[Lvlug] Re: fields of mathematics most relevant to computer
David L. Johnson
david.johnson at Lehigh.EDU
Thu Dec 6 00:01:32 EST 2007
Faber J. Fedor wrote:
> On 05/12/07 20:05 -0500, David L. Johnson wrote:
>> Well, my perspective might be a little different from what you wanted,
>> since I am a mathematician and decidedly not a programmer.
> Mind if I ask for your opinion here?
> I did all the analysis stuff in college 20 years ago (BSEE with a maths
> minor) and I'm prepping myself to go back to school for a Masters in
> Maths and/or Comp Sci within the next year or two.
> My current autodidactic curriculum is Velleman's "How to Prove it" to be
> followed by "Discrete Mathematics and Applications" by S. Epps and then
> 'Concrete Mathematics' by Knuth, et al. Then I start on abstract
> Sound good?
Well, I actually know little about Velleman or Epps. Vellman sounds,
from the title only, like something aimed at a more general audience,
but it could also be something for an undergraduate math major. Epps
could have a wide range of topics. Knuth I only know about via TeX.
None of these are in my realm --- I do concentrate on more continuous
mathematics rather than discrete.
You might ask others here at Lehigh for more pointers, such as Garth
Isaak or Mark Skandera, both of whom study discrete math. You can say I
> Oh, know of any good math blogs? Good Math, Bad Math
> (http://scienceblogs.com/goodmath/) is a favorite of mine.
No clue, never looked.
> And WTF is category theory? I haven't come across an understandable
> explanation of that yet.
Hey, something I know something about. Most areas of mathematics share
a great deal of general structure. There are objects (say, groups, or
vector spaces), and there are assignments, mappings from one object to
another that preserve the structure of the object. From one vector
space to another you would think of linear maps, transformations which
preserve the vector space structure. From one group to another, the
transformations are group homomorphisms. [I am hoping here that you
have seen the definitions of these things] For either of these, you can
talk about compositions of the transformations, and there is an
"identity" transformation from one object to itself, and there are lots
of other similarities.
One of the points of math is to never just study one instance of a
phenomenon, but to study all similar phenomena in general, to say what
you can about all such things.
Category theory studies the structures of the objects and
transformations. To the extent possible, the study is independent of
what the exact objects are, and what the transformations are; the point
is to find out about the relationships that come about for all systems
(all categories) from the general structure alone.
This is a study that many mathematicians call "abstract nonsense"; and
when a mathematician calls something abstract, you know it is abstract.
David L. Johnson
It is probable that television drama of high caliber and produced by
first-rate artists will materially raise the level of dramatic taste
in the nation.
-- David Sarnoff, 1939
More information about the Lvlug