Lecture highlights: Euclidean structure Categories and functors Meth He methed a lot this lecture! In the Greek times, they believed that the Earth is the centre of the universe. They tho...

Today we talk about affine spaces. We only care about stuff over the real numbers in this course. Lecture highlights: Definition We have a ‘dictionary’ between vector space and affine space ...

Update 2024-09-09: Look at how this went. p-adic distance ultra-metric $\sigma$-finite measure: the measure space can be decomposed into a countable sequence of sets with finite measure c...

I cannot claim to have a summary of the whole lecture, that’s why I switched the wording to ‘highlights’ Lecture highlights: tensor algebra graded vector space determinants M: Do abstrac...

Calculus on Mengnifolds I have no idea what happened this lecture. Lecture highlights: Notations Review of linear algebra The set of bases of $V$ may be naturally identified with the set ...

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 t...

Lecture summary (roughly this time, but will get more detailed in later lectures): Waffle about metamathematical content Rough overview of the course Group and field actions A field is som...

The proof of the single-variable chain rule below is based on one given by Prof. Frederick Fong in his MATH1023 lecture notes, taught at HKUST. Before reading this post, it is strongly recommended ...

Inspired by Toby Lam, here is some life update. Lying flat Lie flat is me. Before the midterm, it was still alright, I was engaged in some sort of work for several hours per day, even though some...

So I am really bad at inequalities. Last month I learned something so I will share it here yeah. I will probably upload all my course notes somewhere after I’m done with this course. I think in de...