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Ask HN: Mathematics in computer science

4 points by vaidhy 15y ago

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 :)

egiva 15y ago
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 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 http://www.generation5.org/content/2000/nn_ga.asp YOUTUBE: NN + GA simulation: http://www.youtube.com/watch?v=LXDUqAmdEq4 http://www.youtube.com/watch?v=LXDUqAmdEq4 Neural Network at work: http://www.youtube.com/watch?v=T2aZAWXyw6c http://www.youtube.com/watch?v=T2aZAWXyw6c
stonemetal 15y ago
Semantics, especially Denotational and Axiomatic.
nandemo 15y ago
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.
MaysonL 15y ago
Try graph theory: possibly exploring some of Erdös's work on random graphs.
derrida 15y ago
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?
C-ford 15y ago
Geometric algebra: http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425/ref=sr_1_2?s=books&ie=UTF8&qid=1314888629&sr=1-2 http://www.amazon.com/Geometric-Algebra-Computer-Science-Rev... It is to linear algebra what Lisp is to assembly.

4 points by vaidhy 15y ago

egiva 15y ago

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 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 http://www.generation5.org/content/2000/nn_ga.asp YOUTUBE: NN + GA simulation: http://www.youtube.com/watch?v=LXDUqAmdEq4 http://www.youtube.com/watch?v=LXDUqAmdEq4 Neural Network at work: http://www.youtube.com/watch?v=T2aZAWXyw6c http://www.youtube.com/watch?v=T2aZAWXyw6c

stonemetal 15y ago

Semantics, especially Denotational and Axiomatic.

nandemo 15y ago

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.

MaysonL 15y ago

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

derrida 15y ago

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?

C-ford 15y ago

Geometric algebra: http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425/ref=sr_1_2?s=books&ie=UTF8&qid=1314888629&sr=1-2 http://www.amazon.com/Geometric-Algebra-Computer-Science-Rev... It is to linear algebra what Lisp is to assembly.