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

by COMAP

• ISBN13: 9780716769019
• ISBN10: 0716769018
• Edition: 7th
• Format: Paperback
• Copyright: 2005-11-05
• Publisher: W. H. Freeman

Summary

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Table of Contents

Preface	xiii
PART I MANAGEMENT SCIENCE	1	(176)
Urban Services	3	(33)
Euler Circuits	3	(5)
Spotlight 1.1: Leonhard Euler	7	(1)
Spotlight 1.2: The Human Aspect of Problem Solving	8	(1)
Finding Euler Circuits	8	(4)
Beyond Euler Circuits	12	(7)
Urban Graph Traversal Problems	19	(17)
Spotlight 1.3: Israel Electric Company Reduces Meter-Reading Task	20	(2)
Review Vocabulary	22	(1)
Skills Check	22	(3)
Exercises	25	(9)
Applet Exercises	34	(1)
Writing Projects	34	(1)
Suggested Readings	34	(1)
Suggested Web Sites	35	(1)
Business Efficiency	36	(44)
Hamiltonian Circuits	37	(6)
Traveling Salesman Problem	43	(1)
Helping Traveling Salesmen	44	(11)
Spotlight 2.1: NP-Complete Problems	48	(5)
Spotlight 2.2: AT&T Manager Explains How Long-Distance Calls Run Smoothly	53	(1)
Spotlight 2.3: Common Ancestors?	54	(1)
Critical-Path Analysis	55	(25)
Spotlight 2.4: Every Moment Counts in Rigorous Airline Scheduling	60	(1)
Review Vocabulary	60	(1)
Skills Check	61	(3)
Exercises	64	(13)
Applet Exercises	77	(1)
Writing Projects	78	(1)
Suggested Readings	78	(1)
Suggested Web Sites	79	(1)
Planning and Scheduling	80	(44)
Scheduling Tasks	80	(9)
Critical-Path Schedules	89	(5)
Spotlight 3.1: Management Science and Disaster Recovery	91	(3)
Independent Tasks	94	(3)
Bin Packing	97	(5)
Spotlight 3.2: Using Mathematical Tools	101	(1)
Resolving Conflict via Coloring	102	(22)
Spotlight 3.3: Scheduling Job Interviews	106	(1)
Review Vocabulary	107	(1)
Skills Check	108	(2)
Exercises	110	(12)
Applet Exercises	122	(1)
Writing Projects	122	(1)
Suggested Readings	123	(1)
Suggested Web Sites	123	(1)
Linear Programming	124	(53)
Mixture Problems: Combining Resources to Maximize Profit	126	(8)
Spotlight 4.1: Case Studies in Linear Programming	127	(7)
Finding the Optimal Production Policy	134	(8)
Why the Corner Point Principle Works	142	(4)
Linear Programming: Life Is Complicated	146	(4)
Spotlight 4.2: Father of Linear Programming Recalls Its Origins	147	(3)
Spotlight 4.3: Finding Fast Algorithms Means Better Airline Service	150	(1)
A Transportation Problem: Delivering Perishables	150	(11)
Improving on the Current Solution	161	(16)
Review Vocabulary	163	(1)
Skills Check	164	(3)
Exercises	167	(8)
Writing Projects	175	(1)
Suggested Readings	175	(1)
Suggested Web Sites	175	(2)
PART II STATISTICS: THE SCIENCE OF DATA	177	(160)
Exploring Data: Distributions	179	(43)
Displaying Distributions: Histograms	181	(2)
Interpreting Histograms	183	(3)
Displaying Distributions: Stemplots	186	(2)
Describing Center: Mean and Median	188	(4)
Spotlight 5.1: Think!	191	(1)
Describing Spread: The Quartiles	192	(1)
The Five-Number Summary and Boxplots	193	(2)
Describing Spread: The Standard Deviation	195	(3)
Normal Distributions	198	(7)
Spotlight 5.2: Density Estimation	204	(1)
The 68--95--99.7 Rule	205	(17)
Review Vocabulary	207	(1)
Skills Check	208	(2)
Exercises	210	(9)
Applet Exercises	219	(1)
Writing Projects	220	(1)
Suggested Readings	220	(1)
Suggested Web Sites	221	(1)
Exploring Data: Relationships	222	(32)
Displaying Relationships: Scatterplots	223	(3)
Regression Lines	226	(2)
Correlation	228	(4)
Spotlight 6.1: Scatterplot Smoothers	229	(3)
Least-Squares Regression	232	(3)
Spotlight 6.2: Regression in Action	232	(3)
Interpreting Correlation and Regression	235	(19)
Review Vocabulary	239	(1)
Skills Check	240	(2)
Exercises	242	(9)
Applet Exercises	251	(1)
Writing Projects	252	(1)
Suggested Readings	252	(1)
Suggested Web Sites	253	(1)
Data for Decisions	254	(42)
Sampling	255	(1)
Bad Sampling Methods	256	(1)
Simple Random Samples	257	(6)
Spotlight 7.1: Is It Really Random?	259	(4)
Cautions About Sample Surveys	263	(1)
Experiments	264	(4)
Thinking About Experiments	268	(2)
Inference: From Sample to Population	270	(6)
Confidence Intervals	276	(20)
Spotlight 7.2: How Accurate Is Our Poll?	280	(1)
Review Vocabulary	281	(2)
Skills Check	283	(2)
Exercises	285	(8)
Applet Exercises	293	(1)
Writing Projects	294	(1)
Suggested Readings	295	(1)
Suggested Web Sites	295	(1)
Probability: The Mathematics of Chance	296	(41)
Probability Models and Rules	297	(7)
Spotlight 8.1: Probability and Risk	302	(2)
Discrete Probability Models	304	(1)
Equally Likely Outcomes	305	(4)
Continuous Probability Models	309	(3)
The Mean and Standard Deviation of a Probability Model	312	(4)
The Central Limit Theorem	316	(21)
Spotlight 8.2: Cancer Clusters	317	(6)
Review Vocabulary	323	(1)
Skills Check	324	(2)
Exercises	326	(8)
Applet Exercises	334	(1)
Writing Projects	335	(1)
Suggested Readings	335	(1)
Suggested Web Sites	335	(2)
PART III VOTING AND SOCIAL CHOICE	337	(136)
Social Choice: The Impossible Dream	339	(30)
Majority Rule and Condorcet's Method	341	(4)
Spotlight 9.1: The Historical Record	344	(1)
Other Voting Systems for Three or More Candidates	345	(11)
Insurmountable Difficulties: Arrow's Impossibility Theorem	356	(3)
Spotlight 9.2: Kenneth J. Arrow	357	(2)
A Better Approach? Approval Voting	359	(10)
Review Vocabulary	361	(1)
Skills Check	362	(2)
Exercises	364	(4)
Writing Projects	368	(1)
Suggested Readings	368	(1)
The Manipulability of Voting Systems	369	(21)
Majority Rule and Condorcet's Method	373	(2)
Other Voting Systems for Three or More Candidates	375	(5)
Impossibility	380	(2)
The Chair's Paradox	382	(8)
Review Vocabulary	384	(1)
Skills Check	384	(2)
Exercises	386	(3)
Writing Projects	389	(1)
Suggested Readings	389	(1)
Weighted Voting Systems	390	(41)
Spotlight 11.1: The Electoral College	392	(2)
Spotlight 11.2: Power Indices	394	(1)
The Shapley--Shubik Power Index	394	(8)
The Banzhaf Power Index	402	(14)
Spotlight 11.3: A Mathematical Quagmire	405	(10)
Spotlight 11.4: The Electoral College: Presidential Elections of 2004 and 2008	415	(1)
Comparing Voting Systems	416	(15)
Review Vocabulary	421	(2)
Skills Check	423	(1)
Exercises	424	(5)
Writing Projects	429	(1)
Suggested Readings	430	(1)
Electing the President	431	(42)
Spatial Models for Two-Candidate Elections	433	(9)
Spatial Models for Multicandidate Elections	442	(5)
Winnowing the Field	447	(1)
What Drives Candidates Out?	448	(3)
Election Reform: Approval Voting	451	(3)
The Electoral College	454	(8)
Is There a Better Way to Elect a President?	462	(11)
Review Vocabulary	463	(2)
Skills Check	465	(1)
Exercises	466	(5)
Writing Projects	471	(1)
Suggested Readings	472	(1)
Suggested Web Sites	472	(1)
PART IV FAIRNESS AND GAME THEORY	473	(118)
Fair Division	475	(29)
The Adjusted Winner Procedure	476	(4)
The Knaster Inheritance Procedure	480	(2)
Taking Turns	482	(3)
Divide-and-Choose	485	(1)
Cake-Division Procedures: Proportionality	486	(4)
Spotlight 13.1: Sixty Years of Cake Cutting	488	(2)
Cake-Division Procedures: The Problem of Envy	490	(14)
Review Vocabulary	493	(1)
Skills Check	494	(3)
Exercises	497	(5)
Writing Projects	502	(1)
Suggested Readings	503	(1)
Apportionment	504	(38)
The Apportionment Problem	504	(5)
The Hamilton Method	509	(5)
Divisor Methods	514	(11)
Which Divisor Method is Best?	525	(17)
Spotlight 14.1: A Legal Challenge to Apportionment	526	(4)
Spotlight 14.2: Mathematics and Politics: A Strange Mixture	530	(1)
Review Vocabulary	531	(2)
Skills Check	533	(1)
Exercises	534	(6)
Applet Exercises	540	(1)
Writing Projects	540	(1)
Suggested Readings	541	(1)
Suggested Web Sites	541	(1)
Game Theory: The Mathematics of Competition	542	(49)
Spotlight 15.1: The Early History of Game Theory	543	(1)
Two-Person Total-Conflict Games: Pure Strategies	544	(6)
Two-Person Total-Conflict Games: Mixed Strategies	550	(10)
Partial-Conflict Games	560	(8)
Spotlight 15.2: The 1994 Nobel Prize in Economics	567	(1)
Larger Games	568	(7)
Using Game Theory	575	(16)
Review Vocabulary	580	(1)
Skills Check	581	(3)
Exercises	584	(4)
Applet Exercises	588	(1)
Writing Projects	588	(1)
Suggested Readings	589	(1)
Suggested Web Sites	589	(2)
PART V THE DIGITAL REVOLUTION	591	(70)
Identification Numbers	593	(26)
Check Digits	593	(8)
Spotlight 16.1: Bank Checks	596	(3)
Spotlight 16.2: German Banknotes	599	(1)
Spotlight 16.3: The VIN System	600	(1)
The ZIP Code	601	(2)
Bar Codes	603	(5)
Encoding Personal Data	608	(11)
Spotlight 16.4: Social Security Numbers	609	(2)
Review Vocabulary	611	(1)
Skills Check	612	(1)
Exercises	613	(5)
Writing Projects	618	(1)
Suggested Readings	618	(1)
Suggested Web Sites	618	(1)
Information Science	619	(42)
Binary Codes	619	(4)
Spotlight 17.1: The Ubiquitous Reed--Solomon Codes	621	(1)
Spotlight 17.2: Vera Pless	622	(1)
Encoding with Parity-Check Sums	623	(11)
Spotlight 17.3: Neil Sloane	624	(8)
Spotlight 17.4: David Huffman	632	(2)
Cryptography	634	(10)
Spotlight 17.5: Modeling the Genetic Code	636	(3)
Spotlight 17.6: Adventure of the Dancing Men	639	(5)
Web Searches and Mathematical Logic	644	(17)
Spotlight 17.7: The Network Structure of the Internet	644	(3)
Spotlight 17.8: Six Degrees of Kevin Bacon	647	(5)
Review Vocabulary	652	(1)
Skills Check	653	(1)
Exercises	654	(5)
Writing Projects	659	(1)
Suggested Readings	659	(1)
Suggested Web Sites	659	(2)
PART VI ON SIZE AND GROWTH	661	(132)
Growth and Form	663	(46)
Geometric Similarity	664	(5)
How Much Is That in...?	669	(3)
Scaling a Mountain	672	(6)
Spotlight 18.1: A Mile-High Building?	675	(3)
Sorry, No King Kongs	678	(2)
Spotlight 18.2: Galileo and the Problem of Scale	679	(1)
Dimension Tension	680	(8)
Spotlight 18.3: ``Take That, King Richard!''	684	(4)
How to Grow	688	(21)
Spotlight 18.4: Helping to Find Missing Children	690	(4)
Review Vocabulary	694	(1)
Skills Check	695	(1)
Exercises	696	(10)
Writing Projects	706	(2)
Suggested Readings	708	(1)
Suggested Web Sites	708	(1)
Symmetry and Patterns	709	(46)
Fibonacci Numbers and the Golden Ratio	710	(7)
Spotlight 19.1: Leonardo of Pisa (``Fibonacci'')	711	(2)
Spotlight 19.2: How the Greeks Constructed a Golden Rectangle	713	(2)
Spotlight 19.3: The Consumer Price Index: An Application of the Geometric Mean	715	(2)
Symmetries Preserve the Pattern	717	(3)
Rosette, Strip, and Wallpaper Patterns	720	(5)
Spotlight 19.4: ``Strive Then to Be Perfect''	721	(2)
Spotlight 19.5: Patterns Created by the Bakuba People	723	(2)
Notation for Patterns	725	(6)
Spotlight 19.6: The 17 Wallpaper Patterns	726	(5)
Symmetry Groups	731	(4)
Fractal Patterns and Chaos	735	(20)
Spotlight 19.7: The Father of Fractals	739	(1)
Review Vocabulary	740	(1)
Skills Check	741	(2)
Exercises	743	(10)
Writing Projects	753	(1)
Suggested Readings	753	(1)
Suggested Web Sites	754	(1)
Tilings	755	(38)
Tilings with Regular Polygons	756	(5)
Spotlight 20:1 Regular Polyhedra and Buckyballs	758	(3)
Tilings with Irregular Polygons	761	(5)
Spotlight 20.2: In Praise of Amateurs	765	(1)
Using Translations	766	(3)
Using Translations Plus Half-Turns	769	(5)
Nonperiodic Tilings	774	(19)
Spotlight 20.3: Sir Roger Penrose	776	(6)
Spotlight 20.4: Quasicrystals	782	(1)
Review Vocabulary	783	(1)
Skills Check	784	(1)
Exercises	785	(6)
Writing Projects	791	(1)
Suggested Readings	791	(1)
Suggested Web Sites	791	(2)
PART VII YOUR MONEY AND RESOURCES	793
Savings Models	795	(39)
Arithmetic Growth and Simple Interest	795	(2)
Geometric Growth and Compound Interest	797	(8)
Spotlight 21.1: Thomas Robert Malthus	805	(1)
A Limit to Compounding	805	(4)
Spotlight 21.2: The Number e	807	(2)
A Model for Investment	809	(4)
Exponential Decay and the Consumer Price Index	813	(4)
Real Growth and Valuing Investments	817	(17)
Spotlight 21.3: Nobel Prize for a Model in Economics	821	(1)
Review Vocabulary	822	(1)
Skills Check	823	(1)
Exercises	824	(8)
Applet Exercises	832	(1)
Writing Projects	832	(1)
Suggested Readings	833	(1)
Suggested Web Sites	833	(1)
Borrowing Models	834	(25)
Simple Interest	834	(2)
Compound Interest	836	(3)
Conventional Loans	839	(8)
Spotlight 22.1: What's the Real Rate?	840	(6)
Spotlight 22.2: What We Did with Our House, and What Else You Could Do	846	(1)
Annuities	847	(12)
Spotlight 22.3: What Actuaries Do	849	(1)
Review Vocabulary	850	(1)
Skills Check	850	(2)
Exercises	852	(5)
Applet Exercises	857	(1)
Writing Projects	857	(1)
Suggested Readings	858	(1)
Suggested Web Sites	858	(1)
The Economics of Resources	859
Growth Models for Biological Populations	860	(5)
Spotlight 23.1: 12 Billion by 2050--or Only 9 Billion?	863	(2)
How Long Can a Nonrenewable Resource Last?	865	(5)
Sustaining Renewable Resources	870	(6)
The Economics of Harvesting Resources	876	(5)
Spotlight 23.2: The Tragedy of Easter Island	879	(2)
Dynamical Systems and Chaos	881
Review Vocabulary	885	(1)
Skills Check	886	(1)
Exercises	887	(6)
Writing Projects	893	(1)
Suggested Readings	894	(1)
Suggested Web Sites	894
Answers to Skills Check Exercises	1	(1)
Answers to Odd-Numbered Exercises	1	(1)
Index	1