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JimJinkinsJun 2009

W. W. Sawyer

Mathematician's Delight Prelude to Mathematics

What is Calculus About? This is best intro to calculus I ever saw. When I taught introductory calculus, I recommended it to all my students.

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mechanical_fishSep 2008

A snapshot of my bookshelf's "math" section, which really hasn't changed much since I was in high school and hadn't taken calculus:

W.W. Sawyer, What is Calculus About? and Mathematician's Delight

Courant and Robbins, What is Mathematics?

Hogben, Mathematics for the Million

Steinhaus, Mathematical Snapshots

Ivars Peterson, The Mathematical Tourist

Davis and Hersh, The Mathematical Experience

Polya, How to Solve It

Huff, How to Lie With Statistics

McGervey, Probabilities in Everyday Life

Raymond Smullyan: The Lady or the Tiger, Alice in Puzzle-Land, others

Anything by Martin Gardner. I happen to have picked up Mathematical Magic Show and Mathematical Circus, but I'm sure there are many other collections.

I also recommend cryptography stuff. David Kahn's The Codebreakers is not really a math book, but it is awesome and it stars mathematicians, as does Simon Singh's The Code Book. You could read Schneier's Applied Cryptography.

This is HN, so I would be remiss if I didn't point out that you can learn a lot of fun and useful math by reading SICP, Knuth, or any good algorithms book.

If anybody out there knows a good, spirited statistics book addressed to someone who knows calculus, tell me. I keep planning to go through Fundamentals of Applied Probability Theory but I never get around to it; see "Related Resources" here:

http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Compute...

Having said all of that: I have a Ph.D. in physics/EE, so I've got to tell you, if you haven't tried calculus you haven't lived. ;) I'm not sure how to go about learning calculus in a fun way for a mathematician -- I took fairly standard first- and second-year college courses in calculus and physics and learned it that way. The folks on Amazon seem kind of enthusiastic about Spivak:

http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098918/...

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mechanical_fishJun 2008

* ...an unsupervised learner has the ability to ask a supervisor for useful tasks to train on. In academia, sadly, this doesn't seem to happen below the PhD level.*

That isn't quite true. You're describing much of my high school math and physics education: I had teachers, and I "took" the official classes (i.e. I sat in class, most of the time, and I took the exams and did much of the homework...) but my teachers (who were quite awesome) recognized that I was ahead of the class and enjoyed teaching myself, so they threw me books like PSSC Physics and What is Calculus About? and told me to have fun.

That was, however, unofficial and sort of under the radar. I expect such a style of learning to continue to rise in popularity now that the Web is here. It's just easier than ever before to run an active learning program: There's so much stuff online to steer the students toward, and even the offline stuff is easier to find -- there are book-recommendation services and blogs to help you find the best print books, and used-book services to sell them to you cheap. It really is getting to the point where I could set myself up as a "professor" right here in my home office and mentor folks over Skype as they go from one online resource to another, at big savings over paying a college for the same services.

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Alex3917Jun 2007

Good post. The only other Socratic book I own is "What is Calculus about" by W.W. Sawyer. It's more loosely Socratic though. There are paragraphs of text interspersed with questions that either ask you to look for a pattern, or else follow a statement to its logical conclusion.

Not as good as The Little Schemer, but it's still cool that you can learn traditional (non-lambda) calc knowing only addition and subtraction.

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