I have fewer courses of a quarter, but this quarter is somehow more intense.
I am now involved in two different research, and these experiences are much more different than I originally thought. They are exciting and interesting, but at the same time, they are full of pressure. When I stuck and used plenty of time but made no progress, it was frustrated more than solving Analysis homework. But if things go well, all the frustrations pay off. Moreover, although my research is mentored under some professors, they only provided the directions of my research, and I need to explore the rest of the road. All in all, I am glad that there are challenges in my life, and I am looking forward to my growth in the future.
The Analysis never ends, and I enrolled in the last series of the graduate analysis courses MAT201C told by Professor Luli. During the first two weeks of this quarter, the Professor talked about the convergences of functions and the relations between them. I learned most of them before, and they are kind of like a review of materials. Wednesday’s lecture talked about the Riesz-Thorin Interpolation Theorem which is a further topic in space. I am expecting some topics about Sobolev space and Fourier Transform in the future. They are tough but interesting.
Stochastic Differential Equations:
I enrolled in the Stochastic Differential Equations directed by Professor Sebastian Schreiber. One reason why I enrolled is that it sounds interesting, and I do think that reading can give me a larger sight in the mathematics world. Another reason is that it is related to my Ordinary Differential Equation reading, so I may have a better understanding of both topics in the future because of this. The textbook is Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal combined with An Introduction to Stochastic Differential Equations by Lawrence C. Evans. The week 1 review the materials of basic concepts in measure theory and probability, and the second week comes to the Law of Large Numbers, Central Limit Theorem, and an introduction to Brownian motions. I am familiar with the first two terms but not the Brownian motions. Hope that I can learn something interesting.
Someone told me the following: “If you are a student at UC Davis majoring in mathematics, you need to experience Professor Craig A. Tracy‘s course once.” I hardly had a chance to do so since I have already finished most of the undergraduate courses. However, while I was auditing the first course in probability told by him in the last quarter, I was shocked by the depth and breadth of knowledge contained in this undergraduate course. Therefore, I decided to enroll in the second course in probability told by him this quarter. That is, relax and enjoy the teaching of a master.
I would say that Abstract Algebra is one of my least favorite subjects in mathematics. I was genuinely surprised by the art of symmetric in the representation of group theory years before from the lecture of Professor Gorsky, but it did not go well for me last quarter. Things are not well connected, and the concepts are somehow isolated for me. Since this is mandatory, I have to complete the Algebra series. Hope that I can have more fun in Algebra this quarter.
2020 gets worse, but time goes on. Thrive and fight, for the future.