dbh2ppa wrote:has anyone worked through spivak's "calculus"?
1) is it possible to work through it without prior mathematical training (other that high-school math)?
2) if the answer to the prior question is "no way, never, you're crazy", what's a good book to study to prepare for this one?
3) how long should it take to work though the exercises on the chapters? a day? two days? a week? a month? indefinite? go on until you solve them, regardless of the time? work on them for x hours, then look at the answer book or skip them?
4) is one supposed to solve the exercises based strictly on what's stated in the chapter (using only the definitions, axioms and theorems in the chapter and the previous ones)? or is one supposed to have/use prior knowledge?
I mostly know it by reputation, though I did just now look at a few pages via Amazon preview.
1) Beyond high school algebra, it appears to require only "mathematical maturity". Depending on your high school, logic puzzle experience, and so on you may already have some of this. If you don't, it may well be a decent book to work through in order to develop such maturity. Just understand that things might be slow going until you develop it. Also note that more typical calculus books tend to require and exercise far less mathematical maturity.
Roughly speaking, if you want to learn math for the sake of learning math - if you love puzzles and think you might be a mathematician - then it is probably a decent book to try. If you just want to get ahead of a normal college calc class there are probably easier books with more pretty pictures.
2) To develop mathematical maturity, I recommend searching technical or university bookstores for a book which has proofs and which can be read with work. One size doesn't fit all, but Dover has a range of inexpensive paperbacks which might be a decent place to start.
3) Spivak appears to have stars in front of some problems. At a glance I'd estimate that the star free problems should normally take 5-10 minutes. Starred problems appear to involve more brainstorming, I'd probably be ready to give them 30 minutes or more before asking for help.
4)It does appear to be fairly axiomatic in that sense.