Single Digits - In Praise of Small Numbers
by Marc Chamberland
Princeton University Press | June 2015 | ISBN-10: 0691161143 | True PDF | 240 pages | 38.3 mb

The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics.
Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan's conjecture, and so much more. The book's short sections can be read independently and digested in bite-sized chunks--especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem.
Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.

About the Author 
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Marc Chamberland is the Myra Steele Professor of Mathematics and Natural Science at Grinnell College. He has published over 40 research articles in diverse areas such as number theory, combinatorics, differential equations, and dynamical systems. Marc is a huge proponent of experimental mathematics, a growing paradigm which uses computers to discover, conjecture and prove mathematical results. He is passionate about communicating the beauty and excitement of mathematics. Besides this book, Marc is also the creator of the youtube channel Tipping Point Math which shows "math as you never imagined". He has given about 100 talks on research topics, math problems for students, and creativity.

CONTENTS
Preface xi
Chapter 1 The Number One 1
Chapter 2 The Number Two 24
Chapter 3 The Number Three 69
Chapter 4 The Number Four 111
Chapter 5 The Number Five 132
Chapter 6 The Number Six 156
Chapter 7 The Number Seven 170
Chapter 8 The Number Eight 191
Chapter 9 The Number Nine 205
Chapter 10 Solutions 216
Further reading 219
Credits for illustrations 223
Index 225

Video about this book:
 
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