How to Guard an Art Gallery and Other Discrete Mathematical Adventures

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JHU Press, Aug 7, 2009 - Mathematics - 272 pages
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What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery?

Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery.

This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.

 

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Contents

1 How to Count Pizza Pieces
1
2 Count on Picks Formula
33
3 How to Guard an Art Gallery
73
4 Pixels Lines and Leap Years
113
5 Measure Water with a Vengeance
139
6 From Stamps to Sylver Coins
169
Quadratic Residues
207
References
245
Index
251
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About the author (2009)

T. S. Michael is an associate professor of mathematics at the United States Naval Academy.

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