Single Digits: In Praise of Small Numbers, by Marc Chamberland
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Single Digits: In Praise of Small Numbers, by Marc Chamberland
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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.
Single Digits: In Praise of Small Numbers, by Marc Chamberland - Amazon Sales Rank: #476240 in Books
- Brand: Chamberland, Marc
- Published on: 2015-06-02
- Original language: English
- Number of items: 1
- Dimensions: 9.40" h x 1.00" w x 6.10" l, .0 pounds
- Binding: Hardcover
- 240 pages
Single Digits: In Praise of Small Numbers, by Marc Chamberland Review "Chamberland . . . produces a fascinating, compact set of entries on mathematical problems, conjectures, and theorems. This wonderful book never loses its focus or momentum."--Publishers Weekly, starred review"[B]oth amateur and professional mathematicians alike will find new items of interest here. . . . [A] welcome, splendid, fruitful addition to my math bookshelf."--Math Tango blog"The collection is outright delightful. It will agitate the minds of students and shake the sense of know-all off many a professional and most of the amateurs."--Alexander Bogomolny, Cut the Knot blog"A bracing mathematical adventure."--Booklist"[C]onsistently entertaining and well-written. . . . [Single Digits] would be an ideal gift for a high school student who might have an interest in mathematics. It's also fun just to pick up and browse."-- William J. Satzer, MAA Reviews"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. . . . 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."--DVD, Lunar and Planetary Information Bulletin"Chamberland makes this an entertaining and historical exposition, using wit and humor throughout. . . . Single Digits has made me appreciate the many connections between the digits one to nine and diverse areas of mathematics."--Heather Moon, Math Horizons"To put it simply, this book is a delight. Chamberland (Grinnell College) has assembled a fascinating collection of vignettes, each tied to a digit from one to nine, that inform, entertain, and intrigue readers."--Choice"The range of topics included virtually guarantees that any reader will find new and unfamiliar material to enjoy. . . . [Single Digits] is a very enjoyable book which, at many points, makes some very deep mathematics quite accessible. Highly recommended."--Keith Johnson, CMS Notes"For instructors of math courses of all levels, the vignettes in Single Digits can provide a very readable introduction or jumping-off point for discussions and projects. . . . In an introductory group theory course, it would be a good exercise for students to consider perfect riffle shuffles in decks of size other than 52. Finally, a statistics class collecting and analyzing real-world data sets could consider whether Benford's Law applies in their situation."--Matthew Welz, MAA Focus
From the Back Cover
"A veritable potpourri of mathematical factoids, Single Digits will provide you with conversational ammunition for all manner of nerdy gatherings."--Henry Reich, creator of MinutePhysics and MinuteEarth
"Dispensing incisive, brief expositions of mathematical observations, facts, theorems, proofs, conjectures, and open problems, this cornucopia of a book ranges through geometry, number theory, combinatorics, topology, and many other areas. From the elegantly elementary to the sublimely difficult, each of its short sections is liable to stimulate an eager search for further enlightenment, whether from the internet, the library, or your own mind."--Avner Ash, coauthor of Elliptic Tales
"A survey of mathematical gems, ancient and modern, this book is certain to arouse the curiosity of anyone with even a passing interest in mathematics. Chamberland's clear explanations provide an enticing introduction to each topic and will make you want to learn more."--Jamie Pommersheim, coauthor of Number Theory
"This book describes properties associated with the numbers one to nine and connects important areas of mathematics, including number theory, geometry, chaos theory, and applied mathematics. Single Digits is filled with nuggets of mathematical information, compelling topics, and interesting ideas for anyone curious about the subject."--Lee Fothergill, Mount Saint Mary College
"A celebration of small numbers, Single Digits presents mathematical vignettes organized by their connection to single nonzero digits. Progressing from the elementary to the more elaborate, Chamberland brings together some really interesting mathematics, and his well-told stories will intrigue a general, knowledgeable audience."--Jennifer Quinn, University of Washington, Tacoma
About the Author Marc Chamberland is the Myra Steele Professor of Natural Science and Mathematics at Grinnell College. He is the creator of the YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone.?
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Most helpful customer reviews
1 of 1 people found the following review helpful. This book is a great idea but what appears here is a first draft By Brian M. O'Rourke This book is a great idea but what appears here is a first draft. The book needs more meat to make it understandable. A visual proof of the Pythagorean Theorem is "presented" in Figure 2.4 but the explanation does not match the figure -- and figure and explanation are on the opposite sides of the same page, which you keep turning and turning, trying to figure things out.Here's a quote from The Twin Prime Conjecture:"...PrimeGrid announced the largest known twin primes: 3, 756,801,695 x 2,666,669 +/-1. These numbers have 200,700 decimal digits."That is simply senseless. Like so many places in this book, you read, you stop, you scratch your head, and you ask yourself, "What the heck does that really mean?" This book does not tell you.
1 of 1 people found the following review helpful. Fascination collection for math lovers By James Hopper Cool book. Full of fascinating tidbits from all branches of mathematics. Nine chapters on the numbers 1-9 naturally. No pun intended. Chapter 1 has 13 topics treated briefly, each illustrating the number one,His choices are interesting. Chapter one has a section on the Cantor middle third set. So what does this have to do with the number one? After an infinite number of increasingly smaller middle third intervals of a segment of length one are removed, the total length of all of the removed pieces is one, yet an uncountable set of numbers not removed ( Cantor dust) remains on the interval. Lots of stuff I never saw before. A treasure trove for math teachers and mathophiles everywhere. Loved it.
0 of 0 people found the following review helpful. interesting assortment of mathematical curiosities By XY Regular consumers of 'popular' math books will encounter a few chestnuts they've seen many times before (e.g., Erdos number), but there are enough mathematical curiosities in this book to justify taking a look. I picked up this book in the New Books section of my local library, and am planning to buy it. I only noticed one error: in Figure 3.1, the arrow should loop back to the "4" rather than the "2".
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