/sci/ - Science & Math

>>9462349
Real analysis: Old Classics would be Rudin, Apostol, and Papa Rudin. Newer texts would be Terry Tao's, and Pugh's. I recommend the latter two in conjunction. Pugh follows geometric intuition and gives some less than completely rigorous approach, but you learn how mathematicians think about doing analysis. Terry's is an axiomatic approach, starting with foundations making them a good pair because they approach the same material in a completely different way.

Complex Analysis: Stein & Shakarchi is common, and has loads of good problems but I didn't care for it too much. I really enjoy Ahlfors as a text. A good reference is schaum's outline. A lighter version of Ahlfors is Donald Sarason's complex function theory.

Topology: for point set, I think the schaum's outline is good enough. First Algebraic text grab Fulton. For differential the go to standard is Pollack - but I have no experience in this topic.

Linear algebra: Hoffman & Kunze is a fantastic text but a little dated. Something more recent is Axler's text - which is pretty good but avoids determinants too much. Halmos' finite dimensional vector spaces is a text you can't miss out on. I've heard good things about Advanced Linear Algebra by Roman

Algebra: Google Richard Elman UCLA lecture notes, they're free online and absolutely fantastic. If you want group theory use Rotman. Commutative Rings use Matsumora. Depending on your tastes you might like Lang or Hungerford. Dummit and Foote is a reference text.

Differential geometry: use schaum's as a first text, then spivak's calculus on manifolds. After that John Lee has a trilogy that's pretty good. Riemmanian Geometry by De Carmo is supposed to be the bees knees. Peter Petersen from UCLA also has an interesting text


Calculus: My love here is for spivak's text, but honestly the newer editions of Stewart aren't that bad.

>>9409664
Working on this beauty, just finished all the exercises in chapter 1, moving on to chapter 2 now.