Ask HN: Good Reading/Immersion in Mathematics

I'd definitely recommend Godel, Escher, Bach by Doug Hofstadter. Not just about mathematics, but fascinating.

Also, anything by Martin Gardner.

I really like this one: http://academicearth.org/subjects/mathematics

I agree whole-heartedly. I work at a large company and I find I can typically formulate business rules in set and function theory in mathematic notation, which typically blows away my peers and associates because they either 1) know it and are impressed to see it used in "business rules" or 2) think it looks like some space-alien language (which it may as well be to them).

Otherwise these rules come out as a set of vague half-instructions that always lead to rounds of revisions in UAT. Oh, and "we only scheduled a week of UAT".

A broader knowledge of discreet theory would be much more helpful than understanding a sine or cosine at a... trigonometric level.

It may be helpful if you state your mathematical background, though I'm guessing that, if you had taken any proof-based math course, you wouldn't be asking this.

I recommend The Art of Problem Solving I and II. On the one hand, they're intended for (mathletic) middle and high-schoolers. On the other hand, some of their problems are quite challenging, and much of the material therein is what my school teaches in its intro discrete math courses since very few students learned it in middle and high school.

http://www.artofproblemsolving.com/Store/contests.php

"want to be acquainted with all of the different fields" may actually be quite hard - you can't do complex analysis, differential equations in multiple dimensions etc. without having a very firm grip on standard analysis (including all the proofs and definitions that they normally skip in high school).

If you want to build up your math muscles (as a good preparation for actually studying maths), you should have a look at some discrete mathematics books (the one I had was "Discrete Mathematics" by Norman Biggs) as they teach you to think in terms of proofs.

If you want to get a thorough foundation for non-discrete maths, you should start with a good (university math) analysis textbook (No idea what's a good one in English).

Another approach you could take is to take a math book that is targeted at physicists and EE people - those usually skimp on the proofs and don't contain enough detail to understand the fundamentals behind it all, but bring you to the interesting (to physicists and EE people) stuff much quicker than a real math course would.

Oh, and if you hang out on Youtube, be sure to watch the catsters - this is category theory, presented by actual working mathematicians, at an accessible level (and with a cute UK accent too).