I love combinatorics, but do not really want to do pure math exclusively. I like the format of pure math (that is the theorem-proof-theorem-proof format), but would also like what to do research that immediately applies to something. I understand that lots of pure math eventually has applications, but what I'm looking for is research that is done in the pure math style of theorem-proof, but is an applied problem
Phylogenetics seems like such a field. I would like to know though of any other research areas where one is applying combinatorics (or discrete math in general) to a real world problem, but going about it in a "pure math style/format"
Thanks!
There are a heap of applications in engineering:
- digital transmission: with coding, Hamming distance, error correction, queues, ...
- networks: lattices, graphs, random walks, ...
- structural design: finite elements, finite differences, ...
- Quality Assurance: sampling, reliability, availability, ...
.....
Concerning the requirement at the end of your post, consider for example that the practical questions arising in telephone networks design has given lieu to the totally new sector of Queue Theory in combinatorics/ probability.