I started reading Spivak's Calculus about a month ago and I'm at the end of chapter two, so this is not really calculus yet. However, I find the problems really difficult and the answer keys are not very helpful. I can answer some problems but a lot of them, I've no idea what I should even start with. Also, it takes me a very long time to do each problem. (10-15 minutes on average).
I've no prior experience to writing proofs, but I've watched a few youtube videos on it. The problem is generally not the proofs problems but the one where they say "Find a formula" or "derive this equation". Those, i can never do.
Is there some prior knowledge that I should know before reading this besides knowing how to do proofs? Or, are these problems generally difficult to begin with? Or, am I not paying attention to what's written in the chapter?
Also, should I look at/try every single problem are is doing like the first page of them sufficient? I had plan to do every problem in the first chapter but called it quits after they started putting epsilons everywhere.
Thanks.
Best Answer
Given that you mention that you have "no prior experience [in] writing proofs", you may find Velleman's How to Prove It: A Structured Approach to be a helpful preparation for Spivak's wonderful book. And it is a wonderful book, so please keep at it, or come back to it after Velleman. Note that I haven't read Velleman, but it seems to get universal praise for "preparing students to make the transition from solving problems to proving theorems".
I'd recommend that you do not obsess about finishing all, or even most, of the problems on first reading. I think it's worthwhile to give it a first read without worrying that you are getting every ounce out of it. If you feel like you're getting most of it, keep going. Do plan to give it a second read, though.
Also, there's some good discussion on how to read mathematics books in how-to-read-a-book-in-mathematics.