Skipping basic courses for advanced ones

[rasmhop]

I'm about to start my first year of studying mathematics. My university requires me to take quite a lot of basic courses in the first year and after that there are some strict limits on the number of courses I can take. This means that I will not be able to take all the courses I would like to before graduating. I have done some self-study prior to enrolling and believe that I could fairly easily skip some of the early courses and I know that the university allows this, but I'm unsure how it will be looked upon by graduate schools. If for instance I took "Algebraic topology 2" (second graduate algebraic topology course) and got an A would it be assumed that I know the content of topology and "algebraic topology 1" even if I didn't take them? Would such an approach present a problem if I have made sure I can handle the course? (for instance by auditing some algebraic topology 1 lectures earlier or simply checking the prerequisites and earlier lecture notes)

In addition I know that there is an open lecture policy in place which basically means that I can attend any lecture I want, and since no attendance is kept in any courses I'm thinking of skipping some easy lectures like "intro to analysis" (which is a required course) and go see some more advanced course like commutative algebra, but I'm somewhat worried since this won't show up on my transcript so unless it's part of a sequence like "analysis 1 (real) -> analysis 2 (complex) -> analysis 3 (functional)" where I plan to take the last courses in the sequence, then I won't really have anything to show for it. Is this approach to studying a bad idea? I guess I'm just a bit concerned because it feels like I have to choose between optimal learning and what looks better to graduate schools. Am I simply a bit paranoid about how the system works or are these concerns valid? I would love to hear some other people's perspective on this situation.

 

[Choppy]

I'm assuming that "about to start my first year" is synonamous with "straight out of high school." If this is the case, you might want to just work your way through the standard courses - at least for the first semester. University can be a LOT different than high school and if you start skipping courses right off the bat, you might end up in a situation over your head.

As for graduate school, the important thing is that you take the courses you need in order to complete the degree you need. Sometimes skipping a class will keep you from technically completing the degree requirements. Of course it is logical that if you skip a basic version for something more advanced, you are more likely to understand the material covered in the basic version, but I would be a little wary because sometimes these things work more like a computer program that makes sure all the boxes are checked rather than a rational person assessing each student's progress year by year. If you want to do this, talk your academic advisor and make sure you understand any consequences.

Also, if you intend on auditing (unofficially) a course, it's a good idea to clear that with the professor teaching it - not always necessary, but it is the polite thing to do, if for nothing else to make sure you're not taking the spot of someone who paid for the course.

 

[rasmhop]

I'm assuming that "about to start my first year" is synonamous with "straight out of high school." If this is the case, you might want to just work your way through the standard courses - at least for the first semester. University can be a LOT different than high school and if you start skipping courses right off the bat, you might end up in a situation over your head.

Yes I'm straight out of high school. For the first year there is a large number of mandatory courses which means that I will have very little choice doing my first semester and only slightly more doing my second. Thus I'm basically forced to take a number of the introductory courses whether I wanted to or not. Here I plan to do some auditing (of course clearing with professors first) when I have made sure I can handle the coursework easily because I'm not allowed to sign up for more courses doing this period. It's not until second year I will really get to exercise my freedom and potentially skip some of the mid-level courses.

As for graduate school, the important thing is that you take the courses you need in order to complete the degree you need. Sometimes skipping a class will keep you from technically completing the degree requirements. Of course it is logical that if you skip a basic version for something more advanced, you are more likely to understand the material covered in the basic version, but I would be a little wary because sometimes these things work more like a computer program that makes sure all the boxes are checked rather than a rational person assessing each student's progress year by year. If you want to do this, talk your academic advisor and make sure you understand any consequences.

When you say "these things work more like a computer program" are you referring to my own university's degree requirements or the graduate schools process for checking applicants? I have made sure to verify that this stuff is fine at my university and that it doesn't violate any requirements. I know there are a couple of courses I will have to take, but most of the formal requirements are in the form "x courses from subject A" so it doesn't differentiate between advanced or basic courses.

Also, if you intend on auditing (unofficially) a course, it's a good idea to clear that with the professor teaching it - not always necessary, but it is the polite thing to do, if for nothing else to make sure you're not taking the spot of someone who paid for the course.

Yes I intend to do this, but from what I hear from the older students I know seats are rarely a problem in any math course except introductory ones like Linear algebra which everyone takes (including other majors such as physics, CS, economy).

Thanks for your response; I appreciate the feedback.