How to take notes for physics and math?

I am bad at taking notes. I have always borrowed/bought my friends' notes to brush up for the exams because of that. I want to learn how to take notes for physics and math on paper since I don't want to be too dependent on others. I decide to learn to take paper notes because it is faster to draw diagrams with a pen than with Latex or Inkscape. Any suggestions or good resources? How do you take notes [in STEM classes]/[when you read a STEM textbook]?

Thank you.

I'm not sure there's any single technique that's going to apply for everyone. People learn in different ways and so have different approaches. Some students don't take note at all and prefer to just listen and engage with the lecture content. Others, like me, have a tactile component to learning and need to be writing something keep out brains from wandering. Here are a few tips...

1. Come to lectures prepared. At minimum, make sure you've completed any assigned reading. But beyond that, keep track of what material you're expecting to cover and read up on that before hand. The point is to minimize the amount of brand new information coming at you in a lecture.
2. Develop a short-hand means of getting information down quickly and efficiently. Use point form, but don't sacrifice clarity. On this end I would also suggest making sure you're familiar with the Greek alphabet and any other notation that your professors use. Sometimes a subtle difference in two squiggly lines can mean the difference between understanding an lecture and not.
3. If you have a reliable tablet, I've found that OneNote is awesome software for note-taking. If even has options that allow you to record the lecture, and make time so that you can go back and listen to what the professor was saying at different points in the lecture. (Make sure you conform to all the rules at your school about recording lectures though - if it's even allowed.)
4. Along that last point, take pictures as a last resort (and only if allowed). Sometimes that's the only way to capture all the information on a complex slide, but my understanding is that there is some research out there that demonstrates people tend to remember less about an experience when they photograph it (unfortunately I can't point to any study specifically).
5. Don't be stingy with paper space. Leave yourself a lot of room to go back and add thoughts, details or questions when you're reviewing. Make sure to date and number pages as well so that you can keep them in order.
6. If possible, when the professor works though a sample problem, write out the problem and solution in different regions. That way when you come back in your studying, you can work your way through the problem without simply copying out the solution and this will help to keep you engaged.
7. Write down what the variables mean. If you don't know, ask.
8. Universities often have free workshops for students on note-taking skills - take advantage of them.

Like Choppy said, read the relevant chapters/section before class and develop a short-hand writing system. That way, you'll be able to follow along better in lectures and not fall behind.

I find that writing notes during lectures is actually detrimental to my being able to follow along with the instructor. I know studies say that writing notes is the best way to retain information, but I just can't multitask to save my life. I can either listen to what the instructor is saying or I can write down what they're saying; but I can't do both. And if I'm just writing their words without actually comprehending them, am I really learning anything? No, I'm just regurgitating their words onto paper. Therefore, I don't really write notes during lectures. I only write down the instructor's sample problems/solutions and any key points they make that are not in the textbook.

Developing my own short-hand writing system really helped. Here, let me give you an idea of what I do:

during - dr^g
developing - dvlp^g
including - inc^g
development - dev^m
argument - arg^m
inclusion - inc^n
evolution - evl^n
inclusive - inc^v
at - @
and - &
therefore - ∴
such that - s.t.
with - w/
without - w/o
each - e/
each other - e/o

Do something along those lines. I'm sure your notes will be awful on the eyes, but you're the only one who will be referring to them. So as long as you can understand them, it shouldn't be an issue.

You can use an app that records the lecture and allows you to take notes. Notability is one such app for iPad that can record while you take notes. It also keys the note to the recording so that later, when you tap on the note, it will jump to the relevant point in the lecture.

I've never found it useful to take notes in a math or physics class except for rare nuggets of info or when an idea pops into your brain. It's best to read the chapter beforehand and sit and absorb what the professor is teaching.

One problem is trying to keep track of a professor who writes something down and then erases it moments later, replacing some number or expression or drawing a diagram and then overdrawing it repeatedly. You can't capture that in a meaningful way, so it's best to stay focused and just listen.

Barring an app, a recording device, or using your phone to record the lecture would work too. But the key here is to listen to the recording again as soon as possible, definitely within a few hours, to retain most of what was said and perhaps transcribe what you hear into searchable notes.

Another app for long-term note-taking would be Obsidian. It's popular with grad students doing research and allows them to collect and network their notes like a personal Wikipedia.

Here are some things to consider in any app you use:

https://zapier.com/blog/best-note-taking-apps/

What @Choppy says is mostly the way to think on taking-notes.

Come to lecture time, prepared. Write examples exactly as your teacher/instructor/professor shows them. Write the notes which HELP you to understand the topic or method presented; which you recognize when you come to lecture time prepared. Mostly YOU decide what notes YOU should take because you are picking them to write for your own help.

Maybe I should not tell this, but nobody knew anything about any kind of "note-taking apps" when I was a student.

It may be a good idea if you can find one, two at most, classmates with which you can quickly go over the lecture right afterwards, to avoid going fully off-track. Sort of " So, ##\alpha## here refers to displacement", just to narrow things , to avoid going too far off track. Maybe you can contact someone, two people, at the very beginning of the semester. More than 3 people will likely turn into a bull session.
Then when you go study on your own you have your work cut out for you.

Together with reading ahead and things others have said.

I last went to a lecture during covid, and obtained my last advanced degree over 10 years ago so the rules may gave changed. Back when I took core courses, the teachers used blackboard and chalk and whiteboards were just coming in.
Assuming teachers are using white-boards or blackboards, note taking is relatively easy. When a teacher / professor writes an equation on the blackboard, or makes a diagram on the blackboard, you reproduce it in your notebook. That is taking notes.
You say you can get notes from friends. Try this. Take notes by putting your teachers exposition on the blackboard in your notebook as I have said. Then borrow notes from your friends on the same day as your notetaking. I am ninety percent sure, your notes will almost exactly match your friends notes in content, except for handwriting differences. (Unless you are dyslectic or have some other difficulty.)
Go to and take notes like this in all classes, any you will be a good notetaker, like your friends. Why not?

I tend to put the date and lecture number on each page and begin each lecture on a fresh page and keep all the notes in one place, (a folder or a notebook). If I am as ambitious as I should be (but almost never do), I add to the notes taken every day with my own notes when reviewing the professor's lecture notes.

One intersting story I remember about taking notes in a lecture. One day the professor put a strange symbol at the end of the equation which I did not recognize at all. I reproduced the weird symbol exactly as I saw it and he had written it, in my notebook. I meant to ask him about it later.
I reviewed the notes the next day and although the symbol was no different from what he wrote on the blackboard, I recognized the symbol. (I do not recall what the symbol was, it may even have been a punctuation mark at the end of a sentence, or something like that). If that happens to you the best advice I can give is reproduce the symbol in your notebook as best you can, for when you can examine or refer to it later

[Mentor Note -- Two threads on same subject merged]

Some people dont taking notes at all during lecture...
Often reasons: loosing time for something that is already written in books, writing instead concentrate on lecture, etc..

What is your opinion for this, and what are pros vs cons of taking/not taking notes?

I always taking notes but I notice one thing, I just write in my notebook what professor tell/write on blackbord as quickly as possible to be able to rewrite everything he tell/write. So in that time you cant deeply think... So I understand topic truly only when I solve tasks by myself...

user079622 said:

Some people dont taking notes at all during lecture...
Often reasons: loosing time for something that is already written in books, writing instead concentrate on lecture, etc..

What is your opinion for this, and what are pros vs cons of taking/not taking notes?

This depends very much on personal characteristics. I took notes and worked through them afterward writing them again in a better fashion and with the book at hand. My reason was, that I learned things better if I had written them, and yet even better if I had explained them to someone. That's why I love blackboards and chalk.

I cannot rule out that people learn well by watching YouTube videos but I am none of them. The same holds for only acoustic stimulation. I have to write down things. That's probably the reason I wrote so many insight articles here. They helped me to learn and understand things better than if I just had read them.

I once had the following dialogue with my mentor at university after I read the announcement of his lecture in the upcoming semester: "I did not know that you were an expert in that subject." and he answered: "I am not. That's why I will hold the lecture."

As @fresh_42 said, this is highly personal. I experimented with taking notes during lectures once, it did not work well for me. I found that writing the things down distracted me too much from focusing on what was being said. Others cannot live without their notes - one of my ex girlfriends was one such person. She used to even study in the shower with her notes (appropriately put in a plastic folder to avoid getting wet of course).

The bottom line is that you have to find what works for you.

Orodruin said:

As @fresh_42 said, this is highly personal. I experimented with taking notes during lectures once, it did not work well for me. I found that writing the things down distracted me too much from focusing on what was being said. Others cannot live without their notes - one of my ex girlfriends was one such person. She used to even study in the shower with her notes (appropriately put in a plastic folder to avoid getting wet of course).

The bottom line is that you have to find what works for you.

Any study that shows which camp get better results, in average?

user079622 said:

Any study that shows which camp get better results, in average?

If your purpose is to find out how to study better, I think you are missing the point. The point is that finding what works best for you is likely going to be very different question from if a group that does better with another mode of studying performs better on average. Even if they did it does not mean that you should change your mode of study. The only way to find out is to experiment with it and see what you find works best.

Orodruin said:

She used to even study in the shower with her notes (appropriately put in a plastic folder to avoid getting wet of course).

Oh my gosh, and I thought I was a nerd!

Orodruin said:

She used to even study in the shower

I bet she had no trouble finding a study partner!

mpresic3 said:

I remember one interesting story about taking notes in a lecture. One day, the professor put a strange symbol at the end of the equation, which I did not recognize. I reproduced the weird symbol exactly as I saw it, and he had written it in my notebook. I meant to ask him about it later.

I had a similar experience in grad school, taking advanced Classical Mechanics. The professor lectured us on some topics using the Greek letter ##\xi##, but his writing looked like ##\zeta## to me. It wasn't until I started to review the chapter that I saw I had the wrong Greek letter written in my notes.

Searching online, I found that some folks have used these letters as indices for tensors to totally confuse readers of their papers.

jedishrfu said:

I had a similar experience in grad school, taking advanced Classical Mechanics. The professor lectured us on some topics using the Greek letter ##\xi##, but his writing looked like ##\zeta## to me. It wasn't until I started to review the chapter that I saw I had the wrong Greek letter written in my notes.

Searching online, I found that some folks have used these letters as indices for tensors to totally confuse readers of their papers.

That's peanuts. We had to learn ...

... to write vectors.

When I was an undergrad we used to call ##\xi## ”the grand tremble” based on how many lecturers wrote it.

Orodruin said:

When I was an undergrad we used to call ##\xi## ”the grand tremble” based on how many lecturers wrote it.

Sure? Looks like the small tremble. The great tremble would be ##\underline{\;}- \overline{ \;}## that is not even path connected.

As far as watching you tube videos OR taking notes. Why not watch you tube videos .AND. take notes. I took notes during several of my classes that were recorded for viewing at a future time. When watching many of the youtube videos with a class presentation, I notice many of the students are taking notes in realtime. I would be very surprised if the note takers did worse in the course as the non-note-takers.

mpresic3 said:

Why not watch you tube videos .AND. take notes.

Well, let me tell you how it was back in the eighties, son. In the good old days, we have had ...

mpresic3 said:

I would be very surprised if the note takers did worse in the course as the non-note-takers.

Orodruin said:

The only way to find out is to experiment with it and see what you find works best.

(emphasis mine)