I was thinking the same fashion while I was taking discrete math in the undergraduate and later in the graduate studies, most of the courses (such as Advance Algorithm Analysis and Design, Advance Operating System , Compiler Design, Advance Computer Architecture) involved the higher level of  proofs and only proofs of the algorithms. To transcend in proofs, the principal ingredient is to carry some patient and brassboundness. After I read the book by Edward R. Scheinerman, my brain started to be exploding thus opening the all the loose connections. While you sit for doing proofs, always think in terms of "Class" instead of "an Instance of a Class".  Hope it will help you! Good luck!