I am a great advocate for using flashcards (spaced repetition software, like Anki) for consolidating material from textbooks and lecture notes. So far, for learning theorems and definitions, it has been pretty invaluable. Using cloze deletions (e.g. "The ___ is the longest river in the world.") I have been able to 'internalise' theorems, too - a simple example from general topology would be "A ____ subset of a compact space is compact".
My problem is figuring out exactly how far I should take this, and in what sort of order I should go about things. My current technique is:
Sit down and start reading a chapter.
When I get to a definition or theorem, I write it down (I use a tablet so I can write things down in red, and change the colour to green when I've created a flashcard).
When I get to a proposition, proof, or example, I decide whether or not it could be useful for answering a problem, and if so write it down. My university likes to ask people to prove theorems in exams, so I tend to write most proofs down if this is a university course. The idea is generally to fill in the details behind proofs at the same time, also. The intention is for long proofs to be broken into multiple flashcards detailing their 'steps'.
When I get to the end of a chapter (or subchapter if the chapters are very long), I write up the notes I've just copied in Latex, and then use those to make flashcards.
Once I have made the flashcards, they get added onto a 'new' pile that gets steadily reduced during daily reviews.
Having made it to the end of the chapter, I then do a portion of the exercises, and if I found a useful technique in them I tend to make that into some sort of flashcard as well.
My questions are these:
Is this an effective way to learn material?
What steps could I take to improve this system, in terms of efficiency or effectiveness.
How should I change this system when reading papers instead of textbooks, and when reading textbooks for research rather than university? (I am doing a research project soon).
It is worth pointing out that almost all of the maths I do is of the "conceptual" kind, rather than the "techniques" kind. Abstract algebra, rather than PDEs.
If this is too vague a question, or one which does not have an objective answer then feel free to close it. I do feel that as this is asking about a technique to solve a given problem, it can be answered much the same way as any other question about techniques for solving a certain type of problem. The problem is related to maths, so I feel it is appropriate.
Just the act of creating the notes is an effective way to learn new material. However, I have found that creating "Notes" in Anki can overwhelm my deck if I am not careful about asking a detailed question. Studying multiple subjects, or researching an issue with common terms used in other knowledge areas, can create confusion for me when I review a note in which the question lacks detail. It is important that your question not be too ambiguous.
Since definitions and theorems are standard material to know for future testing, you should create your note directly in Anki rather than on your tablet. Simply use a Cloze card for definitions and a Basic (and reversed card) for theorems. I have never tried breaking proofs into separate steps on different Notes. It isn't helpful to study flashcards you do not understand. If you do not understand the theorem, it is not helpful to memorize it. Once you understand the proof of the theorem, then you can create the Note and memorize it. If I find a particular exercise helpful for some peculiar reason, I will create a Note for that problem and make a Field on the reverse side with an explanation.
Flashcards and spaced-repetition are most helpful when the answer is short. It is very easy to create Notes for details I am likely to forget when researching a specific subject. Of course, the details need to be important enough to make them worth remembering! I find that if the fact is counter-intuitive, surprising, or I can make a comparison that reveals the fact in sharp relief to the thing compared, then it is probably worth memorizing.