Resources

Some open-sourced handouts, notes, interesting stuffs I made (with friends).

I ~~might~~ frequently make mistakes, so corrections are highly recommended through emailing me!

Handouts

23 Fall: Calculus Crash Course [PDF] (Recordings here)

Functions (Pre-Calculus)
Limit
Derivative
Application of Derivative
Taylor Series
Integration and Application of Integration

X-Program Lecture — Introduction to Group Theory [PDF]

This is a very condenced 40-minute (actually 1 hour) mini lecture on introducing the concept of groups, covered contents including

basic axioms of groups
cyclic group and generator
subgroup
group homomorphism and isomorphism
kernel and image

with reference on Paco Adajar's superb dorm lectures in Ross Mathematics Program (thank you so much Paco! )

Here is the recording for X-Program Math Course Oct 20th, recorded by Lola Huang. The first 43 minutes is covered by Lola talking about reconstructions of math and complex numbers, then I started giving the intuition of group theory based on sets, functions, and basic properties of addition and multiplication after 43:00 with some interesting examples.

$\LaTeX$ Guide [PDF]

This is a $\LaTeX$ Quick Guide for students (members in math club) who are going to

participate in HiMCM
write STEM essays (i.e. IA/EE)
be a perfectionist

but didn't know much about $\LaTeX$.

The content includes

Use $\LaTeX$ for math
- Commands
- Inline math
- Displayed math
- New commands
- Align environments
Tables
Figures
Refer
Citation

I also later held a workshop on learning $\LaTeX$ in 1 hour, and the recording is here.

Some recommended resources for further learnings are

TeX Stackexchange
a symbol list and another one
TeXnique to help practice
Typst which I guess is more helpful when you are dealing with annoying CV

I have made a useful (I guess) math problem set solution template, a CV template for high schoolers based on Typst-Chi-CV-template, and a post on good $\LaTeX$ writing habits

InTeRESting StUfF!

Music Recognition App Project

As an extension to my extended essay in math for IB, I am now doing a project on extracting musical notes from audio as an improvement of direct Fourier transform, inspired by Jeff Heaton's Extract Musical Notes from Audio in Python with FFT but with a better approach to determine the fundamental notes played!

I already made a MATLAB demo for my math extended essay result presentation and it seems working well. Will update it to a real applicable repo of code and maybe even to a music sheet converting app! :)

If you are also interested in helping, feel free to contact me and/or contribute in setting it up! I have the motivation to do this because I am a music, piano, DIY, transcripting enjoyer while I do not have perfect pitch. So I hope I can actually build this up and make it benefit music/piano enthusiasts so that they can convert the music sheets for music they want to play on hand instead of asking for transcripting help!