Excursions in Modern Mathematics

by Tannenbaum, Peter

• ISBN13: 9780321568038
• ISBN10: 0321568036
• Edition: 7th
• Format: Hardcover
• Copyright: 2008-12-28
• Publisher: Pearson

Summary

Excursions in Modern Mathematics, Seventh Edition, shows readers that math is a lively, interesting, useful, and surprisingly rich subject. With a new chapter on financial math and an improved supplements package, this book helps students appreciate that math is more than just a set of classroom theories: math can enrich the life of anyone who appreciates and knows how to use it.

This collection of "excursions" into modern mathematics consists of four independent learning modules--1) Social Choice, 2) Management Science, 3) Growth and Symmetry, and 4) Statistics. It is written in an informal, very readable style, with pedagogical features that make material both interesting and clear. Coverage centers around an assortment of real-world examples and applications, demonstrating the beauty and relevance of mathematics.

Author Biography

Peter Tannenbaum has  bachelor's degrees in Mathematics and Political Science and a Ph. D. in Mathematics, all from the University of California, Santa Barbara. He has held faculty positions at the University of Arizona, Universidad Simon Bolivar (Venezuela), and is currently  professor of mathematics at  the California State University, Fresno. His current research interests are in the interface between mathematics, politics and behavioral economics. He is also involved in mathematics curriculum reform and teacher preparation. His hobbies are travel, foreign languages and sports. He is married to Sally Tannenbaum, a professor of communication at CSU Fresno, and is the father of three (twin sons and a daughter).

Table of Contents

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The Mathematics of Social Choice

The Mathematics of Voting: The Paradox of Democracy

Preference Ballots and Preference Schedules

The Plurality Method

The Borda Count Method

The Plurality-with-Elimination Method (Instant Runoff Voting)

The Method of Piecewise Comparisons

Rankings

Profile: Kenneth J. Arrow

Key Concepts

Exercises

Projects and Papers

References and Further Readings

The Mathematics of Power: Weighted Voting

An Introduction to Weighted Voting

The Banzhaf Power Index

Applications of the Banzhaf Power Index

The Shapely-Shubik Power Index

Applications of the Shapely-Shubik Power Index

Profile: Lloyd S. Shapely

Key Concepts

Exercises

Projects and Papers

References and Further Readings

The Mathematics of Sharing: Fair-Division Games

Fair-Division Games

Two Players: The Divider-Chooser Method

The Lone-Divider Method

The Lone-Chooser Method

The Last-Diminisher Method

The Method of Sealed Bids

The Method of Markers

Profile: Hugo Steinhaus

Key Concepts

Exercises

Projects and Papers

References and Further Readings

The Mathematics of Apportionment: Making the Rounds

Apportionment Problems

Hamilton's Method and the Quota Rule

The Alabama and Other Paradoxes

Jefferson's Method

Adams's Method

Webster's Method

His

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