Week 1, Year 2 Fall

Going into Year 2, I am rather uncertain about my goals this year. On the one hand, I have already started working my way into the field of statistical mechanics and random geometry. Yet, I lack the necessary prerequisites to get into some of the more ‘pure’ fields. The biggest roadblock is certainly stochastic processes and stochastic calculus. Complex analysis is also necessary, but I feel like somehow I can intuit my way through this while checking some references.

Now that half of add-drop period has passed, my course choices are more or less finalised. As joked by my friends, I change my mind everyday. Yet, I think this is the point of add-drop period. It is nice to try out different classes, look ahead in textbooks, and make up your mind about which courses would be nicest to take. Learning my lesson from last Spring, I have reduced the workload. You can see my current course choices on the ‘CV’ page. It seems that unintentionally, I have went all in on analysis this term.

I expect to continue to observe Advanced Algebra I. Meng’s lectures are always interesting, although sometimes (most times) not for the ‘correct’ reason. Still, it is nice to review and keep learning some algebra in this otherwise algebra-barren term. I also went to CUHK to attend the Topology of Manifolds class last Wednesday. The teaching was really good. Instead of rambling on about stuff like Meng, he gets straight to the point. I am also officially auditing Applied Analysis. This was not by choice. I wanted to informally observe but the Professor just told me to submit an audit request… Anyway, I suppose it would also be good to work through some of the homework in this course, to provide concrete examples and applications (within mathematics) to the theoretical content that I learned through my courses.

It seems like I still haven’t really addressed the problem I raised in the first sentence of this post. I hope that this term, I will be able to get through the analysis part of the prerequisites (minus complex) through courses, while learning some more about percolation and perhaps more models. These self-studying efforts may culminate in a series of blog posts on Peasant Maths, although I make no promises as usual. (My curve-sketching worksheets and the trinity of posts on solving polynomial equations are nowhere to be seen now…)

In Spring, I would ideally be working on my ‘Guided Study on Research II’, hopefully with the person that I have worked with before, but I am not sure if he has time. I also said that I would do UROP concurrently. I’m thinking either quantum groups, random matrix theory, or Erdős–Rényi graphs. If that certain person does not have time, well, then I will be doing two out of these three topics instead. But then that would be very very sad. Hopefully, some form of representation theory will be offered in Spring by Marberg, either as Advanced Algebra II, or Introduction to Lie Algebras. The new required course for Applied Maths track people, Mathematical Modelling, also looks very interesting. That would be nice to take, although I am not sure if I have time.

Anyway, this is all quite idealistic. I am somewhat sure that as midterm approaches, all of this would be forgotten.