About coding: I would learn some language (like python) until you feel a bit confident, then go over to projecteuler.net. There are tons of mathematical puzzles that require you to code. But you need to do it SMART, otherwise your machine will be running for over a day. The accompanying forums (per puzzle) are VERY helpful and basically learned me how to program smart and correctly. You can't access the forums unless you give the correct answer to the puzzle first.
I think learning to program trains you immensely in indepently solving problems. There's no one there to help you, just the internet (or books) you can search.
I think learning to program trains you immensely in indepently solving problems. There's no one there to help you, just the internet (or books) you can search.