Just some good books about Math, for those who like Math

The math department, every year, gives awards to four students (some with some monetary compensation for college, some not). I was put in charge of thinking of some books to give with these awards. I sent my initial thoughts to my department head:

For the Math/Science award, I suggest:

*D’Arcy Thompson’s On Growth and Form is full of beautiful prose, and relates the sciences to mathematics. The actual science is wrong, but it is considered a classic piece of literature.
*Anthony Zee’s Fearful Symmetry about the important — crucial — role that mathematical symmetry plays in modern physics. A super-well written book for the layman.

For all other awards, I put out there:

*Silvanus P. Thompson’s Calculus Made Easy has a deceptive title. And it was written in 1910. But almost all accounts agree it is one of the best textbooks around. Even for those who might have thought they understood the conceptual undergirdings of calculus, this book will illuminate them further, without any obtuseness.
*Douglas Hofstadter’s Godel, Escher, Bach is standard reading for all math lovers everywhere.
*Calvin C. Clawson’s Mathematical Mysteries is one of the best and most accessible popular math books I’ve read.
*G.H. Hardy’s A Mathematician’s Apology is quite good at explaining what a mathematician actually does philosophically when he works, written by one of the most important mathematicians of modern times.

My final recommendation differed slightly:

Award 1: Timothy Gowers’ The Princeton Companion to Mathematics

Award 2: Douglas Hofstadter’s Godel, Escher, Bach; Thomas Kuhn’s The Structure of Scientific Revolutions; Bruce Hunt’s The Maxwellians; Silvanus P. Thompson’s Calculus Made Easy

Award 3 & 4: G.H. Hardy’s A Mathematician’s Apology

I really enjoyed thinking through which books might be appropriate. Also I didn’t want to give something I hadn’t read. But this process reminded me of all those books about math out there that I haven’t read (yet), but have really want to. Like Polya’s How to Solve It and David Foster Wallace’s Everything and More.

I posted this book award stuff on twitter, and got some great reactions. (Read from the bottom upwards.)

And then I thought: hey, you all must have a favorite math or math-y book that you’d want to have your favorite students read. I’d love to know your favorites! (Plus this list could help inspire me to do some quality reading this summer!)

16 comments

Derbyshire’s book Prime Obsession is perhaps the only time I’ve read a math book and I was in suspense about what was going to happen next, as if it were a murder mystery. It’s also accessible enough to high school I could recommend it to my students.

I’m also a fan of Godel’s Theorem: An Incomplete Guide to Its Use and Abuse. (Not meant for high school, though.)

Finally, The Universal History of Numbers is one of the most astonishing pieces of scholarship I’ve ever come across.

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Here’s what I said.

I’d recommend Dunham’s Journey Through Genius, Abbott’s Flatland, Beckmann’s A History of π, Paulos’s Innumeracy, and Lakatos’ Proofs and Refutations. Also, the MAA has a 14 of Martin Gardner’s books on one CD.

Bell’s Men of Mathematics is a great read, but he takes a lot of liberties for a nonfiction book (besides the problem of only focusing on the *men* of mathematics).

Other responses on Twitter:

cannonsr@JackieB I liked Ian Stewart’s Letters to a Young Mathematician. Don’t actually have a copy on my shelf though. http://tinyurl.com/c23o2k

sumidiot@JackieB “Mathematical Journeys” by Schumer, or Conway & Guy: “The Book of Numbers” might be fun

k8nowak@JackieB _How to Solve It_ is a fantastic book, but might be a little dry for a younger reader.

k8nowak@JackieB I’d consider What is Mathematics? by Courant or Journey Through Genius by Dunham or Mathematics:A V. Short Introduction by Gowers

k8nowak@JackieB or A Tour of the Calculus by Berlinski or The Man Who Loved Only Numbers by Hoffman or Euclid in the Rainforest by Mazur

yuglook@samjshah “50 mathematical ideas you really need to know” Fun for students who may pursue math in future, but haven’t had much exposure.

winyang@samjshah The Man Who Only Loved Numbers.

One more from Twitter:

winyang@samjshah Oh, and also DFW’s Everything and More: A Compact History of Infinity.

My favorite book to give students is “Adam Spencer’s Book of Numbers” because it’s the funniest and I think it has the highest likelihood of students actually reading it over the summer. A few years ago I started each of my classes by having students pick a number and then I’d read the page about it. [The book has a page or two for each number 1-100, with mathematical and cultural facts for each]

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I still have my Men of Mathematics on the shelf. I’ve read it a few times, including since I learned about how free Bell was with some facts… And I’m proud to have won it, but it’s not a very good book.

Devlin’s (I know, I know, I don’t think much of some of the things he’s written recently on pedagogy, but that’s a separate issue) “Language of Mathematics”?

A nice edition of “The Elements”? (thank Kate for reminding us)

A Gardner puzzle book? (There’s a nice CD somewhere)

Livio’s phi book, or Kaplan’s 0 book?

I like The Man Who Counted and the Number Devil, not just for kids (but I do like them for kids), but for older kids they read very easy, and they have a chance to reflect on simpler mathematics in a non-textbook layout.

Jonathan

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The Princeton Companion to Mathematics is a wonderful, wonderful book, but not something I’d give to a high schooler unless I knew they were going to do maths at university. The “prerequisites” chapter includes real analysis and manifolds, for example. (If they are doing maths at university, though, they’ll really enjoy it after their first or second year.)

I would *strongly* recommend Keith Ball’s “Strange Curves, Counting Rabbits, and other Mathematical Explorations”. It’s very well-written, and there’s some extremely nice stuff in there – Pick’s theorem (an incredibly nice way of solving lattice problems of the type often given to children in school), Stirling’s approximation to n factorial, the dragon curve (a continuous bijection from [0,1] to [0,1]x[0,1]) and the irrationality of pi and e all feature. With proofs. In terms of prerequisites, some chapters require calculus but that’s about as far as it goes.

For my own records, I just wanted to link to Maxwell’s Demon which has a good list of books too: http://maxwelldemon.com/2009/07/20/mathematical-materials/

And one more blog post: http://math-blog.com/2009/07/31/my-mid-2009-math-reading-list/

There are some really great picks here, both in the post and in the comments. I’ll add my own recommendations for Derbyshire’s “Unknown Quantity” and Keith Devlin’s “The Millennium Problems”.

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