What is calculus about?

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.

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 mathemati…

… 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 r…

… 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.