How to Guard an Art Gallery: And Other Discrete Mathematical AdventuresAn “accessible and engaging” tool for understanding the branch of mathematics that is so crucial to modern computer science, using real-life problems (Mathematical Reviews). 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 the real world 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. |
Contents
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 |
245 | |
251 | |
Other editions - View all
How to Guard an Art Gallery and Other Discrete Mathematical Adventures T.S. Michael No preview available - 2009 |
How to Guard an Art Gallery and Other Discrete Mathematical Adventures T.S. Michael No preview available - 2009 |
Common terms and phrases
algorithm arithmetic array A(v,w array A(v,−w art gallery problems art gallery theorem attainable numbers less billiard table boundary lattice points Bruce Willis calendar circular pizza code word coin colorful column configuration corners count cuts dark pixels denominations diagonal dimes Diophantine approximation discrete mathematics edges Euler’s formula Example fountain Gauss’s lemma greatest common divisor guarded guards half-guards integer interior lattice point enumerator lattice polygon Legendre symbol less than vw line drawing algorithm Mathematical maximum number modular arithmetic multiple N-largement nonresidue number of guards number of lattice number of pizza number theory numbers greater odd prime partition Pick’s formula pixel x,y pizza pieces pizza-cutter’s problem plane graph polyhedron positive integer primitive lattice triangle protect quadratic nonresidue Quadratic Reciprocity quadratic residue modulo rectangle right triangles right-angled galleries satisfies segment joining 0,0 sequence shaded Show solution staircase sweep-line sylver coinage Sylvester’s units of water vertex water measuring problem