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...

# Calculus III - Lecture 1

# The Chain Rule

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 ...

# Some Inequalities

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...

# Equality Axiom

Note: This is a guest post by my friend Eaton Liu. Everyone is equal. People are saying this way too often, to an extent that they no longer understand what it means. For example, some people may ...

# I Hate Indices

I hate indices, every last one of them. I don’t mean indices as in power, the little number on the top right corner of a bigger number, nor a measure of something, often seen ticking in stock excha...

# An Absolutely Trivial Inequality

In this post I will talk about the absolutely trivial inequality [x \leq \lvert x \rvert .] This is easily seen. If $x$ is positive, it is equal to its absolute value. If it is negative, it is of...

# How I would teach maths to an uninitiated mind

Don’t pull out the Soviet/French curriculum. We assume the average intelligence walking monkey. Modern mathematics (for now at least) builds on sets. Of course mathematics is not all about studyin...

# A neat trick with inverse trigonometric functions

Update 2023-01-25: So I first encountered this in a STEP problem 00-S2-Q4 on STEP Database. Today I found something that is relevant and it’s Machin’s formula and its generalisations. Update 2022-...

# Origin of the Theory of Measure (Family Friendly Edition)

Once upon a time there was an Amazonian tribe with an interesting tradition. Every person plant cucumbers and each year they would measure the length of their longest cucumber. The person with the ...

# Hoarder Culture in Mathematics Learning

I would consider myself somewhat of a hoarder. I just don’t throw away stuff. I collect stuff. I don’t spend fake internet money in games (getting better now). Yet this hoarding culture may in some...