Thank you for stopping by this thread. I'm an engineering student rekindling an interest in Maths. I just love studying Maths in my free time (and sometimes it trespasses into my non free time). I have plenty of fantastic books on my iPad and it's really helping me.
However, I have been reading a lot of different books of late and it's getting a little jumbled in my head. I'm getting the impression that I'm getting a lot of superficial knowledge and then forgetting it very quickly. So, I decided that I have to start taking notes. I think that maybe if I take notes and then revise them I will be able to review them often and will get more out of my learning experience.
I have downloaded the Microsoft OneNote app. It's a neat app and allows you to maintain multiple notebooks. I plan on maintaining a notebook for every book I read. I just love electronic notebooks. You save so much paper, write faster, easier to maintain and so much moe neater ! :)
So, now my question is how do I maintain notes ? I'm a bit confused regarding what I should write. So, if anybody could offer any guidance, it would be excellent !
Also, please tell me how to maintain notes for different kinds of books. For example, books on Maths History like "Journey Through Genius" and "Crest of a Peacock" will require different kinds of notes than a technical books like "Visual complex analysis". And, in all my recently acquired enthusiasm, I want to maintain notes for all of them !
Any help will be much appreciated ! Thanks and may God bless you !
Some advice about studying: do not forget to be as analytical as possible. Why is the theorem this way? Which hypotheses are necessary? What are examples? Counterexamples? Can you reformulate the theorem? Come up with a different proof? Why is this a theorem? What depends on it? What does it follow from? Can you come up with interesting consequences? Find a way to describe how the main techniques used to answer questions? What are the questions the theory is trying to solve? Can you think of other applications? Etc. etc. etc.
These are things you can write down.