[j2kun]

I never liked these kinds of lists. The people who ask the question always seem to be under- or overwhelmed by the answer (programmers don't need any math?! theoretical computer scientists need all math?!). And the people who answer are almost always skewed toward whatever it is they do.

Even the top-voted response to the OP is obviously biased toward the logic flavor of computer science, with awkwardly scattered recommendations for non-logicish topics that are far more useful for all flavors of computer science ("perhaps even eigenvalues," seriously?!).

These lists even ignore the deeper question being asked: how do you figure out what sort of mathematics you need for the things you're interested in? Not all computer scientists (and programmers) like the same things in computer science and programming. It's much more advisable to figure out what you like before you go around trying to learn all the math there is to learn related to CS, and then ask about what math topics are related to that.

[nraynaud]

I agree, I have had to learn Newton's methode for differential equations (for simulation), I've had to use logic and an automatic prover (for system validation), I've had to do some complexity analysis (for everything), I've had to play with linear applications, matrices and all the stuff around 3D, I've had to dig into geographical projection equations for another job (in GIS). I'm currently toying with computational geometry. I think what is important is some kind of math to understand how those people write (which far from obvious), and then random stuff to learn to switch.

[tptacek]

This comment is a little frustrating, because part of the point of linking to the Stack Overflow post is to continue the discussion, which is obviously germane to our site. Why not dig into specifics of how you'd approach the intersection of math and CS?

[j2kun]

It's actually inspired me to write my own article, but that will take time.

Meanwhile, I actually write a blog called "Math Intersect Programming." Even though it's more about my specific interests than how a freshman should approach the topics, and I certainly emphasize the mathematical ideas over the engineering challenges, it still gives a good idea of what I would suggest:

Orient the learning around applications in CS. Find a problem that requires the mathematics you want to learn, and learn it with the persistent contextual understanding that you are trying to do something more than just tinker with definitions. Do this for one application and repeat as desired.

My view is that when this is done, you learn to focus on the things that matter over the things that are used to fill empty space in courses (calculus courses come to mind as a specifically abhorrent example of this). You get better at seeing the forest over the trees.

The problem is this avoids the OP's question (and this ensuing discussion about the OP's questions and the purported answers), since you can't organize a single class around it. Another problem is that very few books are written this way, or are only superficially so.

[apu]

I want to chime in and say that I've found your blog wonderful, and since you're too modest to post a link, let me do it: http://jeremykun.com/

[Betelgeuse90]

I largely agree with your sentiments.

However, you should keep in mind that these lists are intended as an answer to "What Math should we teach freshmen undergrads?", not an answer to "What Math do all the CS-people need to know?". The latter is naturally a very small subset of Math, the 'logicish' type.

I do STRONGLY agree with you that we should help students figure out the areas that they find interesting, and let them know what kind of Math is useful for each.

[j2kun]

But the question is one and the same in this instance: they're asking what should be taught in "the" math class for a CS degree. If that doesn't contain the math that all CS-people need to know, then what should it contain?

The OP describes universal algebra and term rewriting, which is what I claim is the logicish type that is not as crucial as, say, linear algebra if you want to find widely applicable mathematics for CS/programming.

[Betelgeuse90]

It may not be crucial for programming, but I'd say it's more crucial than Linear Algebra for finishing the degree at all, since there are CS subjects that you just can't really take unless you learn the logicish stuff.

I can't imagine not taking calculus either... How do you comfortably take the logarithm of an inequality without it?

This whole idea seems so ridiculously impossible to me...