Favorite mathematical/theoretical topics?

Is there something you never really got to study, but later found that it would have come in handy for your career? Is there something you did study and found to be very useful, having to review it later in life to gain a better understanding?
For me, it's these two:

http://en.wikipedia.org/wiki/Group_theory
http://en.wikipedia.org/wiki/Topology

I studied a little bit of the former, but didn't really go into many details. I would reallly like to know a little more about the latter.

It being part of my job to do research (I'm a graduate student), when something comes up that I don't know well I get to go try to learn something about it. Most recently that has meant learning something about algebraic geometry, which is really not where I want to be, I'm much happier doing topology.

I used to like to calculate the number of inches in a light year...

P2

yay golden mean!!

I was always partial to prime factorization myself, but I have no interest in studying public key cryptography so it's only a hobby.

Oh hey, I bet I can do that faster than you:

http://www.google.com/search?q=one+lightyear+in+inches

Yes, but (ahem) I used to do it when I was 10 years old and pocket calculators hadn't even been invented yet, let alone Google.



P2

There were two classes I could never seem to fit in my schedule or were not offered in the right term, etc. before I graduated with my math degree ... Numerical calculus, wich goes over numeric methods for solving various types of functions, i.e. machine methods/algorithms. The other being mathematical modeling of complex systems. I think both would have been helpful for programming tasks.

-Sol Columbia

*agrees with Sol*

After um... 20+ years as a working programmer, those are precisely the classes I wish that I had found time for while still in school. I also have occasionally found a need for queueing theory - I am not certain where that would fit on a mathematics syllabus.

- Jamie Marlin (who actually does math in her software on occasion, rather than just fiddling with accounting data)

I never really went in for the advanced floating point math stuff... I always preferred good solid integers, set theory, symbolic logic, matrixes, finite automata, game theory etc.

I think most of my college notebooks had more than a few doodled hyper-hyper-cubes (a shadow of a shdow of a shadow of a 5th dimensional object. Nasty scribbly messes!) Had a few RL wireframe models, and even made a few models in SL, despite the absurd number of prims required.

Playing with and discovering interesting permutations, combinations and relationships is what keeps me entertained by llParticleSystem... and gaming in general.

I wish I'd learnt much more Set Theory.

As a side note you might enjoy this: http://www.justinmullins.com

Regards
Leon

Abstract algebra, especially group theory as applied to quantum mechanics, is precisely the reason I went back to university after having graduated in comp sci, and re-enrolled to be a math student. So far, it's been well worth the intellectual growing pains, but hasn't come in handy for anything practical.

How about the opposite? If I eventually never apply the quantum mechanics and general/special relativity that I took as part of EEE bachelors, I'll probably be peeved about the wasted effort forever.

On second thought, if I eventually have to apply it, I'll be even more peeved :/