How to effectively learn by self learning.

Question

I'm a self studying student.I live in a place where I've limited resources,to give an example,in winters to study I've to use candles because there is no electricity,no light and so on. I have no teacher so all that I have is books and sometimes internet,if the internet is not banned .

I'm average in studying but I love to study and try my best to understand. The thing that is the biggest hurdle is as explained below:

I'm going through a text smoothly and then I get stuck.I have a confusion, doubts and questions. I try to think for hours, and then they turn into days. I can't ask anyone near me and I feel I can't move ahead though the text. I feel I haven't understood the previous paragraphs so my motivation to go ahead is dead. The only way I know out is to accept the conclusion that's presented and move on. But I am not able to do it. I have this irresistible urge to know it before I can move ahead.

Could you please tell me how to proceed in such a situation.

Should I note my doubts and move on and try to clear them when possible?

I will be thankful for even a hint that might help me or any other general tips. Warmest regards, Thank you.

Answer 1

Here's a collection of suggestions

no internet required

• Reading about the same topic from different books.

• Study partner, talking about the material with other people.

• Keeping notes (of any kind)

• Keeping organized notes of theorems, definitions, and examples

• Trying to prove results you already know

internet required

• Ask (well-structured) questions related to items you do not understand on this forum

Answer 2

I'm going through a text smoothly and then I get stuck.I have a confusion, doubts and questions. I try to think for hours, and then they turn into days. I can't ask anyone near me and I feel I can't move ahead though the text. I feel I haven't understood the previous paragraphs so my motivation to go ahead is dead. The only way I know out is to accept the conclusion that's presented and move on. But I am not able to do it. I have this irresistible urge to know it before I can move ahead.

There are around three main reasons that I've identified as to why we get stuck/ have confusions. I've ranked them on the order of likeliness:

1. Not going over examples/ Illustration on the topics I am doing

Most of the times, the reason I don't get some thing is because I don't have a clear example of the subject I am handling with relate to in my mind. So, either checking back of the book exercises or trying to conjure your own examples of where a theorem can be applied will help.

2. Lack of some 'prior' knowledge

Sometimes it is like we can't even begin to understand the material we are doing, like we feel a strong disconnect between what we are reading and what we know. This usually means, you've skipped a lot of the basics/ pre - requisites for the subject you are doing. Try find a self contained introduction to the topic you want to study/ do a bit more watered down version before doing the complicated stuff.

3. The materials explanation is not clear

This is an unlikely case (if you searched up what books are good), but can happen. Sometimes it is that the book is just not clear enough to convey the information to you. In this case, look up on youtube / google. If you can't find answers to your queries in that way, look up questions on MSE/ ask on MSE.

I personally am not a big believer for keeping notes in mathematics and all the notes I tried to take for it ended up being waste paper. I think a better way to do it is to keep thinking of what you are studying, and try to write down your thoughts on a piece of paper. Even if you don't get the intended result that you wanted, just do a rough work and save the paper.

The one exception I have for this is when engaging completely new material, then I take a paper and write down important definitions with some cartoons so I don't have to flip back to see them again if I forgot.

I started writing donw my math thoughts like these on an app called obsidian over the months and it has helped me quite a bit in thinking of new ideas and figuring out good questions to ask about the subject.

The kind of self studying while trying to understand everything at some X level is a hard one but very rewarding. Good luck!