So I started my first ever university course, at U of T. (It's a summer course.) The class textbook, which is called "An Introduction to Proofs and Problem Solving", should give you an idea of what the class is about. Anyway, the first thing that my Professor taught us is that you should never make assumptions in math. For instance, the first question that we took up together was "how many squares are there on an ordinary checkerboard?" At first, I thought "64, it's simple." But we soon learnt that we have to take into account the fact that there are 1 x 1, 2 x 2, 3 x 3, etc squares. So the real answer is actually (1/6)n(n + 1)(2n + 1) This was a real eye opener. In high school math, we were taught that assumptions were normal, and the textbooks we used assumed that we made assumptions. It's quite different in uni, I learnt. It's all about generalization. In the first class, I learnt so many things that I didn't know about. Now I have to get into the mathematician state of mind, and read my suggested reading in the textbook, do the problems, finish the problem set, etc etc... I'm gonna have a lot of fun in this course!