This is a

review from my collection of

math book reviews.

**Calculus** by Michael Spivak

This is a book everyone should read. If you don't know calculus and have the time, read it and do all the exercises. Parts 1 and 2 are where I finally learned what a limit was, after three years of "explanations" from bad calculus books. The whole thing is the most coherently envisioned and explained treatment of one-variable calculus I've seen; Spivak's plan and the nature of the insight he's trying to impart are evident throughout.

The book has flaws, of course. The exercises get a little monotonous because Spivak has a few tricks he likes to use repeatedly to construct them. There is perhaps too little material on applications, but this can be found in other books (try Apostol's *Calculus*, or *Differential and integral calculus* by Courant if you're brave). Also, Spivak sometimes avoids sophistication at the expense of clarity, as in the proofs of Three Hard Theorems in chapter 8 (where a lot of epsilon-pushing takes the place of the words "compact" and "connected"). Nevertheless, this is the best calculus book overall, and I've seen it do a wonderful job of brain rectification on many people.

*Addendum from Pete Clark, one of my co-reviewers:* Yes, it's good, although perhaps more of the affection comes from more advanced students who flip back through it? Most of my exposure to this book comes from tutoring and grading for 161 *[the University of Chicago honors first-year calculus class]*, but I seriously believe that working as many problems as possible (it must be acknowledged that many of them are difficult for first year students, and a few of them are really hard!) is invaluable for developing the mathematical maturity and epsilonic technique that no math major should be without.