For All Practical Purposes: Mathematical Literacy in Today's World

930 Pages·2011·34.76 MB·English

by  COMAP

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For All
Practical
Purposes
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Solomon Garfunkel
Project Director
Consortium for Mathematics and Its Applications
Contributing Authors PART I MANAGEMENT SCIENCE
Joseph Malkevitch
York College, CUNY
PART II STATISTICS: THE SCIENCE OF DATA
Lawrence M. Lesser
The University of Texas at El Paso
[Founding FAPP author is David S. Moore, Purdue University]
PART III VOTING AND SOCIAL CHOICE
Alan D. Taylor | Bruce P. Conrad | Steven J. Brams
Union College Temple University New York University
PART IV FAIRNESS AND GAME THEORY
Alan D. Taylor | Bruce P. Conrad | Steven J. Brams
Union College Temple University New York University
PART V THE DIGITAL REVOLUTION
Joseph A. Gallian
University of Minnesota Duluth
PART VI ON SIZE AND GROWTH
Paul J. Campbell
Beloit College
PART VII YOUR MONEY AND RESOURCES
Paul J. Campbell
Beloit College
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9th
Edition
For All
Practical
Purposes
Mathematical Literacy in Today’s World
W. H. FREEMAN AND COMPANY
New York
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Publisher: Ruth Baruth
Executive Acquisitions Editor: Terri Ward
Executive Marketing Manager: Jennifer Somerville
Developmental Editors: Andrew Sylvester and Lisa Collette
Senior Media Acquisitions Editor: Roland Cheyney
Senior Media Editor: Laura Capuano
Associate Editor: Katrina Wilhelm
Assistant Media Editor: Catriona Kaplan
Editorial Assistant: Tyler Holzer
Photo Editor: Bianca Moscatelli
Photo Researcher: Christina Micek
Cover Designer: Vicki Tomaselli
Text Designer: Marsha Cohen
Project Editor: Vivien Weiss
Director of Production: Ellen Cash
Production Manager: Julia DeRosa
Illustrations: MPS Limited, a Macmillan Company
Composition: MPS Limited, a Macmillan Company
Printing and Binding: QuadGraphics
Library of Congress Control Number: 2011937302
Student Edition (hardcover):
ISBN-13: 978-1-4292-4316-2
ISBN-10: 1-4292-4316-3
Student Edition (paperback):
ISBN-13: 978-1-4292-5482-3
ISBN-10: 1-4292-5482-3
Student Edition (looseleaf):
ISBN-13: 978-1-4641-0157-1
ISBN-10: 1-4641-0157-4
Instructor Comp Copy (hardcover):
ISBN-13: 978-1-4641-0156-4
ISBN-10: 1-4641-0156-6
NASTA-spec version:
ISBN-13: 978-1-4292-5481-6
ISBN-10: 1-4292-5481-5
©2013 by COMAP, Inc.
All rights reserved.
Printed in the United States of America
First printing
W. H. Freeman and Company
41 Madison Avenue
New York, NY 10010
Houndmills, Basingstoke RG21 6XS, England
www.whfreeman.com
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Brief Contents
Part I MANAGEMENT SCIENCE 3
Chapter 1 Urban Services 5
Chapter 2 Business Efficiency 35
Chapter 3 Planning and Scheduling 75
Chapter 4 Linear Programming 115
Part II STATISTICS: THE SCIENCE OF DATA 163
Chapter 5 Exploring Data: Distributions 165
Chapter 6 Exploring Data: Relationships 209
Chapter 7 Data for Decisions 241
Chapter 8 Probability: The Mathematics of Chance 281
Part III VOTING AND SOCIAL CHOICE 325
Chapter 9 Social Choice: The Impossible Dream 327
Chapter 10 The Manipulability of Voting Systems 357
Chapter 11 Weighted Voting Systems 377
Chapter 12 Electing the President 415
Part IV FAIRNESS AND GAME THEORY 451
Chapter 13 Fair Division 453
Chapter 14 Apportionment 485
Chapter 15 Game Theory: The Mathematics of Competition 529
Part V THE DIGITAL REVOLUTION 571
Chapter 16 Identification Numbers 573
Chapter 17 Information Science 601
Part VI ON SIZE AND GROWTH 641
Chapter 18 Growth and Form 643
Chapter 19 Symmetry and Patterns 685
Chapter 20 Tilings 731
Part VII YOUR MONEY AND RESOURCES 765
Chapter 21 Savings Models 767
Chapter 22 Borrowing Models 805
Chapter 23 The Economics of Resources 829
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Contents
PART I
Management Science / 3
(cid:2) Exercises 61
Chapter 1 Urban Services 5
(cid:2) Applet Exercises 72
1.1 Euler Circuits 5 (cid:2) Writing Projects 73
Suggested Readings 73
SPOTLIGHT 1.1 Leonhard Euler 9
Suggested Web Sites 73
1.2 Finding Euler Circuits 9
SPOTLIGHT 1.2 The Human Aspect of Problem Chapter 3 Planning and Scheduling 75
Solving 10
3.1 Scheduling Tasks 75
1.3 Beyond Euler Circuits 13
3.2 Critical-Path Schedules 82
1.4 Urban Graph Traversal Problems 19
SPOTLIGHT 3.1 Management Science and Disaster
SPOTLIGHT 1.3 Israel Electric Company Reduces
Recovery 83
Meter-Reading Task 20
3.3 Independent Tasks 86
(cid:2) Review Vocabulary 22
(cid:2) Skills Check 22 3.4 Bin Packing 89
(cid:2) Exercises 25
SPOTLIGHT 3.2 Using Mathematical Tools 92
(cid:2) Applet Exercises 33
(cid:2) Writing Projects 33 3.5 Resolving Conflict via Coloring 93
Suggested Readings 33 SPOTLIGHT 3.3 Four Color Problem 96
Suggested Web Sites 33
SPOTLIGHT 3.4 Scheduling Job Interviews 97
(cid:2) Review Vocabulary 98
Chapter 2 Business Efficiency 35
(cid:2) Skills Check 99
2.1 Hamiltonian Circuits 36 (cid:2) Exercises 101
(cid:2) Applet Exercises 112
2.2 Traveling Salesman Problem 42 (cid:2) Writing Projects 113
2.3 Helping Traveling Salesmen 43
Suggested Readings 113
Suggested Web Sites 113
SPOTLIGHT 2.1 NP-Complete Problems 46
2.4 Minimum-Cost Spanning Trees 47
Chapter 4 Linear Programming 115
SPOTLIGHT 2.2 AT&T Manager Explains How Long-
Distance Calls Run Smoothly 51 4.1 Linear Programming and Mixture Problems:
Combining Resources to Maximize Profit 115
SPOTLIGHT 2.3 Common Ancestors? 52
SPOTLIGHT 4.1 Case Studies in Linear Programming 117
2.5 Critical-Path Analysis 53
ALGEBRA REVIEW Linear Equations and Intercepts 121
SPOTLIGHT 2.4 Every Moment Counts in Rigorous
Airline Scheduling 56 ALGEBRA REVIEW Linear Inequalities 122
(cid:2) Review Vocabulary 57 4.2 Finding the Optimal Production Policy 125
(cid:2) Skills Check 58
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Contents vii
4.5 A Transportation Problem: Delivering
ALGEBRA REVIEW Systems of Linear Equations and
Perishables 140
Inequalities 128
4.6 Improving on the Current Solution 149
4.3 Why the Corner Point Principle Works 132
(cid:2) Review Vocabulary 151
4.4 Linear Programming: Life Is Complicated 135 (cid:2) Skills Check 152
(cid:2) Exercises 154
SPOTLIGHT 4.2 The Father of Linear Programming (cid:2) Writing Projects 161
Recalls Its Origins 137
Suggested Readings 161
SPOTLIGHT 4.3 Finding Fast Algorithms Means Better Suggested Web Sites 161
Airline Service 139
PART II
Statistics: The Science of Data / 163
6.2 Making Predictions: Regression Line 214
Chapter 5 Exploring Data: Distributions 165
ALGEBRA REVIEW Graphing a Line in Slope-Intercept
5.1 Displaying Distributions: Histograms 165
Form 216
5.2 Interpreting Histograms 171
6.3 Correlation 217
5.3 Displaying Distributions: Stemplots 174
SPOTLIGHT 6.1 Correlation Calculation 219
5.4 Describing Center: Mean and Median 176
SPOTLIGHT 6.2 Regression Toward the Mean 220
ALGEBRA REVIEW Using Formulas 177
6.4 Least-Squares Regression 220
SPOTLIGHT 5.1 Which Mean Do You Mean? 179
SPOTLIGHT 6.3 Regression and Correlation in Action:
5.5 Describing Variability: Range and
College Success 221
Quartiles 180
6.5 Interpreting Correlation and Regression 223
5.6 The Five-Number Summary and
(cid:2) Review Vocabulary 228
Boxplots 181
(cid:2) Skills Check 228
5.7 Describing Variability: The Standard (cid:2) Exercises 230
Deviation 183 (cid:2) Applet Exercises 237
(cid:2) Writing Projects 238
ALGEBRA REVIEW Squares and Square Roots 184
Suggested Readings 238
SPOTLIGHT 5.2 Calculating Standard Deviation 186 Suggested Web Sites 239
5.8 Normal Distributions 188
Chapter 7 Data for Decisions 241
SPOTLIGHT 5.3 Density Estimation 193
5.9 The 68–95–99.7 Rule for Normal 7.1 Sampling 241
Distributions 193 7.2 Bad Sampling Methods 243
(cid:2) Review Vocabulary 196
7.3 Simple Random Samples 245
(cid:2) Skills Check 197
(cid:2) Exercises 198 7.4 Cautions About Sample Surveys 248
(cid:2) Applet Exercises 206
7.5 Experiments 250
(cid:2) Writing Projects 207
SPOTLIGHT 7.1 Ethics in Experiments 254
Suggested Readings 207
Suggested Web Sites 207 7.6 Experiments versus Observational
Studies 254
Chapter 6 Exploring Data: Relationships 209 7.7 Inference: From Sample to Population 258
7.8 Confidence Intervals 262
6.1 Displaying Relationships: Scatterplot 210
ALGEBRA REVIEW Slope of a Line 212 SPOTLIGHT 7.2 Truth in Polling 267
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viii Contents
(cid:2) Review Vocabulary 267
SPOTLIGHT 8.2 Birthday Coincidences 297
(cid:2) Skills Check 268
(cid:2) Exercises 270 8.4 Continuous Probability Models 297
(cid:2) Applet Exercises 277 8.5 The Mean and Standard Deviation
(cid:2) Writing Projects 278
of a Probability Model 301
Suggested Readings 279
8.6 The Central Limit Theorem 304
Suggested Web Sites 279
SPOTLIGHT 8.3 Probability and Fairness 311
Chapter 8 P robability: The Mathematics (cid:2) Review Vocabulary 312
(cid:2) Skills Check 313
of Chance 281
(cid:2) Exercises 315
8.1 Probability Models and Rules 282 (cid:2) Applet Exercises 321
(cid:2) Writing Projects 322
SPOTLIGHT 8.1 Probability and Psychology 288
Suggested Readings 322
8.2 Discrete Probability Models 290 Suggested Web Sites 322
8.3 Equally Likely Outcomes 291
PART III
Voting and Social Choice / 325
(cid:2) Review Vocabulary 370
Chapter 9 S ocial Choice: The Impossible
(cid:2) Skills Check 370
Dream 327
(cid:2) Exercises 372
9.1 An Introduction to Social Choice 327 (cid:2) Writing Projects 375
Suggested Readings 375
9.2 Majority Rule and Condorcet’s Method 328
SPOTLIGHT 9.1 The Historical Record 331
Chapter 11 Weighted Voting Systems 377
9.3 Other Voting Systems for Three or More
Candidates 332 11.1 How Weighted Voting Works 378
9.4 Insurmountable Difficulties: Arrow’s SPOTLIGHT 11.1 The Electoral College 378
Impossibility Theorem 342
SPOTLIGHT 11.2 Power Indices 381
SPOTLIGHT 9.2 Kenneth J. Arrow 344
11.2 The Shapley-Shubik Power Index 381
9.5 A Better Approach? Approval Voting 346
11.3 The Banzhaf Power Index 388
(cid:2) Review Vocabulary 348
(cid:2) Skills Check 349 SPOTLIGHT 11.3 A Mathematical Quagmire 390
(cid:2) Exercises 350
(cid:2) Writing Projects 355 ALGEBRA REVIEW Counting in Binary 392
Suggested Readings 355 SPOTLIGHT 11.4 The Electoral College: The Presidential
Elections of 2012, 2016, and 2020 400
Chapter 10 T he Manipulability of Voting 11.4 Comparing Voting Systems 401
Systems 357 (cid:2) Review Vocabulary 405
(cid:2) Skills Check 406
10.1 An Introduction to Manipulability 358
(cid:2) Exercises 408
10.2 Majority Rule and Condorcet’s Method 360 (cid:2) Writing Projects 412
10.3 The Manipulability of Other Voting Systems SPOTLIGHT 11.5 What Are Your Chances of Being a
for Three or More Candidates 362 Critical Voter? 413
10.4 Impossibility 366
Suggested Readings 413
10.5 The Chair’s Paradox 368 Suggested Web Sites 413
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