Taking Notes for Self-Study "advice"

[ahmed markhoos]

Hello,

from my experience, taking notes while self-studying is the most frustrating thing I ever faced. I am one of those people who doesn't want to miss any small detail!

I started this summer self-studying "mathematical methods in the physical sciences - By Mary Boas" because I found it covering most of what I need for the next semester "quantum/optics/thermal" since I didn't had the opportunity to take calculus 3 nor algebra, so I wanted to fill the gap of the semester.

I read complex numbers, more than 2/3 of linear algebra, multiple integral, and I'm heading after a week for vector analysis.

The thing is, since I started I took notes of too too many papers. I don't know! I feel sad that I may spent unnecessary time in it "I did a lot of problems too".

Do you guys think it's unnecessary to take the notes and prefer writing with pencil on the book? or it's better to write your own notes? "Of course doing the problems is undoubtedly a vital thing"

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for the past two months I used the library book so I didn't had the opportunity to write on the book. Now after I had the book, I may not complete the notes, I'll just write with pencil on the book and solve the problems.

What do you think?

 

[ahmed markhoos]

something to say: At first I wrote a lot of things, gradually I tend to ignore writing the examples, and just sticking with the main Idea no more than that"with some of my own notes"

 

[verty]

I would still make notes. Multiple integrals are pretty difficult and you learned them using notes, so for me that proves they are good notes and you should keep using them because they are working for you and you are having good success with them.

 

[ahmed markhoos]

I would still make notes. Multiple integrals are pretty difficult and you learned them using notes, so for me that proves they are good notes and you should keep using them because they are working for you and you are having good success with them.

The thing is:
1- I really don't go back and search for the info. from notes whenever I had a problem- I basically go to the book.
2- The book is not deep, it scratches the methods only. And it shorten the info. in a very good way.

 

[JBosma]

For me, taking notes is still the most effective way to really learn things. I simply remember things much better when I write them down (I'm quite sure this has been scientifically proven, but I don't know any references from the top of my hat), although I rarely ever look back at my notes. Taking notes also helps me understand more complicated arguments and derivations, and even uncovers gaps in my understanding that I didn't realize where there when I just read the text. On the other hand, taking notes takes a lot of time which sometimes feels unnecessary, as you said.

So I guess it really depends on what you want to achieve. If you're studying for an exam, take notes and review them (again and again). If you're just working through the material to make sure you understand it and will be able to look up results on an as-need basis later (which is what you seem to be doing), I'd only write out more complicated arguments and do exercises.

As for writing in books, I write down questions I have about passages, left-out intermediate steps that I didn't see immediately, and remarks I might have about the text (alternative derivations, connections to other subjects, whatever). It's also very satisfying to check off exercises that you have finished.

 

[bacte2013]

Quite a lot of undergraduate-mathematics books, in my opinion, are pretty good at getting to the point in a timely manner, and also presenting the main ideas (definitions, theorems, and proofs) without being unnecessarily unordered. That makes taking notes quite difficult as all information presented in the books seem to be very important. I suffered from my bad note-taking habit before by copying down everything in the books and basically produced my own books about those books. The result was that I did not have an enough time to dedicate myself to the problems.

I fixed my issue by implementing the following strategy after a long trial-and-error: copy down the main ideas (theorems and definitions) in my own words, and add my own perception and remarks (different approach to understand the main ideas and construct the proofs, tempted to apply the ideas to other fields of mathematics, etc.), and also write inside the books (perceiving the math textbook as a near-complete notebook). Then I do the examples and problems. Then I try to produce my own problem sets by incorporating the information from the textbooks, their problem sets, and my own perception and ideas about what l learned . Producing the problem sets by yourself is actually a very good method to increase your creativity and also prepare yourself for the examination.

In the end, everybody had a different tastes and methodologies. Although I cannot guarantee the full effect of my strategy, I hope it can help you too.