[Math] Up-to-date advice on the best way to take notes (maths)

Question

I have read some old discussions about this topic and would like to get some up-to-date advice if possible. I'm going to start university next year (maths), and I know how important is to have a set of well-organized, well-taken notes, since you have an extremely larger bounch of material to study (compared to high school). Then my questions are:
–what are the best techniques to take good notes "in real-time" (if you know what I mean) and without getting distracted (I mean, without getting everything stright from the blackboard to my notebook without passing through my head)?
–should I use a tablet/computer to take notes? If so, which app/program do you suggest? Is it advisable to write mathematics with a stylus on a tablet, or it is better to use something like mathamatica? Is it possible to use such devices in real-time?

Any piece of advice on this topic (from professors or students) is really welcome. Thank you in advance!

Answer 1

It's really an art, not a science. I can tell you what has worked for me:

1. Use a legal pad with three-ring punches where the sheets rip off clean at the top. I prefer a white one. After class, tear all your notes out from that day and put a paper clip on them. Store them in a manila folder dedicated to that class at your house. Also in this folder should be graded homeworks and other class materials.
2. When you write notes, put the date of the class at the top of the first page of notes, so later when you've got a bunch of various days of notes, you can tell at a glance the chronology.
3. Number each page of notes from that day in the lower left-hand corner (so if they get mixed up, you can quickly get them back in the right order). Start back over at page 1 with each new class. If you end up having to insert a page in the middle, call that page "6b" or something, and change the previous one to "6a", so you can tell there should be a page between 6a and 7.

4. If you're on page 3, say, and you want to refer to something on page 1, mark it with an equation number or a star or something and save yourself time by abbreviating it: for instance, writing "then using (1.5), we get that (1.1) becomes (1.3)" is a lot quicker than writing out all those equations again.

5. Directly after each class, do the following:

   --Go over the notes quickly and write on the top of the front page, by the date, keywords representing the topics covered that day. For instance, "Poisson's formula", or "Proof that $e^{i\pi}=-1$". This way you'll be able to tell in which set of notes a topic is covered when you're looking for it later.

   -- Go over the notes and isolate the things that require follow-up work for you, and put those in your to-do list (you should have one!) For instance, "Understand second fundamental form". Then later, use your resources to take care of these. Do not just stow the notes away and promise yourself that you'll "go over them" later. Unless you isolate specific things that you need to do, they will just pile up and turn into lumps of stuff you haven't taken care of.

Remember that the art of organization is the art of being honest with yourself: what are you really going to go back and do? What parts of the notes are you really going to look over and use later? Are you writing notes with the goal of advancing your understanding, or just because you want to feel like you're doing something?

For general organization tips (and getting the most out of notes is largely about organization), I recommend reading Getting Things Done by Allen.

EDIT: After a number of years, I would now recommend something like Notability for capture, and Anki for retention. Above all, don't rely on your intuition for when good learning is happening. Read the evidence (e.g. the book "Make it Stick" or www.learningscientists.org). Notes are generally low-utility. (Though of course you do need notes to capture information.)