I have a mathematics background but also consider career in some form of software development. In particular I'm interested in finding out what sort of industries are most likely to have more algorithm development/mathematical and logical problem solving slant rather than pure application development etc.

Obviously, I'm assuming that some subset of the canonical data structures and associated algorithms (trees, lists, hash tables, sets, maps with search, insert, traversals etc.) are mostly going to be present in software development. However, where am I more likely to encounter problems of more discrete maths nature (combinatorial, graph theory, sets, strings, ...) explicitly or more likely in disguise.

Any pointers much appreciated (including possible open source projects that I could use for my further search for applications and also possibly contribute to).