Gilbert Strang's Linear algebra book was great for me after taking A-level as a mature student, linear algebra comes in everywhere (I think there are videos of Strang floating around as well). Make sure to work through as many exercises as you can if you're studying independently.
An approach that might work for some is to take a good undergrad textbook of something you're interested in, but that is a bit too hard (preferably not too dense, with enough explanatory text). Try to plough through it, and look up all the stuff you don't understand! Don't expect to get very far very quickly, but at least you'll get led to useful reading material for the fields you care about, and it might also motivate you more than starting from axioms.
(For me it was Information Theory, Inference, and Learning Algorithms that sparked off a lot of study: free online at http://www.inference.phy.cam.ac.uk/mackay/itila/ ).