Excursions in Modern Mathematics

Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgments
New in This Edition
Part 1: Social Choice
	1. The Mathematics of Elections The Paradoxes of Democracy
		1.1. The Basic Elements of an Election
		1.2. The Plurality Method
		1.3. The Borda Count Method
		1.4. The Plurality-with-Elimination Method
		1.5. The Method of Pairwise Comparisons
		1.6. Fairness Criteria and Arrow’s Impossibility Theorem
		Conclusion
		Key Concepts
		Exercises
	2. The Mathematics of Power Weighted Voting
		2.1. An Introduction to Weighted Voting
		2.2. Banzhaf Power
		2.3. Shapley-Shubik Power
		2.4. Subsets and Permutations
		Conclusion
		Key Concepts
		Exercises
	3. The Mathematics of Sharing Fair-Division Games
		3.1. Fair-Division Games
		3.2. The Divider-Chooser Method
		3.3. The Lone-Divider Method
		3.4. The Lone-Chooser Method
		3.5. The Method of Sealed Bids
		3.6. The Method of Markers
		Conclusion
		Key Concepts
		Exercises
	4. The Mathematics of Apportionment Making the Rounds
		4.1. Apportionment Problems and Apportionment Methods
		4.2. Hamilton’s Method
		4.3. Jefferson’s Method
		4.4. Adams’s and Webster’s Methods
		4.5. The Huntington-Hill Method
		4.6. The Quota Rule and Apportionment Paradoxes
		Conclusion
		Key Concepts
		Exercises
Part 2: Management Science
	5. The Mathematics of Getting Around Euler Paths and Circuits
		5.1. Street-Routing Problems
		5.2. An Introduction to Graphs
		5.3. Euler’s Theorems and Fleury’s Algorithm
		5.4. Eulerizing and Semi-Eulerizing Graphs
		Conclusion
		Key Concepts
		Exercises
	6. The Mathematics of Touring Traveling Salesman Problems
		6.1. What Is a Traveling Salesman Problem?
		6.2. Hamilton Paths and Circuits
		6.3. The Brute-Force Algorithm
		6.4. The Nearest-Neighbor and Repetitive Nearest-Neighbor Algorithms
		6.5. The Cheapest-Link Algorithm
		Conclusion
		Key Concepts
		Exercises
	7. The Mathematics of Networks The Cost of Being Connected
		7.1. Networks and Trees
		7.2. Spanning Trees, MSTs, and MaxSTs
		7.3. Kruskal’s Algorithm
		Conclusion
		Key Concepts
		Exercises
	8. The Mathematics of Scheduling Chasing the Critical Path
		8.1. An Introduction to Scheduling
		8.2. Directed Graphs
		8.3. Priority-List Scheduling
		8.4. The Decreasing-Time Algorithm
		8.5. Critical Paths and the Critical-Path Algorithm
		Conclusion
		Key Concepts
		Exercises
Part 3: Growth
	9. Population Growth Models There Is Strength in Numbers
		9.1. Sequences and Population Sequences
		9.2. The Linear Growth Model
		9.3. The Exponential Growth Model
		9.4. The Logistic Growth Model
		Conclusion
		Key Concepts
		Exercises
	10. Financial Mathematics Money Matters
		10.1. Percentages
		10.2. Simple Interest
		10.3. Compound Interest
		10.4. Retirement Savings
		10.5. Consumer Debt
		Conclusion
		Key Concepts
		Exercises
Part 4: Shape And Form
	11. The Mathematics of Symmetry Beyond Reflection
		11.1. Rigid Motions
		11.2. Reflections
		11.3. Rotations
		11.4. Translations
		11.5. Glide Reflections
		11.6. Symmetries and Symmetry Types
		11.7. Patterns
		Conclusion
		Key Concepts
		Exercises
	12. Fractal Geometry: The Kinky Nature of Nature
		12.1. The Koch Snowflake and Self-Similarity
		12.2. The Sierpinski Gasket and the Chaos Game
		12.3. The Twisted Sierpinski Gasket
		12.4. The Mandelbrot Set
		Conclusion
		Key Concepts
		Exercises
	13. Fibonacci Numbers and the Golden Ratio Tales of Rabbits and Gnomons
		13.1. Fibonacci Numbers
		13.2. The Golden Ratio
		13.3. Gnomons
		13.4. Spiral Growth in Nature
		Conclusion
		Key Concepts
		Exercises
Part 5: Statistics
	14. Censuses, Surveys, Polls, and Studies The Joys of Collecting Data
		14.1. Enumeration
		14.2. Measurement
		14.3. Cause and Effect
		Conclusion
		Key Concepts
		Exercises
	15. Graphs, Charts, and Numbers The Data Show and Tell
		15.1. Graphs and Charts
		15.2. Means, Medians, and Percentiles
		15.3. Ranges and Standard Deviations
		Conclusion
		Key Concepts
		Exercises
	16. Probabilities, Odds, and Expectations Measuring Uncertainty and Risk
		16.1. Sample Spaces and Events
		16.2. The Multiplication Rule, Permutations, and Combinations
		16.3. Probabilities and Odds
		16.4. Expectations
		16.5. Measuring Risk
		Conclusion
		Key Concepts
		Exercises
	17. The Mathematics of Normality The Call of the Bell
		17.1. Approximately Normal Data Sets
		17.2. Normal Curves and Normal Distributions
		17.3. Modeling Approximately Normal Distributions
		17.4. Normality in Random Events
		Conclusion
		Key Concepts
		Exercises
Answers To Selected Exercises
Index
Credits
Index of Applications