How to Learn MathMath is a much more diverse subject than physics, in a way: there are lots of branches you can learn without needing to know other branches first... though you only deeply understand a subject after you see how it relates to all the others!

After basic schooling, the customary track through math starts with a bit of:

Finite mathematics (combinatorics)

Calculus

Multivariable calculus

Linear algebra

Ordinary differential equations

Partial differential equations

Complex analysis

Real analysis

Topology

Set theory and logic

and

Abstract algebranot necessarily in exactly this order. (For example, you need to know a little set theory and logic to really understand what a proof is.) Then, the study of math branches out into a dizzying variety of more advanced topics! It's hard to get the "big picture" of mathematics until you've gone fairly far into it; indeed, the more I learn, the more I laugh at my previous pathetically naive ideas of what math is "all about". But if you want a glimpse, try these books:

F. William Lawvere and Stephen H. Schanuel, Conceptual Mathematics: a First Introduction to Categories, Cambridge University Press, 1997. (A great place to start.)

Saunders Mac Lane, Mathematics, Form and Function, Springer-Verlag, New York, 1986. (More advanced.)

Jean Dieudonne, A Panorama of Pure Mathematics, as seen by N. Bourbaki, translated by I.G. Macdonald, Academic Press, 1982. (Very advanced - best if you know a lot of math already. Beware: many people disagree with Bourbaki's outlook.)

I haven't decided on my favorite books on all the basic math topics, but here are a few. In this list I'm trying to pick the clearest books I know, not the deepest ones - you'll want to dig deeper later:

Finite mathematics (combinatorics):

Ronald L. Graham, Donald Knuth, and Oren Patshnik, Concrete Mathematics, Addison-Wesley, Reading, Massachusetts, 1994. (Too advanced for a first course in finite mathematics, but this book is fun - quirky, full of jokes, it'll teach you tricks for counting stuff that will blow your friends minds!)

Calculus:

Silvanus P. Thompson, Calculus Made Easy, St. Martin's Press, 1914. Also available free online at

http://www.gutenberg.org/ebooks/33283. (Most college calculus texts weigh a ton; this one does not - it just gets to the point. This is how I learned calculus: my uncle gave me a copy.)

Gilbert Strang, Calculus, Wellesley-Cambridge Press, Cambridge, 1991. Also available free online at

http://ocw.mit.edu/ans7870/resources/St ... ngtext.htm. (Another classic, with lots of applications to real-world problems.)

Multivariable calculus:

James Nearing, Mathematical Tools for Physics, available at

http://www.physics.miami.edu/~nearing/mathmethods/. See especially the sections on multvariable calculus, vector calculus 1, and vector calculus 2. (Very nice explanations!)

George Cain and James Herod, Multivariable Calculus. Available free online at

http://www.math.gatech.edu/~cain/notes/calculus.htmlLinear algebra:

I don't have any favorite linear algebra books, so I'll just list some free ones:

Keith Matthews, Elementary Linear Algebra, available free online at

http://www.numbertheory.org/book/.

Jim Hefferon, Linear Algebra, available free online at

http://joshua.smcvt.edu/linalg.html/.

Robert A. Beezer, A First Course in Linear Algebra, available free online at

http://linear.ups.edu/.

Ordinary differential equations - some free online books:

Bob Terrell, Notes on Differential Equations, available free online at

http://www.math.cornell.edu/~bterrell/dn.pdf. (Does both ordinary and partial differential equations.)

James Nearing, Mathematical Tools for Physics, available at

http://www.physics.miami.edu/~nearing/mathmethods/. See especially the sections on ordinary differential equations and Fourier series (which are good for solving such equations).

Partial differential equations - some free online books:

Bob Terrell, Notes on Differential Equations, available free online at

http://www.math.cornell.edu/~bterrell/dn.pdf. (Does both ordinary and partial differential equations.)

James Nearing, Mathematical Tools for Physics, available at

http://www.physics.miami.edu/~nearing/mathmethods/. See especially the section on partial differential equations.

Complex analysis:

George Cain, Complex Analysis, available free online at

http://www.math.gatech.edu/~cain/winter99/complex.html. (How can you not like free online?)

James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, McGraw-Hill, New York, 2003. (A practical introduction to complex analysis.)

Serge Lang, Complex Analysis, Springer, Berlin, 1999. (More advanced.)

Real analysis:

Richard R. Goldberg, Methods of Real Analysis, Wiley, New York, 1976. (A gentle introduction.)

Halsey L. Royden, Real Analysis, Prentice Hall, New York, 1988. (A bit more deep; here you get Lebesgue integration and measure spaces.)

Topology:

James R. Munkres, Topology, James R. Munkres, Prentice Hall, New York, 1999.

Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology, Dover, New York, 1995. (It's fun to see how crazy topological spaces can get: also, counterexamples help you understand definitions and theorems. But, don't get fooled into thinking this stuff is the point of topology!)

Set theory and logic:

Herbert B. Enderton, Elements of Set Theory, Academic Press, New York, 1977.

Herbert B. Enderton, A Mathematical Introduction to Logic, Academic Press, New York, 2000.

F. William Lawvere and Robert Rosebrugh, Sets for Mathematics, Cambridge U. Press, Cambridge, 2002. (An unorthodox choice, since this book takes an approach based on category theory instead of the old-fashioned Zermelo-Fraenkel axioms. But this is the wave of the future, so you might as well hop on now!)

Abstract algebra:

I didn't like abstract algebra as an undergrad. Now I love it! Textbooks that seem pleasant now seemed dry as dust back then. So, I'm not confident that I could recommend an all-around textbook on algebra that my earlier self would have enjoyed. But, I would have liked these:

Hermann Weyl, Symmetry, Princeton University Press, Princeton, New Jersey, 1983. (Before diving into group theory, find out why it's fun.)

Ian Stewart, Galois Theory, 3rd edition, Chapman and Hall, New York, 2004. (A fun-filled introduction to a wonderful application of group theory that's often explained very badly.)