I'm a second year Physics and Mathematics student.
Although I haven't attended many different professor's lectures, from what I have experienced, and what I know about the professors in both of my departments, I generally don't like the style that the lecturers uses in both departments. What I mean by this is that, for example, in physics courses, generally lecturers tend to justify their claim by doing "sloppy mathematics" and generally without clearly stating their assumptions, and they don't explicitly state what is an experimental result and what is a mathematical result, so this generally confuses me.Of course this is just one of the examples only in physics department.Therefore, mostly I studied the subject by myself, and ask the questions either to the T.A, or the professor's itself depending on situation.
I should also note that, in both departments, there are some professors whose way of explains things coincides with how I think, so if I cannot understand a subject that I'm self-studying, I generally go to those professors and ask them.
So, for this reason, I'm going to ended up studying lots of subject by myself, and for that reason I will not take course on those subject because why should I waste time by taking the lectures on subjects that I have already know.Instead I can take different course that I really benefit from.
However, the only problem in this way is that I will not have an official account on those subjects that I will have beed studied when I apply to graduate school.
So my question is that how can I make these studies official ? I mean, for example, I will study point-set topology in the next spring break and I will not take this course from the department, but how can I prove that I know this subject when I apply to graduate school.
I'm hoping that I'm able to clearly express what I'm asking.If not, please say it what is not clear.
Note that, I have seen this question, but even though I don't exactly know the content of GRE tests, I don't think it will be a valid method in my case.