Math Readings
"A mathematician is a machine for turning coffee into theorems."--Paul Erdös
Edwin Abbott
Flatland. A clever, almost science-fictional treatment of geometry from the viewpoint of 2-dimensional creatures whose society can also be seen as a Victorian social commentary/satire. A good analogy leading up to the idea of shapes in higher dimensions.
Robbie Bell & Michael Cornelius
Board Games Round the World: A Resource Book for Mathematical Investigations. A survey of games, oriented toward the grade school teacher interested in introducing mathematical concepts to kids through games.
Barry Cipra
Misteaks and How to Find Them Before the Teacher Does. Geared toward high school or first-year college (single-variable) calculus students. Tricks on how to catch those darn integration errors. And yes, the title is correct.
Philip J. Davis & Reuben Hersh
The Mathematical Experience and Descartes' Dream. I read the first book twice in high school. The first time it convinced me that math wasn't such a Dreadful Subject. The second time was for fun. It tells a nonmathematician what life is like for mathematicians, as well as some of the philosophical and historical underpinnings, and has a little bit of everything. I have a used copy, 1st edition; I'm not sure what differences appeared in the later edition(s?). The second is a follow-up on the "mathematization" of society.
Hans Magnus Enzensberger
The Number Devil: A Mathematical Adventure. Illustrated by Rotraut Susanne Berner; translated by Michael Henry Heim (originally Der Zahlenteufel: Ein Kopfkissenbuch für alle, die Angst vor der Mathematik haben). An entertaining tale, ostensibly for children, about a math-phobic boy who meets a number devil in his dreams and is initiated into the mysteries of "hopping numbers" (exponents), "prima donna numbers" (primes), the Goldbach conjecture, and more. Even better, the in-jokes and references ensure that the reader who does know some math will be amused: Felix Klein makes an appearance as "Professory Happy Little," for example, and the index includes both the number devil's terminology as well as standard terminology.
Graham Flegg
From Geometry to Topology. A gentle introduction to topology from a geometrical angle.
Martin Gardner
Aha! Gotcha!: Paradoxes to Puzzle and Delight.
Time Travel and Other Mathematical Bewilderments. The 12th collection of his "Mathematical Games" column in Scientific American. I skimmed this (finals week), but many neat subjects are covered: time travel, polygonal tilings, tangrams, anamorphisms, and more.
James Gleick
Chaos. A popular introduction to chaos theory and its development. It's at least worth looking at for the diagrams and the cool color plates of fractals. (I think the idea that math can be beautiful is valuable no matter what.)
Timothy Gowers
"The Two Cultures of Mathematics" [PDF]. On the problem-focused vs. theory-focused cultural divide in research mathematics.
Douglas A. Hofstadter
This isn't a book; it's a commitment and a work of art, but very much worth the time. Hofstadter discusses Gödel's incompleteness theorem, Escher's art, recursion in Bach's music, artificial intelligence...
Darrell Huff
How to Lie with Statistics. This book was first published in 1954 and remains depressingly relevant; with little modification, all of its examples could apply to statistical flimflammery perpetuated on the public today. This should almost be required reading in some math course, somewhere.
George Ghevergese Joseph
The Crest of the Peacock. A revised edition is available in the U.S., but I read the British edition, courtesy of Jo Boaler. A fascinating, though somewhat technical (from the lay reader's viewpoint), survey of non-European roots of mathematics. Though Joseph is adamant that non-European civilizations made sophisticated discoveries, he is careful to acknowledge gaps in the available data and interpretations, and explains his choice of foci. I enjoyed it as a much-needed corrective to the perception that only Europeans produced significant mathematics.
Leapfrogs Group
Images of Infinity. Written and compiled by Ray Hemmings & Dick Tahta; design and artwork by David Cutting Graphics; calligraphy by Gaynor Goffe; illustrations by Klaas Bil and Vicky Squires. A wonderful book that introduces mathematical conceptions of infinity through an interweaving of text, literary references, examples, and illustrations: Escher's hands drawing hands, recursion and sequences, Jorge Luis Borges and Zeno, fractals and Hotel Infinity; and it culminates with Cantor's "diagonal slash" proof that the cardinality of the reals is different from the cardinality of the integers. I was fascinated by this when I came across it in my high school library, and delighted to come across it in the Stanford Bookstore (as you may guess, I couldn't resist the opportunity to pick up my own copy). The book's creators have managed to take some very rich mathematics and make it accessible and visually appealing without losing the flavor of the topic.
Paul Lockhart
"A Mathematician's Lament" [PDF]. A powerful critique of the backwardness of early math education. If you are in elementary/secondary math pedagogy and you haven't seen this, please read this.
Ivan Moscovich
The Magic Cylinder Book: Hidden Pictures to Colour and Discover. An entertaining book of anamorphisms that requires no math background to enjoy, but does demystify their construction for the curious. Another excellent offering from Tarquin Publications.
Theoni Pappas
The Joy of Mathematics and Mathematical Footprints. Pappas delights with an astonishing variety of interesting, intelligent, and accessible-yet-challenging mathematics and mathematical history. This might even appeal to your favorite math-phobe.
John Allen Paulos
Innumeracy: Mathematical Literacy and Its Consequences and Beyond Numeracy: Ruminations of a Numbers Man. The first is a lament on the state of math education, the second an eclectic math survey with anecdotes.
A Mathematician Reads the Newspaper. This time Paulos discusses the many mathematical fallacies that appear, often for the purpose of misleading the reader, in the newspaper. Along the way he touches on politics, health statistics, psychology and more, with special reference to notable (U.S.) issues near the time of his writing (1995).
Ivars Peterson
The Mathematical Tourist: Snapshots of Modern Mathematics, Islands of Truth: A Mathematical Mystery Cruise, and Jungles of Randomness. Surveys of modern mathematical research, written on a level such that someone with a layman's math background can appreciate math as a living, growing and fascinating field.
William Poundstone
Labyrinths of Reason. A collection of paradoxes and their implications. It almost convinced me I wanted to study philosophy. (And then, in college, I hit Hume.)
R.L. Rivest, A. Shamir, & A. Adleman
"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems" [PDF]. RSA encryption! We were given copies of this in at the end of an undergrad applied algebra course, and it was a wonderful way to end the semester.
Reg Sheppard & John Wilkinson
Strategy Games: A Collection of 50 Games & Puzzles to Stimulate Mathematical Thinking. As the authors note, none of these games involves any dice, but the strategies therein can make for both entertaining and mathematically interesting diversions. Helpfully, the authors also include commentary and brief analyses on each game for the teacher's benefit. Far too neat for words.
Raymond Smullyan
The Lady or the Tiger; The Riddle of Scheherazade; Satan, Cantor, and Infinity; and What Is the Name of This Book? Collections of mathematical puzzles and anecdotes, leaning toward logic, though combinatorics, algebra, Gödel's incompleteness theorems and Cantorian infinities also make appearances. Quite accessible and lots of fun.
M. Mitchell Waldrop
Complexity. This does for complexity theory what Gleick did for chaos theory in explaining the field's origins, rationales and applications.
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