For courses in Liberal Arts Mathematics.
Discover the power and beauty of math
Excursions in Modern Mathematics by Peter Tannenbaum helps learners develop an appreciation for the aesthetics and applicability of mathematics. Contemporary topics ranging from COVID-19 to election polling demonstrate that math is a usable tool, applicable and interesting for anyone. Refinement and updating of examples and exercises, plus increased resources for both students and instructors, make the 10th Edition a relevant, accessible, and complete program.
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Table of Contents:
PART I: 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-ShubikPower
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 II: 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
5.4Eulerizingand Semi-EulerizingGraphs
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, andMaxSTs
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 III: 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 IV: 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 V: 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
Credits
Index
Index of Applications
About the Author :
About our author Peter Tannenbaum is Professor Emeritus of Mathematics at the California State University, Fresno. He has also held faculty positions at the Universidad Simon Bolivar in Caracas, Venezuela, the University of Arizona in Tucson, Arizona, and as a Fulbright visiting scholar at the Universidad de San Luis in San Luis, Argentina.
Professor Tannenbaum received Bachelor's degrees in Political Science and Mathematics, and a Ph.D. in Pure Mathematics, all from the University of California, Santa Barbara. His mathematical research interests focus primarily in the interface between combinatorics, finite groups and probability, and he has published papers in combinatorial designs, finite projective geometries, partitions of groups, probability, generating functions and the computation of power indexes.
Professor Tannenbaum has also worked on various aspects of mathematics education, including curriculum development for undergraduate general education mathematics, the preparation of secondary teachers, and Young Scholar Institutes (summer camps for talented high school students). In recognition of this work he has received many grants and awards, including a Mathematical Association of America Award for “Distinguished College or University Teaching of Mathematics.”
Professor Tannenbaum was born in Genoa, Italy, and at the age of 4 his family moved to Montevideo, Uruguay, where he spent his formative years. Beyond mathematics, his interests and hobbies include travel, languages (he speaks 5), hiking, riding (bikes and horses), cooking and most recently, painting. He and his wife Sally have 3 children (twin boys and a girl) and currently live in Santa Barbara, California.
