How do you actually take maths notes so that it’s not in vain?

[Garvett]

I have hit a bit of a roadblock in my undergraduate studies. Our lectures assume that we should be taking notes, and that is entirely understandable: after all, what else can you be doing during a lecture besides listening and note-taking?

However, I have not the foggiest idea as to how to integrate notes into my studying process. I understand that if I take notes during class, I can engage much more with my material, and therefore give myself a head-start on reviewing it later on, (and I am not even talking about the case when you simply don’t know how to take notes matching the tempo of the lecture,)

But consider this: my Linear Algebra course, for example, has a rather unorthodox professor teaching it, and the arrangement of the topics is rather different from how it is in the textbook, not to mention that it doesn’t cover a lot of the material that, frankly, would be really nice to know. If I take notes during that class, I will, in the best case scenario, be left with a set of notes that are rather scanty, and hard to elaborate upon if trying to combine processing those notes with processing the material of textbook as well.

So what should I do? Should I just trust my lecturer (however hard it may be) with the comprehensiveness and structure of the course, and mostly study the notes, or should I spend god-awful stretches in order to create as god-awful a set of notes that is a blasted Frankenstein of my lecturer’s words and those of the textbook? How do you generally work with maths notes after class?

 

[fresh_42]

So what should I do?

You already mentioned it. It depends on a whole variety of parameters to decide what is best. The most important, however, is to figure out what is good for you! E.g. I need to write down things in order to memorize them. At the blackboard if I have the chance, on paper otherwise. But every person learns differently, some have an eidetic memory, and others like me need to write down things - and typing on a computer doesn't work, I have tried. And videos on youtube channels only offer the illusion of insights as far as I am concerned.

Then there is the professor as you correctly recognized: his style (ppt vs. chalk), his distance to the book, and last but not least, his speed. Look at the remark here:
https://www.physicsforums.com/threads/random-thoughts-part-6.875108/page-178#post-6340655

So if he is as fast as von Neumann was, then it's probably hopeless to take notes. If he draws a lot, then it's probably essential for your understanding. Proofs can be found in books and drawings with explanations not so many.

Then there is a trap to be considered. If you take your notes to learn something, e.g. before an exam, then you charge your short-term memory. This must not be confused with your long-term memory or with understanding. Your goal should be to charge your long-term memory and to understand the principles behind a concept or a proof. Practice, practice, practice is one way to achieve this. Solve as many exercises as you can and learn the ideas behind proofs instead of the wording.

Sorry, I know, this might not be the answer that you expected, since I do not offer a solution. It simply depends on so many things, and firstly on what fits you!

 

[symbolipoint]

Maybe this does not help and is only a reaction:
Study the material to be presented BEFORE lecture time. Now having studied the expected material, you have a better more reliable impulse for what to write & draw during lecture time, which you feel will help you.

Any instructive example which professor shows, write and copy THAT as accurately as you can, and be sure to study it later at whatever opportunity is convenient.

 

[Vanadium 50]

Notes are a means, not an end.

That said, when you are solving a problem, what do you wish you remembered about what the professor said? Should have written that down. As time goes on, you will learn more about yourself and the subject to better anticipate when this will be.

 

[mpresic3]

Taking notes can tell you what the professor thinks is important. Notes are even more important if you have an uorthodox prof, or a bad textbook. Ideally, notes should be reviewed daily, but the most important time to review notes are the night before the exams.
Sometimes, especially in math like calculus and maybe linear algebra, the notes illustrate proofs, and the textbook may concentrate on applications. The tests my concentrate on proofs as well.

I miss my notes. Until 1988, I kept all my notes of my undergrad courses. I left them behind after I moved. Now, as a retrospective I kind of like to know specifically what I was studying 40 years ago today. Also my notes were personal, in that my notes before class started might involve a list of groceries I needed before preparing dinner for that special someone. Or preparing for a country hike, or Christmas, or a swim meet etc.
If you can take notes and keep them. Maybe you can use them later preparing for the qualifying exams or the GRE's.