I don't think complex K-theory's a thing (unless you mean complex topological K-theory), @RobertCardona. Usually one speaks of albebraic, topological, or operator K-theory, all related but definitely distinct.
@TedShifrin: I have two exams coming up, in General Relativity and Differential Geometry (in that order) with a break of a week in between. Usually, I study last for the first exam, but I'm a bit scared because it's quite a lot for General Relativity. How did you use to study?
A connected planar graph has 26 faces and V vertices, and all its vertices have the same degree. What are all possible values of V? What I have so far: V + F = E + 2 . -> V + 26 = E + 2. V-E = -24. What do I do next?
@TedShifrin: We hardly covered anything (compared to usual diff geo courses). We did some immersions and submersion, Lie stuff, Riemannien metric, geodesics, tensor and vector bundles, Riemannian curvature, second fundamental form, etc. Those are the things I can remember just off the top of my head. The prof who held the diff geo lecture is well known for being the slowest lecturer in the whole maths department
I think Weibel's K-book is now the canonical source on algebraic K-theory, but (for its motivating examples), it assumes you know a chunk of algebraic topology, IIRC.
@TedShifrin: I'm not sure actually because I missed a lot of classes because they took place during my linear algebra tutoring classes. I'll have to check.
@MikeMiller, thanks. I'll look into it. I'm about to get started on Magurn's "An Algebraic Introduction to K-Theory", but will keep Weibel's book in mind!
@TedShifrin: I am not a fan of lectures. Also, as I said, two of the four lectures took place during my TA class, so I couldn't attend them. And by the end of the semester, I focused on different things so I couldn't attend the other two anymore either.
I was given a book on the subject and told I would like it, but haven't gotten around to it. That list is more of a list of things I'm studying or going to study :P
@MikeMiller: I did work hard throughout one of my semesters, but still had to study because I didn't manage to keep up with every subject all the time. And, just to be sure.
@TedShifrin: There was a course about String Theory this semester but unfortunately I didn't dare to enrol, given that I hardly managed to visit any other lectures...
@TedShifrin: You know, if there was no such thing such as responsibility and necessity to earn money, I would much rather just visit lots and lots of lectures, because there are so many awesome lectures at my uni but I can't visit them all due to time shortage. That makes me sad.
@AlexanderGruber: I know hardly anything about them. I had a course about algorithms and complexity, and the first part about algorithms I hated everything, but the complexity part was rather interesting.
@AlexanderGruber: I loved linear algebra. I didn't understand much of abstract algebra, however my best mark so far was in abstract algebra. So I guess I just understood more than most other students.
@AlexanderGruber: Yes. I also took an extra course about finite fields, however never took the exam. It was rather interesting though. We did some sort of sudoku. It was called magic something.
@Studentmath Do you remember for the problem I asked you about, where there were 5 vertices, and I had to find how many ways edges can be drawn between pairs of vertices (since it is a simple graph) such that the graph was connected? And I also had to find it for 4, 5, 6 edges? That was what I was referring to.
@AlexanderGruber: I'm sure I would be interested in but I think if I have time to study something I should focus on my exams right now. And after that I have to study game theory in order to prepare a course at high school about it. =_=
If you end up wanting the link again sometime just ping me, I haven't posted this publicly yet cause there are a couple calculation details I wanted to make sure were right
@AlexanderGruber: I won't need to go into too much depth. I just need to know enough to being able to present stuff to my high schoolers and create new problems.
@Huy: Total mixed bag. Some would be at the beginning of my graduate course, some would be at the end of my undergraduate, and others would be in the middle of my grad course. Weird.
