Not gonna lie, quarantine somehow makes me more efficient in studying.
I feel like mathematics is a kind of subject really easy to stay focus on. Once I get into the state of beginning to learn mathematics, I can easily focus several hours to read, think, and learn. During the corona quarantine, I can listen to the lecture at home, and it makes my study schedule continuous. Meanwhile, I can pause the lecture whenever I feel lost or want to deduce something by myself. Even though we can’t ask a question right away, I mean, the format of recorded lectures works well for me for far.
This week is like a combination of Measure Theory and Analysis rewind. Professor Kuli talks about the approximation of functions. With the help of the Riesz-Representation Theorem for Hilbert space, we proved the Riesz-Representation Theorem for . He then introduced the weak convergence to enhance illustrate the dual space of , but I learned these from the Analysis course last quarter. We then talked about the Hardy-Littlewood maximal function and the Vitali covering argument from the measure theory. Well, at least I now have a better understanding of them.
The Algebra class is more organized and interesting than the Algebra I learned last quarter. After some definitions and theorems about unique factorization domains and principal ideal domains, we then talked about the factorization of integer polynomials, along with the Gauss’ lemma and the Eisenstein Criterion. The homework makes a connection between Algebra to some number theory and complex analysis. Maybe I have more background knowledge of this part of Algebra, but I indeed understand the materials quickly.
I am again so glad that it is the right decision to enroll Professor Craig Tracy‘s class. We talked about the properties of Markov Chain, which I was looking for, and more Random walks. One homework question is a very reasonable extension of the Random walk on Lattices taught in the lecture, which helps me a lot in understanding the materials. We also talk about the Random Walk on the graph, which is unexpected but surprised! I then can make a connection to what I learned in the combinatorial optimization. Hope that I have time to write down my thoughts on those in the future.