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Excursions in Modern Mathematics,9780130177629
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Excursions in Modern Mathematics

by ;
Edition:
4th
ISBN13:

9780130177629

ISBN10:
0130177628
Format:
Hardcover
Pub. Date:
8/1/2000
Publisher(s):
PRENTICE HALL
List Price: $104.00

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Summary

For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education.This very successful liberal arts mathematics textbook is a collection of " excursions" into the real-world applications of modern mathematics. The excursions are organized into four independent parts: 1) The Mathematics of Social Choice, 2) Management Science, 3) Growth and Symmetry, and 4) Statistics. Each part consists of four chapters plus a mini-excursion (new feature in 6/e). The book is written in an informal, very readable style, with pedagogical features that make the material both interesting and clear. The presentation is centered on an assortment of real-world examples and applications specifically chosen to illustrate the usefulness, relevance, and beauty of liberal arts mathematics.

Table of Contents

Preface xiii
PART 1 The Mathematics of Social Choice
The Mathematics of Voting
The Paradoxes of Democracy
2(2)
Preference Ballots and Preference Schedules
4(1)
The Plurality Method
5(3)
The Borda Count Method
8(1)
The Plurality-with-Elimination Method
9(5)
The Method of Pairwise Comparisons
14(5)
Rankings
19(27)
Conclusion: Fairness and Arrow's Impossibility Theorem
24(1)
Key Concepts
25(1)
Exercises
25(13)
Appendix 1: Breaking Ties
38(2)
Appendix 2: A Sampler of Elections in the Real World
40(3)
References and Further Readings
43(1)
Weighted Voting Systems
The Power Game
44(2)
Weighted Voting Systems
46(2)
The Banzhaf Power Index
48(6)
Applications of the Banzhaf Power Index
54(2)
The Shapley-Shubik Power Index
56(5)
Applications of the Shapley-Shubik Power Index
61(17)
Conclusion
62(1)
Key Concepts
63(1)
Exercises
63(11)
Appendix: Power in the Electoral College
74(1)
References and Further Readings
75(1)
Fair Division
The Mathematics of Sharing
76(2)
Fair-Division Problems and Fair-Division Schemes
78(2)
Two Players: The Divider-Chooser Method
80(1)
The Lone-Divider Method
81(4)
The Lone-Chooser Method
85(3)
The Last-Diminisher Method
88(5)
The Method of Sealed Bids
93(2)
The Method of Markers
95(27)
Conclusion
98(1)
Key Concepts
99(1)
Exercises
99(20)
References and Further Readings
119(1)
The Mathematics of Apportionment
Making the Rounds
120(2)
Apportionment Problems
122(2)
A Little Bit of U.S. History
124(2)
The Mathematics of Apportionment: Basic Concepts
126(2)
Hamilton's Method
128(1)
The Quota Rule
129(1)
The Alabama Paradox
129(2)
More Problems with Hamilton's Method
131(2)
Jefferson's Method
133(2)
Jefferson's Method and the Quota Rule
135(1)
Adam's Method
136(1)
Webster's Method
137(21)
Conclusion: Balinski and Young's Impossibility Theorem
139(1)
Key Concepts
140(1)
Exercises
140(9)
Appendix 1: The Huntington-Hill Method
149(2)
Appendix 2: A Brief History of Apportionment in the United States
151(3)
References and Further Readings
154(2)
PART 2 Management Science
Euler Circuits
The Circuit Comes to Town
156(2)
Routing Problems
158(4)
Graphs
162(2)
Graph Concepts and Terminology
164(2)
Graph Models
166(2)
Euler's Theorems
168(2)
Fleury's Algorithm
170(3)
Eulerizing Graphs
173(24)
Conclusion
177(1)
Key Concepts
178(1)
Exercises
178(15)
References and Further Readings
193(1)
The Traveling Salesman Problem
Hamilton Joins the Circuit
194(3)
Hamilton Circuits and Hamilton Paths
197(2)
Complete Graphs
199(2)
Traveling-Salesman Problems
201(3)
Simple Strategies for Solving TSPs
204(3)
The Brute-Force and Nearest-Neighbor Algorithms
207(2)
Approximate Algorithms
209(1)
The Repetitive Nearest-Neighbor Algorithm
210(2)
The Cheapest-Link Algorithm
212(28)
Conclusion
216(1)
Key Concepts
217(1)
Exercises
218(18)
References and Further Readings
236(2)
The Mathematics of Networks
www.connections.net
238(2)
Trees
240(3)
Minimum Spanning Trees
243(1)
Kruskal's Algorithm
244(2)
The Shortest Distance Between Three Points
246(5)
The Shortest Network Linking More Than Three Points
251(27)
Conclusion
255(2)
Key Concepts
257(1)
Exercises
258(16)
Appendix: The Soap-Bubble Solution
274(1)
References and Further Readings
275(1)
The Mathematics of Scheduling
Directed Graphs and Critical Paths
276(2)
The Basic Elements of Scheduling
278(6)
Directed Graphs
284(1)
The Priority List Model for Scheduling
285(6)
The Decreasing-Time Algorith
291(1)
Critical Paths
292(4)
The Critical-Path Algorithm
296(1)
Scheduling with Independent Tasks
297(21)
Conclusion
300(1)
Key Concepts
301(1)
Exercises
301(13)
References and Further Readings
314(2)
PART 3 Growth and Symmetry
Spiral Growth in Nature
Fibonacci Numbers and the Golden Ratio
316(2)
Fibonacci Numbers
318(3)
The Equation x2 = x + 1 and the Golden Ratio
321(2)
Gnomons
323(7)
Gnomonic Growth
330(16)
Conclusion
331(1)
Key Concepts
332(1)
Exercises
332(11)
References and Further Readings
343(1)
The Mathematics of Population Growth
There Is Strength in Numbers
344(2)
The Dynamics of Population Growth
346(3)
The Linear Growth Model
349(5)
The Exponential Growth Model
354(7)
The Logistic Growth Model
361(17)
Conclusion
365(1)
Key Concepts
366(1)
Exercises
366(9)
References and Further Readings
375(1)
Symmetry
Mirror, Mirror, Off the Wall...
376(2)
Geometric Symmetry
378(1)
Rigid Motions
379(1)
Reflections
380(2)
Rotations
382(1)
Translations
383(1)
Glide Reflections
384(1)
Symmetry Revisited
385(5)
Patterns
390(24)
Conclusion
393(1)
Key Concepts
394(1)
Exercises
394(14)
Appendix: The Seventeen Wallpaper Symmetry Types
408(3)
References and Further Readings
411(1)
Fractal Geometry
Fractally Speaking
412(2)
The Koch Snowflake
414(5)
The Sierpinski Gasket
419(2)
The Chaos Game
421(1)
The Twisted Sierpinski Gasket
422(2)
Symmetry of Scale in Art and Literature
424(2)
The Mandelbrot Set
426(22)
Conclusion: Fractals
432(2)
Key Concepts
434(1)
Exercises
434(10)
References and Further Readings
444(2)
PART 4 Statistics
Collecting Statistical Data
Censuses, Surveys, and Clinical Studies
446(2)
The Population
448(3)
Surveys
451(5)
Random Sampling
456(3)
Sampling: Terminology and Key Concepts
459(2)
Clinical Studies
461(15)
Conclusion
465(1)
Key Concepts
465(1)
Exercises
466(7)
References and Further Readings
473(1)
Descriptive Statistics
Graphing and Summarizing Data
474(2)
Graphical Descriptions of Data
476(3)
Variables: Quantitative and Qualitative; Continuous and Discrete
479(5)
Numerical Summaries of Data
484(9)
Measures of Spread
493(21)
Conclusion
496(1)
Key Concepts
497(1)
Exercises
497(14)
References and Further Readings
511(1)
Chances, Probabilities, and Odds
Measuring Uncertainty
512(2)
Random Experiments and Sample Spaces
514(2)
Counting: The Multiplication Rule
516(2)
Permutations and Combinations
518(4)
What Is a Probability?
522(1)
Probability Spaces
523(2)
Probability Spaces with Equally Likely Outcomes
525(3)
Odds
528(16)
Conclusion
530(1)
Key Concepts
530(1)
Exercises
530(11)
References and Further Readings
541(1)
Normal Distributions
Everything Is Back to Normal (Almost)
542(2)
Approximately Normal Distributions of Data
544(2)
Normal Curves and Normal Distributions of Data
546(2)
Standardizing Normal Data Sets
548(2)
The 68-95-99.7 Rule
550(1)
Normal Curves as Models of Real-Life Data Sets
551(1)
Normal Distributions of Random Events
552(2)
Statistical Inference
554(17)
Conclusion
558(1)
Key Concepts
559(1)
Exercises
559(10)
References and Further Readings
569(2)
Answers to Selected Problems 571(58)
Index 629(6)
Photo Credits 635


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