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?)

in most all schools i know of, math and physics for science and engineering majors are the top courses you can take. I haven't seen schools with a unique math course for, say, scientists and physicists, and another unique one for mathematicians. Mathematicians essentially count as scientists. they get BS degrees.

Read SICP.

>>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
FFFFFFFFFFFFFFFFFFFFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

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. ¬_¬

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. ¬_¬

Scheme is still developed. And even though MIT has decided to obsolete it, Gerald Sussman has remarked that the book and the exercises within it are still "right-on" with modern computer science. There are also projects/wikis/ect. out there all over Internet land that are interpreting the exercises in languages other than Scheme.

So, I wouldn't consider it obsolete, but rather, SICP is entering a new era. An era where the people control the future of SICP and not MIT and its authors.

>>5
>An era where the people control the future of SICP and not MIT and its authors.

'Cuz basement-dwelling neckbeards know more than MIT professors, amirite?

>>6
I'd reply to you in a serious manner, but because:

quote failure

and using the term

neckbeards

So learn some ^{B B} _CODE and Back to img.4chan.org, please. before you go ahead and make another post.

>>6


    '-._                  ___.....___
        `.__           ,-'        .-'  \
            `''-------'          / o )  `._
                                  `-'      (
                                            \ you make me feel sad
                                             \
                                       ______)
       ................._          .-''    /
                         `-.._         _.-'
                              `'-----''

>>7
Translation: I'm right and you know it, so you're changing the subject to who knows more bbcode.

>>9
Translation: I didn't achieve satori by reading SICP, so I'll just call it obsolete and troll its biggest fanbase^[1] because I am an incompetent fool who can't even quote and ^{B B} _CODE properly.

_____________________
References:
[1] http://dis.4chan.org/prog/

http://www.demonoid.com/files/details/1923787/37521603/

>>1
It's better than nothing.  I hear mathematicians prefer positive definite metrics, which Lorentzian ones aren't.  That shouldn't matter too much.  A lot of GR is brute forcing Einstein's eq/geodesic equations.

>>5
I thought scheme's popularity died out decades ago?

>>10
He wasn't trolling /prog/...  gb2 /prog/ if you're so butthurt about it

Why is there such obsession over this book?  It/scheme sucked, except for comic value.

>>4
using text emoticons makes you an incredibly massive faggot and invalidates anything you have to say. go away now.

>>12
Yes, I am a [cdoe]Scheme[/code] programmer. So? I don't see any problem. I embraced my functional dick long ago and I am happy together with my cdr (who is my other car!). We have a fucking lot of friends in and outside of the fandom and I am pretty tail-recursive.

But thanks anyway asshole. Go and make love to your von Neumann machine while I write SEXP with my boyfriend!

>>14
Scheme

BBCODE FAILURE! Father Sussman, please forgive me!

>>14
Wait, wat?  So Sussfags are furries too?

>>16
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