Hey. I'm studying discrete mathematics and for some reason we're taking abstract algebra in our first semester (pretty sure it's because there's literally only 1 student on the 3rd year and he needs the course so they shoe-horned it onto us freshmen). Anyways, naturally, me and everyone else that have NOT been studying mathematics on a university level for the past three years are having terrible trouble grasping the subject fully. I can only speak for myself, though and my problem is that I can't seem to ''see it'' like I can see other mathematics.

I can claw my way through problems algebraically, geometrically etc. but this idea of groups and stuff in Abstract Algebra is just completely new and I've never seen anything like it so when I'm left alone with a problem I'm just stumped...However, if I receive help, just hints even, then usually the lights go on and I can throw some sort of proof together using theorems in the book...But I won't be having anyone helping me on the finals in a month obviously...So what am I to do? How can I use this month to vastly improve my problem-solving techniques for this course? Any hints? Thanks!