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"


  • $\begingroup$ The Hamiltonian Path Problem has plenty of applications and its universality of application gives it tremendous theoretical significance. If you don't mind interfaces between the discrete and the continuous, Mixed Integer Programming has, again, a tremendous list of applications. $\endgroup$ – avs May 23 at 21:58

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.

  • $\begingroup$ See my new edit clarifying what I am asking $\endgroup$ – graphtheory123 May 23 at 22:13
  • $\begingroup$ @graphtheory123 - I don't know what part of this Answer is unsatisfactory, nor what your "new edit" clarifications are. But if you're emphasizing the "theorem-proof" aspect, then (at minimum) coding theory is one such -- nobody would use a code without going through proofs. Same for encryption, many kinds of algorithm design, etc. $\endgroup$ – antkam May 24 at 18:35
  • $\begingroup$ I suppose what I'm getting at is are there applied areas of combinatorics where one is not just running computer simulations? From what I have seen, and perhaps this is completely wrong, is that applied math is a lot of computer programming and running simulations $\endgroup$ – graphtheory123 May 27 at 23:41

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