Ask HN: Mathematics in computer science | Hacker News Reader

Ask HN: Mathematics in computer science

4 pointsvaidhy6 comments

I have been asked to give a talk on applications of mathematics in computer science to a set of post-graduate and doctorate students in math. I am looking for ideas to convey the beauty of math in CS. The obvious topics are probability and stat in ML, Trig in graphics, number theory in cryptography, category theory in OO, sets in relational algebra. Let me know if you can think of more connections :)

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One of the most beautiful applications of math+cs (for me) involves genetic algorithms. Being able to have two models duke it out (via survivorship), or mutate - to see your code select the best models to fit a set of data is beautiful.

Basic Info: http://en.wikipedia.org/wiki/Genetic_algorithm

You can also increase the complexity of this field by using GAs to train neural networks for fitting data or processing it in innovative ways: http://www.generation5.org/content/2000/nn_ga.asp

YOUTUBE: NN + GA simulation: http://www.youtube.com/watch?v=LXDUqAmdEq4

Neural Network at work: http://www.youtube.com/watch?v=T2aZAWXyw6c

I'd call these "interplay" rather than applications:

* combinatorics in computational complexity, analysis of algorithms, optimization, etc. * logic in formal methods. * lambda calculus and category theory in programming languages (more so in functional languages than OO). * linear algebra in graphics, graph theory, etc.

Geometric algebra: http://www.amazon.com/Geometric-Algebra-Computer-Science-Rev...

It is to linear algebra what Lisp is to assembly.

Kolmogorov / Chaitin complexity. A measure of the simplicity which a given pattern (program output) can be represented. A question that will get the applied math majors going -> Is Kolmogorov complexity a good measure of the generality of a physical law or mathematical theorem?

Try graph theory: possibly exploring some of Erdös's work on random graphs.

Semantics, especially Denotational and Axiomatic.

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