Math Textbooks

So, last semester I decided to go from being a physics major to a physics + pure math double major after taking a few high level math classes that I really liked (namely algebraic topology and real analysis.) The trouble is that I took less rigorous versions of multivariable calculus, partial differential equations, and complex analysis than I think I should have (they were more aimed at engineers + scientists than for mathematicians.)  So my query is if anyone here knows of texts which give a highly rigorous treatment of those topics aimed at people with previous exposure and also available as an e-book.  Sorry if I'm asking too much.  (Also, are there any other Physics+math guys here who can tell me if differential geometry is as useful for general relativity as I hear it is?)

>>1
First off, gigapedia.com is the single best site for finding ebooks that I know of.  Since I heard about it, I've probably had a 90% success rate finding books I want there. Go there, sign up for a (free) account, and select "gigapedia" instead of "google" in the drop-down next to the search box.  (If you don't sign up first, only the google search shows up, and that won't find anything)

There are dozens of good books, I suppose.  Serge Lang writes pretty good, very rigorous textbooks on just about every subject (except topology, actually), and they're definitely aimed at mathematicians.  His "Undergraduate Analysis" is a good book at a reasonable difficulty level for real analysis, and his "Complex Analysis" is good as well.  Also, if you actually want to buy them, they're not too expensive, at least compared to the math textbooks they probably make you buy at school.  You can always just go to gigapedia, type in "real analysis" or whatever, and read through the dozens of books that will come up.

For regular and algebraic topology, I think Munkres' Topology is a pretty widely read book, though I haven't read it myself.

>>2
>math and physics for science and engineering majors are the top courses you can take

Hahaha, no.  Applied math courses are shit compared to proper, theoretical math courses.

>>3
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WHY ARE ALL THESE FUCKING /prog/ LOSERS HERE TODAY??

Seriously, though, if you want to read an old, outdated textbook on the soon-to-be obsolete skill of computer software design, then yeah, go ahead and read SICP. ¬_¬