How to Guard an Art Gallery and Other Discrete Mathematical Adventures

by T.S. Michael

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.

Genres: Mathematics, Nonfiction, Science

272 pages, Paperback

First published July 27, 2009

Reviews

[Ed Smiley · Rating 3 out of 5]

Interesting exploration of algorithms. (Rules of calculation for you non-math types.)
Turns out that there is a lot of math in something even as simple as stationing guards or cameras in any polygonal room so that there is line-of-sight to every part of every wall.

[Ajay · Rating 2 out of 5]

Liked the book for the reason that they have so many ways of solving one problem- even the Die Hard water bottle problem. Helped me solve my Tartaglian Problem.

[Matt · Rating 4 out of 5]

I won't pretend I understood even half the concepts in this book, but the moments of clarity were a lot of fun!

[Chris Herdt]

Flipped through this at the bookstore. Looks like an entertaining exploration of combinatorics.