Some Thoughts From 'Enu'

Intro: 'Enu' is a fellow blogger - a link to his blog is on the right margin. A software professional by trade, he is a serious solver of Math problems by choice. He often helps me when I come up short in my own amateurish searches in Math. Recently, he shared with me some thoughts on learning new Math stuff, purely as an avocation and since he is not as prolific a blogger as he should be, I record this thoughts here. His observations could be useful to anyone trying to learn anything, seriously. Over to Enu!

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Of late I had begun to find problem-solving tending to be an excercise in recalling some old trick or the other learnt in high school or thereabouts. That was not a happy situation, really.

I wondered: When will I use something like a real new trick? I guess the straight answer lies in *learning* something new. I was recently inspired by this website.

http://therisingsea.org/?page_id=3

( the title is a hat tip to a book by Grothendieck)

This guy has painstakingly put up notes on stuff he's learnt. I dont pretend to understand any of it yet. But, drawing inspiration from him, I have too started writing notes in latex. I am on the verge of finishing up a book "Linear algebra" from which I have been taking notes on weekends( a 5 month long effort). I still have two more chapters to finish up. I even went as far as to write up a definition of a math term I learnt from the book in the great wikipedia.org - see en.wikipedia.org/wiki/Semi-Simple_Operator ( my first wikipedia contribution)

I found that taking notes helps - because every time I revisit the book( during weekends), I have forgotten most of what I learnt and have to start from scratch, creating a kind of disgust. It also helps me avoid my habit of skipping details and sort of consolidates my understanding. Also of use is documenting answers to excersice problems, so the problems dont seem new every time I look at them.

Of course, this is hard work. It's tough to keep the concentration going; with only few hours in the weekends and some leisure hours snatched here and there, the progress can be really slow (esp , with nobody guiding you through the difficult parts )

I have also had to resist the devil in me that constantly tries to write before thinking.

The notes are still not a complete substitute for memory. Writing notes involves spending lot more time with a single page of a book than you usually do. The longer I spend with the proof or an idea, the tougher it seems for me to forget. Most problems in problems require you to have results at your fingertips and I havent reached that proficiency yet - that perhaps is a luxury of a professional mathematician who spends all time with them :)