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I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material completely and thoroughly, I started to write the important propositions and definitions along with working out every single exercise on my blog.

I am wondering if this is a good way to go about. The reason for why I am asking this is, it is time consuming. Should I work out problems and exercises using pen and paper (or) can I write them out on my blog since the latter involves bit more time than the former? Are there any specific advantages for doing mathematics on blog as opposed to pen and paper?

Another question on these lines is does doing math on pen and paper allows a person to be more creative and think better than doing mathematics on a blog? This question is motivated by a bbc video on Fermat's last theorem which I watched today. In the video, Andrew Wiles says, I quote

"I never use a computer. I sometimes scribble... I do doodles... I start trying to... find patterns really. So I am doing calculations which try to explain some little piece of mathematics. I try to fit it in with some previous broad conceptual understanding of some parts of mathematics. Sometimes that involve going and looking up in a book to see how it is done there. Sometimes it is a question of modifying things a bit. Sometimes do a little extra calculation and sometimes you realize that nothing that has ever been done before is of any use at all. You just have to find something completely new. And its a mystery where it comes from".

I am wondering if doing mathematics on a blog allows the same degree of freedom as doing mathematics on a pen and paper.

Thanks, Adhvaitha

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It really depends on what you're most comfortable with. If you think doing things on the computer is a bother, then don't! If you want to spare the trees and thus prefer using the keyboard instead of the pen, then go ahead! You should know best what you really want to do. –  J. M. Sep 6 '11 at 11:44
    
Adhvaitha:What is doing math or physics according to you?Well according to me doing math or any other science is to solve problems? How do you solve problems Eventually? Either by pen/pencil and paper or on a computer.{If you intend to design and write algorithms}.It's in your hands to figure out the best way of learning.There's plenty of resources {almost unlimited} and plenty of ways to make use of those resources. –  alok Sep 6 '11 at 12:23
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I think honesty is the most important part. Use pen and paper as long as you are honest with yourself that you have a complete solution. Blogging keeps me honest. If I "solve" something and am feeling a little uncomfortable with it I decide to blog it. Knowing that others might read it I have to be way more careful to make sure I haven't said something false or left a gap. So I use a combination. It is easy to fool yourself so having an honesty check is nice. –  Matt Sep 6 '11 at 14:23
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I voted to close as "too localized". The OP is asking which of two reasonable methods of learning mathematics will work better for him/her. Well, her/his guess is better than ours, isn't it? –  Pete L. Clark Sep 6 '11 at 14:40
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Thanks to those who have answered. To those who want to close this question, shouldn't I ask how to do mathematics here? I saw this question (math.stackexchange.com/questions/41973/…) in the related questions which I think is more localized going by the comment to close down this question. If questions on doing mathematics should not be asked on the site, there should be a universal rule. –  Adhvaitha Sep 7 '11 at 2:56

1 Answer 1

Perhaps the question in general is more concerned with cognitive processes than with mathematics alone. Having said that, there are differences between typing (interpret it as your "blogging") and handwriting: Marieke Longcampa, Marie-Thérèse Zerbato-Poudoub, Jean-Luc Velaya, "The influence of writing practice on letter recognition in preschool children: A comparison between handwriting and typing", Acta Psychologica Volume 119, Issue 1, May 2005, Pages 67–79. And I quote part of the abstract: "The results showed that in the older children, the handwriting training gave rise to a better letter recognition than the typing training." (my emphasis). Mathematics is composed not only of letters, but also of many different symbols. The above mentioned study should suggest that if letters are better recognized by handwriting, then mathematical symbols (specially if you are in such pure abstract field as topology) even more so. And there are several other similar studies, for example: Marieke Longcampa, b, , , Céline Boucardb, Jean-Claude Gilhodesb, Jean-Luc Velayb, "Remembering the orientation of newly learned characters depends on the associated writing knowledge: A comparison between handwriting and typing", Human Movement Science Volume 25, Issues 4–5, October 2006, Pages 646–656. I quote part of their abstract: " Results showed that when the characters had been learned by typing, they were more frequently confused with their mirror images than when they had been written by hand. This handwriting advantage did not appear immediately, but mostly three weeks after the end of the training.".

Finally, let me quote Janet Emig "Writing as a mode of Learning", College Composition and Communication, Vol. 28, No. 2, May, 1977. Mind you, Emig does not compare the usage of typing into a computer, as opposite to handwriting, but she does implies all along that when she is speaking about "writing" she means "handwriting". Emig says: "what is striking about writing as a process is that by its very nature, all three ways of dealing with actuality [1) enactive - learn by doing; 2) iconic - we learn 'by depiction in an image' and 3) representational or symbolic] are simultaneously or almost simultaneously deployed. That is, the symbolic transformation of experience through the specific symbol system of verbal language is shaped into an icon (the graphic product) by the enactive hand.If the most efficacious learning occurs when learning is re-inforced, then writing through its inherent re-inforcing cycle involving hand, eye, and brain marks a uniquely powerful multi-representational mode of learning".

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