0
$\begingroup$

My background

I'm a third year student. I study mathematics combined with computer science (with focus on modeling, simulations and visualization). In order to get my degree, I have to make a half-year project where I combine mathematics with computer science.

What I want to do

I am in love with algebra and group theory. But I don't know how it would fit with the interdisciplinary project, where I have to combine it with computer science. Someone suggested cryptology, but I don't know alot about it (any thoughts? and useful references?).

My problem/question

Is it possible to combine computer science with algebra? I also need project ideas (I would also like references).

  • 0
    @w$h$oisitnow Okay, sounds good :)2012-10-02

3 Answers 3

2

This is a bit challengeing, but who known that you won't like that? Homotopy type theory has definite connections to algebra (the groupoid model) but also to computer science (implementations in Coq). Take a peek at http://homotopytypetheory.org/

Maybe you can find something more suitable in denotational semantics (http://en.wikipedia.org/wiki/Denotational_semantics). This is an application of algebra to the study of programming languages.

0

Perhaps a project using Sage?

http://www.sagemath.org/doc/thematic_tutorials/group_theory.html

0

You may consider this old hat, but you could write a solver/simulator for a Rubik's Cube or some other puzzle that can be described with groups.

As for cryptography, there have been proposals for cryptosystems based on braid groups (an overview). I believe they use the conjugacy search problem or something similar as the trap door (i.e. given $a$ and $b$ that are conjugate, find $x$ such that $a=xbx^{-1}$). You might be able to visualize the way the computer manipulates the braids (puts them into normal form and such).