Hey friends, I spent some time this quarter typing up some notes for Vector Calculus and thought I'd share it on my website.

I also share certain misconceptions about Mathematics and how I previously appraoched it, the rationale for typing up the notes, how you can benefit from this Study Guide etc.

If that bores you and you want to get to the notes right away, feel free to use the Table of Contents (ToC) below!


I've never properly taken any notes for Mathematics.

Sure, I've copied equations off the whiteboard. And sure, I've directly replicated every symbol and every word from an example problem into my notebook.

That's has worked out well for most of my pre-university Mathematics courses (although I admit there were some huge warning signs). In High School and A-Levels, I used to brute force my way through as many questions as possible, identify my mistakes and memorize the correct procedures.

Undergrad Mathematics, however, is quite different. It requires you to be able to reconstruct certain arguments to prove or disprove a certain statement. It requires you to understand Mathematical concepts on a first principle basis, such that you will be able to apply and manipulate these concepts in a valid way in order to solve problems.

The purpose is not to memorize algebraic details that you could work out on your own with a strong understanding and sufficient exposure to practice.


In attempts to intuitively understand concepts, I explored multiple resources that was within my reach. Once I came across analogies, proofs, derivations and/or example questions that were vital for my personal understanding of a certain topic, I documented them using LaTeX (Had some guidance from Jarell).

It was a significant time investment but I think it was well worth it. (Plus it looks cool and gives me a dopamine kick whenever I review at it!)

Last week, my monthly domain hosting invoice came in, reminding me that I had a personal website which I built to document cool stuff that I could look back on, and perhaps bring value to some people along the way.

I carved out some time this weekend, lo and behold, the post is here!


This is the first Study Guide I've ever created and I'm by no means as good a student of Mathematics as I hope to be. Perhaps by learning in public and receiving your feedback, I can.

I openly welcome anyone to point out typos, incorrect statements, or send other suggestions on how to improve this Study Guide. Please email me at hi@jia-shing.com.

With that said, here are my first two Study Guides for UCLA MATH 32A.

1. Vectors Basic Formula Sheet

2. Vector Calculus Study Guide

A Quote

I'll end this short article with a quote. Hopefully, it'll act as a self reminder and I'll hold on to it for the remainder of my academic journey!

"Mathematics that is hastily learnt is easily forgotten."