8
  Patterns Created by the Bakuba People 795
- SPOTLIGHT 19.9
  The 17 Wallpaper Patterns 797
19.3 Notation for Patterns 798
19.4 Symmetry Groups 802
19.5 Fractal Patterns and Chaos 807
- SPOTLIGHT 19.10
  The Father of Fractals 808
- Review Vocabulary 812
- Self Check Answers 812
- Skills Check 813
- Chapter Exercises 814
- Writing Projects 825
- Suggested Readings 825
- Suggested Websites 826
Chapter 20Tilings827
20.1 Tilings with Regular Polygons 828
- SPOTLIGHT 20.1
  Regular Polyhedra and Buckyballs 829
20.2 Tilings with Irregular Polygons 833
- SPOTLIGHT 20.2
  In Praise of Amateurs 836
- SPOTLIGHT 20.3
  Maurits Escher 837
20.3 Using Only Translations 838
20.4 Using Translations Plus Half-Turns 840
20.5 Nonperiodic Tilings 845
- SPOTLIGHT 20.4
  Sir Roger Penrose 846
- SPOTLIGHT 20.5
  Mathematics and Autism 851
- SPOTLIGHT 20.6
  Quasicrystals 854
xiii
- Review Vocabulary 856
- Self Check Answers 856
- Skills Check 857
- Chapter Exercises 858
- Writing Projects 864
- Suggested Readings 864
- Suggested Websites 865
Part VII YOUR MGNEY AND RESOURCES / 866
Chapter 21Savings Models869
21.1 Simple Interest and Arithmetic Growth 870
21.2 Compound Interest and Geometric Growth 872
- SPOTLIGHT 21.1
  Thomas Robert Malthus 878
21.3 Effective Rate and APY 878
21.4 A Limit to Compounding 880
- SPOTLIGHT 21.2
  The Number e 881
21.5 A Model for Saving 882
- SPOTLIGHT 21.3
  Using a Spreadsheet for Financial Calculations 888
21.6 Inflation 888
- SPOTLIGHT 21.4
  What Is a Financial Derivative? 893
- Review Vocabulary 896
- Self Check Answers 897
- Skills Check 897
- Chapter Exercises 898
- Applet Exercise 906
- Writing Projects 906
- Suggested Readings 907
- Suggested Websites 908
Chapter 22Borrowing Models909
22.1 Simple Interest 910
22.2 Compound Interest 911
- SPOTLIGHT 22.1
  What’s the Real Rate? 913
22.3 Conventional Loans 914
- SPOTLIGHT 22.2
  What We Did with Our House, and What Else You Could Do 921
- SPOTLIGHT 22.3
  The Mortgage Crisis 922
22.4 Other Loans 923
22.5 Annuities 929
- SPOTLIGHT 22.4
  What Is an Actuary? 930
- Review Vocabulary 933
- Self Check Answers 933
- Skills Check 934
- Chapter Exercises 935
- Applet Exercise 941
- Writing Projects 941
- Suggested Readings 942
- Suggested Websites 942
Chapter 23The Economics of
Resources943
- SPOTLIGHT 23.1
  The Formulas We Use in This Chapter 944
23.1 Growth Models for Biological Populations 944
- SPOTLIGHT 23.2
  12 Billion by 2050—or Only 9 Billion? 947
23.2 How Long Can a Nonrenewable Resource Last? 950
- SPOTLIGHT 23.3
  What Are Reserves? Or, How Much Is Out There, Really? 953
xiv
23.3 Radioactive Decay 955
23.4 Harvesting Renewable Resources 960
- SPOTLIGHT 23.4
  Fishing: Out to Sea? 965
- SPOTLIGHT 23.5
  The Tragedy of Easter Island 969
23.5 Dynamical Systems and Chaos 971
- Review Vocabulary 976
- Self Check Answers 977
- Skills Check 978
- Chapter Exercises 979
- Writing Projects 986
- Suggested Readings 986
- Suggested Websites 986
Appendix Algebra Review AR-1
Algebra Review I: Handling Operations AR-1
A. Order of Operations AR-1
B. Distributive Law AR-2
C. Operations with Rational Numbers (Fractions) AR-2
Algebra Review II: Representing Numbers AR-3
A. Fractions, Percents, and Percentages AR-3
B. Remainders AR-3
C. Prime and Composite Numbers AR-4
D. Significant Digits AR-4
E. Scientific Notation AR-5
F. Rounding Numbers AR-5
G. Counting in Binary AR-6
Algebra Review III: Working with Formulas AR-7
A. Using Formulas AR-7
B. Solving for One Variable in Terms of Another AR-8
C. Formulas Related to Geometric Shapes AR-9
Algebra Review IV: Linear Equations and Inequalities AR-10
A. Linear Equations in One Variable AR-10
B. Plotting Points in the Plane AR-11
C. Distance and Midpoint between Two Points in the Plane AR-12
D. Linear Equations in Two Variables AR-13
E. Slope of a Line AR-14
F. Graphing a Line in Slope-Intercept Form AR-15
G. Linear Inequalities in Two Variables AR-16
H. Systems of Linear Equations and Inequalities AR-17
Algebra Review V: Summation Notation, Sequences, and Series AR-19
A. Summation Notation AR-19
B. Sequences AR-20
C. Arithmetic and Geometric Sequences and Series AR-21
Algebra Review VI: Exponents, Roots, and Logarithms AR-22
A. Powers and Roots AR-22
B. Natural and Fractional Exponents AR-23
C. Graphs of Exponential Equations AR-24
D. Rules for Exponents and Roots AR-25
E. Logarithms AR-26
F. Using Logarithms to Solve Equations AR-26
Algebra Review VII: Functions AR-27
A. Determining If a Relation Is a Function AR-27
B. Function Notation AR-28
Algebra Review VIII: Permutations and Combinations AR-29
A. Permutations AR-29
B. Combinations AR-29
Answers to Algebra Review Exercises AR-31
Answers to
Skills Check ExercisesSC-1
Answers to
Odd-Numbered ExercisesA-1
IndexI-1

Contents