>>11078360For math, I would say...
Precalculus and elementary algebra: Basic Mathematics by Lang, any book by Gelfand, Precalc by Axler.
Proofs: Velleman, Hammack, Polya, I think Axler also has some notes on this.
Calculus: Spivak, Courant, Apostol (he has a more geometric book of a very different flavor as well).
Linear algebra: Axler, Treil, Friedberg and Insel, H&K (later on, after getting some algebra, Roman). For something more applied, look at Strang. For "geometric algebra," check out Macdonald.
Vector calculus: Callahan, Hubbard^2, Fortney, Bressoud, Edwards.
Real Analysis: Pugh, Bartle, Abbott, Zorich, Tao, etc. There are many good books you can choose from here on out, so look around.
Complex Analysis: Palka, Gamelin, Wegert, Needham, etc. There aren't that many books here at an undergrad level, so you may want to check out graduate-level books like Ahlfors, Conway, Lang, Narsimhan, Freitag and Busam, and Remmert.
Algebra: Artin, Vinberg, Dummit and Foote, Fraleigh, Gallian, etc.
Topology: Munkres, Simmons, Croom, Brown, etc.
This should cover a large portion of the undergrad curriculum. From here you can choose whatever topic you want at this level, such as classical geometry (Coxeter, Berger), number theory (Hardy and Wright, Ireland and Rosen), combinatorics, mathematical logic, algebraic topology, differential geometry, differential topology, functional analysis, harmonic analysis, differential equations, complex geometry, ergodic theory, category theory, game theory, Galois theory, graph theory, axiomatic set theory, and some others that don't end with 'theory'
