Year 4 · Fall 2025

I took 18 credits this semester. My GPA was 4.05.

Algebra (I)

My first encounter with abstract algebra. Compared with analysis, the toolkit is much smaller, and that is the upside: you usually know which tool a problem wants the moment you see it, and it is the kind of subject where simply writing forward shows you how the proof should go — relatively low-stress. The content is still rigorous, taught in a style that balances interaction with formal precision and plenty of worked examples, and the otherwise hard exams are softened by going through past papers beforehand. Special thanks to the TA — the recitation sessions were invaluable. I don’t love the subject, but I get along with it.

Softball

Attendance is 40% — full attendance guarantees a pass.

Directed Individual Study (I)

Honestly this was less “research” than a guided reading: I worked through Section 5.1 of Lawler and Limic. What made it a real challenge is that the book leaves many gaps in its proofs — filling those in, from a graduate text, was a fair stretch for a senior. I presented the work in my home department and was later invited to give a talk at NTNU. It is a separate thread from my NSTC random-walk project: this study is about symmetric random walks and estimating a hitting probability, whereas the NSTC project concerns simple random walks and the distribution and expectation of the hitting-time random variable.

Advanced Statistics

In practice the continuation of Professor Wang’s Statistics — together a fairly standard math-department statistics sequence. Gently paced, graded on a midterm and a take-home final, with no attendance or homework.

Machine Learning

I love Professor Lin’s teaching as much as ever, though this course is a touch harder because the material is somewhat scattered. He orbits topics near his own research — backpropagation, function approximation by neural networks, gradient descent–ascent, score matching, stochastic differential equations, Fokker–Planck equations, reverse-time SDEs, physics-informed neural networks (PINNs), and neural ODEs — alongside the more standard regression, dimension reduction, and PCA. It stays mathematically demanding throughout. As in his ODE course, he teaches tools through the problems that motivate them, so you never sit there wondering what something is good for. Graded roughly 80% homework and 20% final project — the assignments are manageable if you put the work in, while the project rewards a design that is actually your own.

Financial Management

Typical of Professor Tsai’s courses: light workload, minimal homework, the exam scope shared beforehand, and attendance required. The report doesn’t need to be long — it just asks you to pin down the single most important point of the article or event study you choose.

Futures and Options

The hardest course of the semester for me, and the one that settled my decision to stay away from the investment track. The instructor — a math major by training — is remarkably articulate at unpacking complex ideas, and I appreciated his teaching. My problem is intuition, not computation: I can crunch the numbers, and I could do every Financial Management problem, but ask me to put together a trading strategy or spot an arbitrage and I am lost, with no idea where to begin. Finance and trading simply aren’t how my head works.

Accounting (I)

Taken in the preceding summer (Summer 2025).

Typical of Professor Tsai’s courses: manageable workload, minimal homework, the exam scope shared beforehand, and attendance emphasized.