Maths for programmers (Re: [Techtalk] Theory vs. practice)

[Mary Gardiner]

Follow-ups to grrltalk please.

On Tue, Jan 15, 2002 at 09:01:24AM -0800, jhamilto at n2h2.com wrote:
> I actually feel that I would have benefited from doing lots more math
> in high school and college. I think working with computers requires
> learning step-by-step logical thinking which is what I believe exactly
> what math teaches you. a+b+<plug in a formula> = the answer. I'm
> coming from a system administration point of view where 75% of my job
> is solving problems. I quit taking math after math analysis (anal
> math, I liked to call it), and am now playing catch-up with real world
> problem solving.  I've read a couple of books on logical/critical
> thinking to sharpen my skills. 

I agree with Glenda that maths courses are not the only places to learn
such skills. However, as someone who is, quite frankly, terrible at
calculus and analysis, I found that the maths courses most directly
relevant to programming are courses in logic and discrete maths.

Logic will give you a formal appreciation of the if-then construct, if
nothing else, and discrete maths an appreciation of state machines,
which is very very useful if you ever want to write a parser or
compiler, or understand one. Since most programs are state machines
(well they all are Turing machines in some sense), you might be able to
relate the theory to some of your own practices and also to the history
of computing.

The amount of formal mathematical background required for getting to
grips with the basis of both of these areas is nothing more than high
school algebra, and if you are interested in them I'd suggest trying to
find an introductory textbook. People who have done some programming
will also have a whole reference framework to fit all the concepts in.

Linear algebra at first year university level (vectors and matrices) is
very useful for graphics programming. You can learn the amount you need
from most graphics textbooks but may find a dedicated linear algebra
textbook handy if you want to work through it a bit more. Again, high
school algebra is sufficient preparation.

Logic courses are also sometimes taught to philosophy students, and
people who feel like approaching it from a humanities pov (albeit a very
abstract one) might want to start with texts designed for philosophy
students and moving on to ontology, perhaps.

I'm sorry I can't recommend any texts by name - all of mine were written
by lecturers specifically for their own courses!

-Mary.

-- 
Mary Gardiner
<mary at puzzling.org>
GPG Key ID: 77625870 (wwwkeys.eu.pgp.net)