"For the programmer who is truly interested in improving their mathematical skills, the first line of attack should now be obvious. Become an expert at applying

"For the programmer who is truly interested in improving their mathematical skills, the first line of attack should now be obvious. Become an expert at applying the basic methods of proof" This may be good advice if you want to get into pure mathematics, but huge parts of maths are not pure. Applied mathematics is very relevant for programmers - especially game programmers. It's not a sin to sacrifice mathematical rigour for the sake of discovery. It doesn't even have to be a direct map (e.g. actual implementations of calculus or such). Just understanding various bits and pieces in granular detail can help you get precise and testable quantitative ideas for problems. For instance, a while ago I wanted to implement a kind of smooth up-and-down motion for an object in my game. Almost immediately I thought of equations of this form: (y position) = (some amplitude)* sin((some frequency)*(time)) + (some value to denote the origin) This is a first step for some fairly interesting up-and-down motion - the rest is all a matter of finding suitable constants. Similar things come to mind when you want to move an object smoothly to another position along a line, with a decreasing speed: position = ((position you want to move to) - (current position)) / (some constant) + (some minimum speed) This stuff just flashes before your mind if you've done plenty of physics (or 'mechanics' in mathematics) before. What's more, you'll know countless other ways of increasing the complexity of your equations without having to do much trial & error hacking (except to find things like constants and such). For games, I'm convinced that there's still an incredibly huge variety of mathematical behaviour that has yet to be harnessed for the implementation of actual game mechanics. (Games usually just use some game engine's implementation of only some parts of classical mechanics, for instance.) Never underestimate the relevance of applied mathematics to real-world programming, even though it doesn't really occupy a spectacularly prominent position in CS-focused courses.