Note taking for Mathematics at University

I have been doing a lot of tutoring recently, and a student of mine asked about how I took notes during university so I thought I would share how I took notes for my mathematics class in both my undergraduate degree and my master’s.

Lectures

For my in-person lectures, I took notes on my tablet (I used a reMarkable) and I copied nearly everything down, as it helped me pay attention. After the lecture, I then type up my lecture notes using LaTeX and Overleaf. I found this particularly helpful because often in lectures I didn’t feel that I had fully understood some of the proofs, but going back over them when typing them up really helped me get to grips with them.

I know some people who don’t take notes but instead just focus on what the lecturer is saying and go through it afterwards. I think this could also work well if you can genuinely focus without writing.

Lecture Notes

Most maths courses at university provide lecture notes. I didn’t read them before the lectures, but when I was typing up my handwritten notes, I would read through the official lecture notes and add details from them to my typed notes. I found this useful as sometimes a proof might not be done in a lecture, but is done in the lecture notes.

Problem Sets

During my undergrad, I did the problem sets but I didn’t make any notes from them. However, during my master’s, I noticed that the problem sets tended to include more useful results that you might need later, so in hindsight I would have gone through the problem sheet and updated my typed notes with any results from them that aren’t in the notes.

Books

Textbooks can be useful extra resources when studying a maths course. Particularly in the 3rd year of my undergrad, I would read a section of a relevant textbook around the same time as I was typing up my notes for a lecture. I often didn’t add anything to my lecture notes from the text, but I did find it useful seeing the same content presented in a different way.

During my master’s, I found that the lecture notes were less detailed so in hindsight, I probably would have added details from the textbook to my typed notes as well.