MATH GU4044

Learn to carefully listen to the lecture and abstractly think in maths

1 problem set every week,2 tests, 2 quizzes (All of them very straightforward, no tricks)

Learned about major theorems in Representation Theory (the theory of representing algebraic structures-here finite groups-by matrices/through linear algebra), their proofs, and how to apply them

The first half of the class concerns the general theory of the representation of groups (over the Complex Numbers, roughly corresponding to Chapters 1-3, 5-7.3 of Serre's Linear Representations of Finite Groups). Some brief digressions for discussions of applications of representations (to probability, the Heisenberg group, etc.) were made. Then, in the second half of the class the specific theory of the representation of the symmetric group is developed (roughly in the manner laid out in A NEW APPROACH TO THE REPRESENTATION THEORY OF THE SYMMETRIC GROUPS by Vershik and Okounkov). Throughout the class, particularly the second half, we also learned to use the SageMath software and how to apply it to solve problems in computational representation theory.

Professor K is a really awesome guy and I think everyone enjoyed this class. He has a really good sense of humor and is always cracking jokes related to the material. For example, the light-switch started beeping once during class, as if it were going to shut off soon. We had to toggle all three switches to stop the beeping and Michael quipped that it was "the group Z2xZ2xZ2." On another occasion, he remarked "When I was young, I tried to picture the 3-sphere....and I almost succeeded except for one point!" We went through the material in a very non-rushed manner and Michael was happy to answer any question no matter how stupid. The TA (You Qi) had a round table discussion for an hour every week which was great. You Qi is extremely smart and he likes to talk about math. The homework and tests were extremely easy (small computations usually) but the material is rather advanced and there are some difficult patches. There is a wonderful website for the course with many useful links and even a few online books. We loosely followed one of these books for about 2/3 of the course. For the rest of the course Michael came up with this interesting way to present the last topic which wasn't in any book or article but the TA wrote up the notes for this section. They are excellent. What I appreciated most was that we covered necessary topics that you don't see covered in any of the other u…

I think this course is great for those with specific interests. There needs to be a much stronger foundation in linear algebra than I had, and I often did not fully understand what was going on

not suitable for students not major in math or want to do math phd. It is highly abstract.

The first half of the course is a standard (and quite solid) introduction to representation theory of finite groups. The second half is a very interesting and unique learning experience on a way to build up the specific representation theory of the symmetric group. My understanding is Professor Okounkov was a primary developer of this particular method of studying the representation of the symmetric group, which makes this course taught by him a very special opportunity. That being said, because the technique is so novel, there aren't really references (that I could find) on it. So you really have to make sure you're paying attention in class and asking lots of questions in office hours with Professor Okounkov and the TA, otherwise it will be hard to understand something you don't know about. The course structure/teaching style is different from many undergraduate courses, with Professor Okounkov not really using the "Definition-Lemma-Proof-Theorem-Proof" style that is most common, but emphasizing more "ideas" (though of course propositions and proofs are still a central element of the course). The homework assignments and midterm were, I think, generally fair, if sometimes confusing. The final project was a very interesting application of SageMath. Professor Okounkov generally made the class feel low-stress, he was more interested in us getting an understanding of the subject…