An Eventful Three Days

The first (incomplete) week of the Spring term has ended. The term commenced on Wednesday, Jan 31. I am writing on Saturday, Feb 3, and I am already exhausted. But I did learn a lot from the past three days.

Day 1

It felt great to be back on campus. I started off the term with Honors Mathematical Analysis, taught by Prof. Ivan Ip. Interestingly, my first lecture as an undergraduate student at HKUST, so my first lecture of the Fall term just past, was Honors in Linear and Abstract Algebra I, also taught by Prof. Ivan Ip.

His lecture was just average. But it was average by his standards so it was pretty good anyway. I knew most of the stuff so I just ignored him and worked on the homework.

After lunch, it was time for the first lecture of Honors in Linear and Abstract Algebra II, taught by Prof. Qingyuan Jiang, a new professor specialising in derived categories and derived algebraic geometry, aka abstract nonsense. As soon as he walked into the classroom with some sort of signature swag and carrying a tray of platonic solids, I knew this lecture was going to be fire. He delivered! His enthusiasm was great and definitely made us excited as well. He had a grand vision for this course: exploring the landscape of algebra and visiting the realms of groups, rings, modules, and fields; as well as venturing towards Galois theory and algebraic geometry. Well, I sure hope he can finished this monstrosity he started.

The last session of the day was the tutorial of mathematical analysis. It was ok. Nothing on the TA, he seems nice, but the content was mostly review so it was destined to be boring. Small complaint of the day: the rooms were far too small; I nearly suffocated. I will not be attending mathematical analysis lectures since I can just watch the recording at 2x speed anyway.

Day 2

AH. The day of six hours of four consecutive lectures. We started the day off with Honors Probability by Prof. Zhigang Bao. He actually looked very different to his photo on website. Very striking, I would say. Anyway, the classroom was filled, as expected from the long waitlist, which I am unfortunate enough to be a part of. I didn’t really listen though, since I knew all the stuff from self-study over the winter break.

Then, it was time for Complex Analysis, taught by Dr. Henry Cheng. Last time I saw Dr. Cheng in real life was back in Dual Program, while he was still a postdoc. The first lecture was simple enough, just a review of basic complex number stuff. Anyway, that very evening I submitted an audit request, and he let me through. Depending on the status with my Honors Probability waitlist and whether Prof. Bao will increase quota, I might actually take this course for real.

This was the first of two shocking events in these three days. After Complex Analysis, I rushed to the Calculus on Manifolds lecture, given by Prof. Guowu Meng. During my stalking research on the maths professors at UST, Prof. Meng stood out to me. Through my (possible naive) undergraduate eyes, he is one who used the tenure system to its full potential. It is clear, through the stuff he put on his website, past and present, that he is doing what he love. Now, the dear reader might think that I am hinting at something bad, that someone isn’t doing their ‘moral duty’. No! I think one can definitely see that he is doing legit research, although I cannot judge the quality with my untrained eye. His teaching is also very good from what I have seen.

I think the foremost quality of his lecture is elegance. He explains abstract topics beautifully. Perhaps it is just an illusion, but I feel like he is capable of explaining complex topics in an effortless way. He said it himself. He is going to teach us the true geometric interpretation of the chain rule: if you see it once, you will remember it for life. That’s why he hates those thousand-page calculus textbooks. Indeed, cookbook style ‘math’ is no good for those who want to truly understand. Anyway, I am definitely holding him to that promise. I feel like his course is even more advanced than Prof. Frederick Fong and Prof. Min Yan’s version, although I haven’t carefully compared the lecture notes.

I am not sure which one of the above contributed the most, but together, this lecture shocked me. It completely changed my expectation expectation of the quality of education I will receive at HKUST. More on this in another post. I have decided to open a blog series on Peasant Maths, taking notes on his lectures as I observe throughout the term. My first post is here. Now I should stop fanboying.

Finally, we conclude the day with Honors Calculus II, taught by the beloved Prof. Frederick Fong. Not much to say. Interesting approach of the Riemann integral though. He is defining area by Jordan measure, basically Lebesgue measure with LEGO. This makes it slightly easier to work with, but obviously poses problems. Again, more on this in another post, likely to be in Peasant Maths.

Day 3

Yesteray started off with Multivariable Calculus, taught by Prof. Quoc Ho. He looked younger than half the class. lmao. It’s quite boring though, normal for such an elementary course. I will be very interested in taking his grad-level courses in the future. Going to multivariable calculus was at the expense of missing the first lecture of Topology by Prof. Min Yan, which I will likely attend later, as I am sure I can self-study multivariable calculus well enough.

Now we come to the second lecture of abstract algebra, where Prof. Jiang surprised us all by introducing and defining categories, which he will use in this course. Interestingly, the number of people in the room halved as compared to last time, likely due to the previous lecture being too easy. I am sure many of them will be coming back for future lectures.

Right after that, I attended the tutorial for topology, led by the most amazing TA I have met so far: Mr. Liu Wenwei. He also led the tutorial for Honors Calculus I in the Fall term, which I have throroughly enjoyed. In calculus, he extensively copied referenced a famous set of notes by Huimin Xie (謝惠民), or so I suspect, and brought us much joy. But anyway, onto topology. He really surprised us (at least me) by talking about the monomorphism interpretation of, phrasing it as the universal property of injection. But the second shocking part of the week came next, when he talked about replacing the notion of a function with its graph. Then, he reinterpreted function composition with what he called the ‘convolution of graphs’. It was unlike anything I had ever seen.