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

by COMAP

• ISBN13: 9780716735144
• ISBN10: 0716735148
• Additional ISBN(s): 9780716738176
• Edition: 5th
• Format: Hardcover
• Copyright: 1999-09-08
• Publisher: W. H. Freeman
• More Book Details
• Purchase Benefits

Summary

"If there were a course designed to help impart mathematical literacy to today's students what should it include? Like previous revisions, the new edition of FAPP carefully re-examines this question to better reflect our changing world. The text continues to focus on mathematics relevant to consumers, business, history, and social sciences, incorporating a number of content and pedagogical changes, and adding new interactive features on the Web. The result the ideal text for students who think that mathematics is irrelevant and dull, and for instructors who want to focus on active participation and a real-world approach to problem-solving."

Table of Contents

Preface	xvii
PART I Management Science
Street Networks	3	(28)
Euler Circuits	3	(5)
Finding Euler Circuits	8	(4)
Circuits with Reused Edges	12	(6)
Circuits with More Complications	18	(2)
Review Vocabulary	20	(1)
Suggested Readings	21	(1)
Suggested Web Sites	21	(1)
Skills Check	21	(1)
Exercises	22	(7)
Technology Corner	29	(1)
Writing Projects	30	(1)
Visiting Vertices	31	(41)
Hamiltonian Circuits	31	(7)
Fundamental Principle of Counting	37	(1)
Traveling Salesman Problem	38	(1)
Strategies for Solving the Traveling Salesman Problem	39	(4)
Nearest-Neighbor Algorithm	40	(1)
Sorted-Edges Algorithm	41	(2)
Minimum-Cost Spanning Trees	43	(7)
Kruskal's Algorithm	47	(3)
Critical-Path Analysis	50	(5)
Review Vocabulary	55	(1)
Suggested Readings	55	(1)
Suggested Web Sites	56	(1)
Skills Check	56	(1)
Exercises	57	(13)
Technology Corner	70	(1)
Writing Projects	71	(1)
Planning and Scheduling	72	(43)
Scheduling Tasks	72	(10)
Assumption and Goals	73	(2)
List-Processing Algorithm	75	(1)
When Is a Schedule Optimal?	76	(2)
Strange Happenings	78	(4)
Critical-Path Schedules	82	(4)
Independent Tasks	86	(4)
Decreasing-Time Lists	87	(3)
Bin Packing	90	(3)
Bin-Packing Heuristics	90	(2)
Decreasing-Time Heuristics	92	(1)
Resolving Conflict	93	(6)
Review Vocabulary	99	(1)
Suggested Readings	100	(1)
Suggested Web Sites	100	(1)
Skills Check	100	(1)
Exercises	101	(11)
Technology Corner	112	(2)
Writing Projects	114	(1)
Linear Programming	115	(52)
Mixture Problems	117	(2)
Mixture Problems Having One Resource	119	(18)
One Product and One Resource: Making Skateboards	119	(1)
Common Features of Mixture Problems	120	(1)
Two Products and One Resource: Skateboards and Dolls, Part 1	121	(1)
Mixture Charts	122	(2)
Resource Contraints	124	(1)
Graphing the Constraints to Form the Feasible Region	125	(3)
Finding the Optimal Production Policy	128	(1)
General Shape of Feasible Regions	129	(1)
The Role of the Profit Formula: Skateboards and Dolls, Part 2	130	(1)
Setting Minimum Quantities for Products: Skateboards and Dolls, Part 3	131	(1)
Drawing a Feasible Region When There Are Nonzero Minimum Constraints	132	(2)
Finding Corner Points of a Feasible Region Having Nonzero Minimums	134	(1)
Evaluating the Profit Formula at the Corners of a Feasible Region with Nonzero Minimums	135	(1)
Summary of the Pictorial Method	136	(1)
Mixture Problems Having Two Resources	137	(7)
Two Products and Two Resources: Skateboards and Dolls, Part 4	137	(7)
The Corner Point Principle	144	(5)
Using a Computer to Calculate Profit at the Corner Points	149	(1)
Linear Programming: The Wider Picture	149	(6)
Characteristics of Linear Programming Algorithms	149	(1)
The Simplex Method	150	(2)
An Alternative to the Simplex Method	152	(3)
Review Vocabulary	155	(1)
Suggested Readings	155	(1)
Suggested Web Site	156	(1)
Skills Check	156	(1)
Exercises	157	(5)
Technology Corner	162	(1)
Writing Projects	163	(4)
PART II Statistics: The Science of Data
Producing Data	167	(37)
Sampling	168	(1)
Bad Sampling Methods	169	(2)
Simple Random Samples	171	(4)
Statistical Estimation	175	(4)
Experiments	179	(2)
Randomized Comparative Experiments	181	(4)
Statistical Evidence	185	(2)
Statistics in Practice	187	(2)
Review Vocabulary	189	(1)
Suggested Readings	190	(1)
Suggested Web Sites	190	(1)
Skills Check	190	(1)
Exercises	191	(9)
Technology Corner	200	(2)
Writing Projects	202	(2)
Exploring Data	204	(47)
Displaying Distributions: Histograms	205	(3)
Interpreting Histograms	208	(2)
Displaying Distributions: Stemplots	210	(3)
Describing Center: Mean and Median	213	(2)
Describing Spread: The Quartiles	215	(2)
The Five-Number Summary and Boxplots	217	(1)
Describing Spread: The Standard Deviation	218	(3)
Displaying Relations Between Two Variables	221	(2)
Regression Lines	223	(2)
Correlation	225	(3)
Least Squares Regression	228	(2)
Modern Data Analysis	230	(3)
Review Vocabulary	233	(1)
Suggested Readings	234	(1)
Suggested Web Sites	234	(1)
Skills Check	234	(1)
Exercises	235	(13)
Technology Corner	248	(2)
Writing Projects	250	(1)
Probability: The Mathematics of Chance	251	(43)
What Is Probability?	252	(1)
Probability Models	253	(2)
Probability Rules	255	(4)
Equally Likely Outcomes	259	(3)
The Mean of a Probability Model	262	(3)
Sampling Distributions	265	(3)
Normal Distributions	268	(2)
The Shape of Normal Curves	270	(3)
The 68--95--99.7 Rule	273	(2)
The Central Limit Theorem	275	(2)
Applying the Central Limit Theorem	277	(5)
Review Vocabulary	282	(1)
Suggested Readings	283	(1)
Suggested Web Sites	283	(1)
Skills Check	283	(1)
Exercises	284	(8)
Technology Corner	292	(1)
Writing Projects	293	(1)
Statistical Inference	294	(37)
Estimating a Population Proportion	296	(3)
Confidence Intervals	299	(5)
Estimating a Population Mean	304	(4)
Statistical Process Control	308	(3)
The Perils of Data Analysis	311	(3)
Review Vocabulary	314	(1)
Suggested Readings	314	(1)
Suggested Web Sites	314	(1)
Skills Check	315	(1)
Exercises	316	(10)
Technology Corner	326	(1)
Writing Projects	327	(4)
PART III Coding Information
Identification Numbers	331	(27)
The ZIP Code	339	(2)
Bar Codes	341	(10)
ZIP Code Bar Code	342	(2)
The UPC Bar Code	344	(7)
Review Vocabulary	351	(1)
Suggested Readings	351	(1)
Suggested Web Sites	352	(1)
Skills Check	352	(1)
Exercises	353	(3)
Technology Corner	356	(1)
Writing Projects	357	(1)
Transmitting Information	358	(27)
Binary Codes	358	(3)
Encoding with Parity-Check Sums	361	(9)
Data Compression	368	(2)
Cryptography	370	(6)
Review Vocabulary	376	(1)
Suggested Readings	377	(1)
Suggested Web Sites	377	(1)
Skills Check	377	(1)
Exercises	378	(2)
Technology Corner	380	(1)
Writing Projects	381	(4)
PART IV Social Choice and Decision Making
Social Choice: The Impossible Dream	385	(31)
Elections with Only Two Alternatives	387	(1)
Elections with Only Two Alternatives: Procedures and Problems	388	(10)
Plurality Voting and the Condorcet Winner Criterion	388	(2)
The Borda Count and Independence of Irrelevant Alternatives	390	(4)
Sequential Pairwise Voting and the Pareto Condition	394	(2)
The Hare System and Monotonicity	396	(1)
Summary	397	(1)
Insurmountable Difficulties: From Paradox to Impossibility	398	(7)
The Voting Paradox of Condorcet	398	(1)
Manipulability	399	(2)
Impossibility	401	(4)
A Better Approach? Approval Voting	405	(1)
Review Vocabulary	406	(1)
Suggested Readings	407	(1)
Suggested Web Sites	408	(1)
Skills Check	408	(1)
Exercises	409	(5)
Technology Corner	414	(1)
Writing Projects	415	(1)
Weighted Voting Systems	416	(38)
How Weighted Voting Works	416	(5)
Notation for Weighted Voting	418	(3)
The Banzhar Power Index	421	(10)
How to Count Combinations	427	(4)
Equivalent Voting Systems	431	(4)
The Shapley-Shubik Power Index	435	(6)
How to Compute the Shapley-Shubik Power Index	438	(3)
Comparing the Banzhaf and Shapley-Shubik Models	441	(1)
Systems with Large Numbers of Voters	441	(3)
Review Vocabulary	444	(1)
Suggested Readings	445	(1)
Suggested Web Sites	445	(1)
Skills Check	446	(1)
Exercises	446	(6)
Technology Corner	452	(1)
Writing Projects	453	(1)
Fair Division	454	(35)
The Adjusted Winner Divorce Procedure	455	(4)
The Knaster Inheritance Procedure	459	(2)
Taking Turns	461	(3)
Divide-and-Choose	464	(2)
Cake-Division Schemes: Proportionality	466	(6)
Cake-Division Schemes: The Problem of Envy	472	(6)
Review Vocabulary	478	(1)
Suggested Readings	479	(1)
Suggested Web Sites	479	(1)
Skills Check	480	(1)
Exercises	481	(6)
Technology Corner	487	(1)
Writing Projects	488	(1)
Apportionment	489	(36)
The Hamilton Method	492	(4)
Paradoxes of the Hamilton Method	494	(2)
Divisor Methods	496	(9)
The Jefferson Method	496	(1)
Critical Multipliers	497	(3)
The Webster Method	500	(4)
The Hill-Huntington Method	504	(1)
Which Divisor Method Is the Best?	505	(7)
Review Vocabulary	512	(1)
Suggested Readings	513	(1)
Suggested Web Site	514	(1)
Skills Check	514	(1)
Exercises	515	(5)
Technology Corner	520	(4)
Writing Projects	524	(1)
Game Theory: The Mathematics of Competition	525	(56)
Two-Person Total-Conflict Games: Pure Strategies	526	(7)
Two-Person Total-Conflict Games: Mixed Strategies	533	(9)
A Flawed Approach	534	(1)
A Better Idea	535	(7)
Partial-Conflict Games	542	(7)
Larger Games	549	(12)
Using Game Theory	561	(5)
Solving Games	561	(2)
Practical Applications	563	(3)
Review Vocabulary	566	(1)
Suggested Readings	567	(2)
Suggested Web Sites	569	(1)
Skills Check	569	(1)
Exercises	570	(5)
Technology Corner	575	(1)
Writing Projects	576	(5)
PART V On Size and Shape
Growth and Form	581	(48)
Geometric Similarity	582	(3)
The Language of Growth, Enlargement, and Decrease	585	(1)
Numerical Similarity	586	(2)
Measuring Length, Area, Volume, and Weight	588	(4)
U.S. Customary System	588	(1)
Metric System	589	(1)
Converting Between Systems	590	(2)
Scaling Real Objects	592	(3)
Sorry, No King Kongs	595	(5)
Solving the Problem of Scale	600	(1)
Falls, Jumps, and Flights	601	(3)
Keeping Cool (and Warm)	604	(3)
Warm-Blooded Animals	604	(2)
Cold-Blooded Animals	606	(1)
Similarity and Growth	607	(6)
Conclusion	613	(1)
Review Vocabulary	613	(1)
Suggested Readings	613	(1)
Suggested Web Sites	614	(1)
Skills Check	615	(1)
Exercises	615	(8)
Technology Corner	623	(1)
Writing Projects	624	(5)
Symmetry and Patterns	629	(39)
Spirals	629	(1)
Fibonacci Numbers	630	(1)
The Golden Ratio	631	(6)
Balance in Symmetry	637	(1)
Rigid Motions	637	(4)
Preserving the Pattern	641	(2)
Analyzing Patterns	643	(1)
Strip Patterns	644	(3)
Symmetry Groups	647	(4)
Notation for Patterns	651	(2)
Imperfect Patterns	653	(1)
Review Vocabulary	654	(1)
Suggested Readings	655	(1)
Suggested Web Sites	656	(1)
Skills Check	656	(1)
Exercises	657	(7)
Technology Corner	664	(1)
Writing Projects	665	(3)
Tilings	668	(45)
Regular Polygons	669	(2)
Regular Tilings	671	(4)
Tilings with Irregular Polygons	675	(5)
M. C. Escher and Tilings	680	(1)
Tiling by Translations	680	(6)
Tiling by Translations and Half-Turns	686	(4)
Further Considerations	690	(1)
Nonperiodic Tilings	691	(1)
The Penrose Tiles	691	(7)
Quasicrystals and Barlow's Law	698	(3)
Review Vocabulary	701	(1)
Suggested Readings	702	(1)
Suggested Web Sites	703	(1)
Skills Check	703	(1)
Exercises	704	(3)
Technology Corner	707	(1)
Writing Projects	708	(5)
PART VI Modeling in Mathematics
Logic and Modeling	713	(27)
The English Language	714	(1)
The Basic Symbols of Propositional Logic	715	(2)
Using Symbolism in Analytical Reasoning	717	(4)
Truth and Falsity for ℸ and ⟹	721	(3)
The Other Connectives	724	(5)
An Important Open Question	729	(1)
A Model of Deduction	730	(2)
First-Order Logic	732	(2)
Review Vocabulary	734	(1)
Suggested Readings	735	(1)
Suggested Web Sites	735	(1)
Skills Check	735	(1)
Exercises	736	(2)
Technology Corner	738	(1)
Writing Projects	739	(1)
Consumer Finance Models	740	(1)
Models for Savings	740	(2)
The Mathematics of Geometric Growth	742	(3)
Arithmetic Growth	745	(2)
A Limit to Compounding	747	(3)
A Model for Accumulation	750	(4)
A Model for Financial Derivatives	754	(2)
Exponential Decay	756	(2)
Growth Models for Biological Populations	758	(2)
Nonrenewable Resources	760	(3)
Renewable Resources	763	(1)
Reproduction Curves	764	(2)
Sustained-Yield Harvesting	766	(1)
Considerations from Economics	767	(3)
Why Eliminate a Renewable Resource?	770	(3)
Review Vocabulary	773	(1)
Suggested Readings	774	(1)
Suggested Web Sites	775	(1)
Skills Check	775	(1)
Exercises	776	(6)
Technology Corner	782	(1)
Writing Projects	783
Answer to Skills Check Exercises	A-3
Answer to Odd-Numbered Exercises	A-5
Answers to Technology Corner Exercises	A-47
Credits	C-1
Index	I-1