- #1

TheLastMagician

- 6

- 0

Foundations: Algebra and Geometry by Beardon

Calculus/analysis: Calculus by Spivak

Linear algebra: Firedberg Insel

Abstract algebra: Allan Clarke

This is the main skeleton of my study for the next year. I will also be kept busy by homework assignments, lectures, etc. so I think this is enough, however I am seeking your opinions on how good my study plan is (for someone who doesn't know any university math). I am also open to suggestions for books I should read alongside the current ones (but I am not interested in "further reading" except for calc/analysis -- the rest can wait until next year as I said).

What I'm thinking for doing alongside are the following:

Foundations: I think the book I listed is comprehensive enough itself

Calculus/analysis: As I said, I want to push ahead with calculus/analysis so I'm thinking of reading something like Pugh's analysis right after Spivak.

Linear algebra: Are there enough problems in Friedberg Insel? If not then would you recommend Schaum's outline for problems? What about Halmos' problem book?

Abstract algebra: Allan Clarke is basically a "learn through problems" book. There is minimal exposition. I am good at solving problems and did very well in my national olympiad so I thought it would suit me (in fact it was recommended to me by one of the national team's IMO members). But I think I may need a reference in any case, so would Dummit Foote work for that?

There is also the issue of learning physics. I am interesting in taking some (optional) applied modules in my first year so I can decide if I want to continue with "math and physics" or just pure math. I don't know any physics except for the very basics from high school, such as the kind of thing taught in Hewlitt's conceptual physics. In particular, I don't know any "calculus physics" -- how physics is done using calculus. Any recommendations for starting?

Thanks for your help!