OT/misc: maths (software vs traditional...).



observation:
the math I know and use as a programmer is VERY different from the math used
in math classes, physics classes, ...

I had re-discovered this a few months back, after doing terribly at a
math-related class I had, this being the first real re-exposure to
traditional math in my case for ~5 years (I did well at this one, but bombed
another class ~2 years earlier). (actually, me and academics in general is
very "hit-or-miss", sometimes because of being rather confused, but more
often had been due to being either depressed or apathetic and blowing stuff
off, or sometimes due to procrastinating too much, or some combination
thereof...).


actually, after some recent exposure, and having looked some at another book
and thought about it some, I am left to wonder:
why is there such a drastic difference?...

now, my personal bias would be, granted, that it is a mystery why other
people don't do math like on computers:
via methodologies such as OOP, relational-logic, black-box abstraction, ...
or why they would use complex continuous systems (such as ODE's, ...), as
opposed to simpler discrete-step, linear, or piecewise systems, ...

or, for that matter, why integrals rather than defining the concept in terms
of maybe a few nested loops or similar, ...

or, for that matter, why there is such an emphasis on proving and solving
things, rather than throwing something together and following the "make it
work" mindset?... (even if it involves mindlessly beating on it until it
works, or ugly kludges, ...). (a computer may "prove" something, but the
means by which this is done and the usual sort of result produced are
somewhat different...).

or for that matter why mathy people use so many sets when sets are, IMO,
confusing and difficult to work with, or at least in the form mathy people
use them (as opposed to, say, a collection of items in a linked list).

or, for that matter, detailed analysis and decomposition of problems, rather
than attempting to establish a fundamental set of lego-like blocks which can
then be assembled in order to produce a workable result.

or having people memorize fixed-form calculations, and testing people more
on their ability to recall then and run some numbers through to get a
result, or figuring out how to throw calculations together to get something
which can do more elaborate calculations (since presumably this is more
likely what people would be doing on a job)?...

....

maybe it is just myself, but there would seem to be a severe difference
somewhere, despite those things which would seem to be similar from a
distance.


over the past several months I have been faced with this issue, I can't
really seem to find an adequate answer to explain these differences.

(or, IOW, why the world of "math like done in classes" is almost like an
alien landscape vs "math as done by a programmer"...).


for example, I have generally had good success with mathy-tasks when they
come up in software, but when faced with similar situations in a class, it
turns into a horrid and confusing mess...

for example, I have done things like audio filtering and synthesis (speech
synth, midi, speech-via-midi, ...), as well as graphics
processing/compression, and a fair amount of 3D stuff (including writing a
rigid-body physics engine, which is just the same as the last class I took,
and bombed, where I would have thought I would have done well already having
had a presumably good grasp on the basic algos, ...).

all this stuff is not exactly absent mathy stuff (it just manifests itself a
bit differently, and in a way which actually makes sense...).


similarly, as far as "absorbing" information and using it to solve problems,
I seem well-enough skilled at this.

for example, mathy problem comes up:
summon up google, skim any relevant pages on the subject, understand problem
(including many of its side issues, since often they will be stated
somewhere, ...), and then one can go about implementing the solution.

(nevermind it doesn't always work, since after several years now, I still
don't fully understand things like SSA form, pure-functional languages,
....).


assuming they are similar, one who is skilled at one "should" be similarly
skilled at the other, yet it seems like I am able to write code plenty well
(in several different programming languages), but am largely screwed over
when faced with "traditional math"...


any thoughts?...



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