If I were you, I'd study only linear algebra. Other subjects, including calculus, are of little use to programners. The quickest way to learn linear algebra is to pick a high level topic, say... spectral decomposition of a matrix, look it up on wikipedia, see what theorems this topic is made of, and try to repeat the proofs. You'll quickly see that those proofs rely on lower level theorems, so you'll need to look them up too, and so on, until you descend to the definitions of numbers and sets.