>I would like to know what kind of mathematics are important to know
>for a programmer or computer scientist.

Don't know about a CS, but I can give you one
programmer data point.

> so I did not take a lot of math courses.

Though never much of a mathematician, I took courses
up through calc and differential equations, and physics up
through basic quantum physics. For a brief moment
in time (long enough to pass the test), I could actually
derive Schr�dinger's equation!

When I wrote computer graphics code, I needed geometry
and transformation system information. It was nice that I had
once studied such things, but in fact I had to dig out the books
and as often as not the information/technique I needed was
not something my formal studies had covered, so it's not clear
that having studied it was a real big leg up.

When I got into computer animation, I needed knowledge of
physics. Again, nice to have had some background, but a large
amount of information seemed to be really specific to the problems
at hand, and not simply "pulled up" from having taken relevant
courses.

For the vast majority of the areas I've worked in (file systems,
communications, EFT, databases, user interface design,
anti-submarine warfare, etc.), I have not found much need for
math beyond the high school level at all.

Of course, my high school taught both algebra and trig, and
I find that those two subjects are useful on a surprisingly
regular basis for getting through life, not just for random
programming problems. If you didn't get a good grasp of those
two things already, that sure might be a worthwhile area
of study.

>So I have not yet encountered a situation where my background was
>insufficient.

I'm betting that when you do, it will require information specific
to the problem domain that you will be unlikely to have encountered
in formal study, though some formal study might make it easier
to locate and understand the information you need.

I have found areas of knowledge that were of fairly general
use in a variety of programming situations, but they were
usually not mathematics. For example, an understanding of
automata is something I've relied on over and over again.
OTOH, that understanding arose not from the automata theory
class I took in college, but from having spent a summer
implementing my own version of Lex (lexical analyzer
generator) from the ground up. I learn best by doing; YMMV :-)

In general, I think being good at research and learning is
more valuable than specific knowledge for programmers
in these days of highly specialized areas of endeavour.



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