Advanced Mathematics for Computer Science

DevLiquidKnight · 2012-04-14T15:55:55

What do you feel are some of the more important mathematical courses / topics that one should learn for computer science? For example: Abstract algebra? Number theory? Chaos theory/nonlinear dynamics? Combitorics? Graph Theory? Optimization?

Math and Physics Programming

Started by DevLiquidKnight March 17, 2012 10:46 AM

32 comments, last by taby 12 years ago

daviangel

604

March 21, 2012 06:38 AM

For a lot of the topics mentioned (topology, differential geometry, nonlinear dynamics, etc), basically anything where there is a continuum instead of just finite structures, it will be difficult to make much progress without a solid grounding in real analysis. There's a great set of video lectures by Francis Su from Harvey Mudd where I did my undergrad,
http://beta.learnstream.org/course/6/
(or http:/
and click through to the other videos)

Cool beans

Been looking for an easy i.e. video intro to real analysis. I tried to read Mandelbrot's Fractal book and Kip Thorne's gravitation books a while back and both of them quickly lost me since right off the bat they both go into metric spaces

I can also brush up on monoids too now

[size="2"]Don't talk about writing games, don't write design docs, don't spend your time on web boards. Sit in your house write 20 games when you complete them you will either want to do it the rest of your life or not * Andre Lamothe

taby

1,505

March 22, 2012 12:08 AM

I have used a few things from Abstract Algebra and Number Theory for hashing and pseudo-random number generators. I've used statistics quite a bit (Are those numbers really random? Is this version of my chess program stronger than the previous one?). Probability is really important for almost anything in Artificial Intelligence. If you do graphics, Euclidean and Projective Geometry are pretty important.

I only know a little bit about Chaos Theory, but my understanding is that it's pretty useless. It's just one of these things that have a sexy name and produce pretty pictures, but I don't think you can really do a whole lot with it.

Alvaro, surely you know that chaos theory applies to any system with more than two parts. A very interesting article is "On the nature of turbulence". Another interesting book is "Galactic Dynamics". Surely Poincare would be offended if he had heard you disparaging his theory of chaos as such.

Anyway, otherwise inexplicable behaviour in physics, chemistry, and biology that was once labeled as noise and swept under the rug is now labeled as chaos. It's similar to how lightning was once labeled as the anger of the gods, but is now labeled as electrons and photons. I personally have no interest in knowing what makes up a lightning bolt, but science isn't about subjective opinion.

taby

1,505

March 22, 2012 12:12 AM

Category theory is basically object oriented programming on steroids.

alvaro

21,604

March 22, 2012 02:23 AM

Alvaro, surely you know that chaos theory applies to any system with more than two parts. A very interesting article is "On the nature of turbulence". Another interesting book is "Galactic Dynamics". Surely Poincare would be offended if he had heard you disparaging his theory of chaos as such.

I am not saying that you won't encounter chaotic systems. If you do pretty much anything that involves iterating a function, you'll get there pretty soon. However, there isn't all that much that is useful that you can do with "Chaos Theory".

Anyway, otherwise inexplicable behaviour in physics, chemistry, and biology that was once labeled as noise and swept under the rug is now labeled as chaos. It's similar to how lightning was once labeled as the anger of the gods, but is now labeled as electrons and photons

We understand lightning and we have the lightning rod to show for it. What has Chaos Theory given us? And if you do find some application, is it relevant to a CS professional?

Category theory is basically object oriented programming on steroids.

They are both forms of abstraction, and the people that invented OOP borrowed lots of terms from category theory, although I don't think you can push the parallels beyond superficial similarities.

taby

1,505

March 22, 2012 04:45 PM

While googling for topological mixing and bifurcation diagrams, I ran across this PhD thesis "CHAOTIC COMPUTATION By ABRAHAM MILIOTIS" from 2009:
http://etd.fcla.edu/UF/UFE0024234/miliotis_a.pdf

References 25-28, and the entire thesis actually, seem to be about the marriage of chaos theory and computation.

Then again, I really don't put any faith whatsoever in people with university educations, so it might be as much bunk as anything else. I'm sure there are many university educated people in this thread who have a subjective opinion on the matter. Hopefully they'll grace us with their knowledge.

taby

1,505

April 02, 2012 05:51 PM

This came across the Twitter today via @CompSciFact ...

"First of all, one of the most important features of category theory is that it is a guide to computation."

http://www.cs.man.ac.uk/~david/categories/book/book.pdf

Just an FYI for those who are curious.

alvaro

21,604

April 02, 2012 06:41 PM

I had to learn category theory in college and putting that stuff in my brain felt like hammering a square peg into a round hole. I had a similar feeling when I tried to learn functional programming. So I am not too surprised that the two are somehow connected.

taby

1,505

April 02, 2012 07:22 PM

Maze Master

510

April 03, 2012 01:35 AM

I had to learn category theory in college and putting that stuff in my brain felt like hammering a square peg into a round hole. I had a similar feeling when I tried to learn functional programming. So I am not too surprised that the two are somehow connected.

Do you have any recommendations for category theory learning materials (books, videos, websites, online courses, etc..)? I've been trying to learn the basics for a while now without much success..

http://maze5.net

alvaro

21,604

April 03, 2012 01:06 PM

Do you have any recommendations for category theory learning materials (books, videos, websites, online courses, etc..)? I've been trying to learn the basics for a while now without much success..

No, sorry. I ended up learning enough of our text book to pass the exam, but it's about the only time in my life when I memorized a bunch of material without understanding most of it. At the exam they asked me about the Yoneda lemma, of which by now I only remember the name.

Advanced Mathematics for Computer Science

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Advanced Mathematics for Computer Science

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