How to Read Mathematics
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How to Read Mathematics
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Re: How to Read Mathematics
#2One thing that I really would like to impress upon computer people is that mathematics is not (usually) a formal computer language. Symbols and technical terms change meaning depending on the author, people write with different "accents". There's a little ambiguity and informality at times, but a whole lot less than other kinds of writing.
Mathematics is (usually) written for humans, not computers. Don't attempt to read mathematics as you read code. To keep making bad analogies, it's a bit more like reading music. Picking the right tempo, the notes to accentuate, the interpretation -- this all requires a human. Computer still make crude approximations.
Re: How to Read Mathematics
#3How I read Mathematics.
First try to find the paper. First use http://front.math.ucdavis.edu . If you can't find it then use google scholar. If that fails then go on the authors academic website. If that fails then see if the author is live and try to contact them. Then repeat for their grad students. If all else fails post it to r/math or HN and ask for the pdf.
First you want to see if this paper is even worth reading. Scan the Abstract and the conclusions. If it is still relevant then do a quick scan of the whole text and look for the things you don't understand. For everything you don't understand look up on wikipedia. Once you have found those pages then look on the citations on wikipedia to gain more understanding. If you still can't understand the paper reread it and then attempt to redo their calculations. If all else fails ask someone to help you read it. Whenever you get confused write on the paper questions. If you figure out that this paper is meaningless then look for another one.
If you figure out a new question that you want to persue more then try to answer that question. If you don't have access to professor or if they are impeding your work then use stackexchange. Either that or try to invalidate your new theory yourself. Recognize that you can be wrong.
Re: How to Read Mathematics
#4How I read Mathematics. First try to find the paper. First use http://front.math.ucdavis.edu . If you can't find it then use google scholar. If that fails then go on the authors academic website. If that fails then see if the author is live and try to contact them. Then repeat for their grad students. If all else fails post it to r/math or HN and ask for the pdf. First you want to see if this paper is even worth read…
Also a very good advice I had received a long time ago but that I had dismissed until recently: some articles are just badly written.
The author sometimes forget to mention what B actually is, changes the meaning of the multiplication operator implicitly, assumes the formula given is inside an integral.... I could go on.
A maths article is an article. A lot are imperfect, quite a few are bad. Some times it is not the reader that is lacking.
That being said, do your homeworks and only consider that possibility after giving the article one hour of your time or so.
Re: How to Read Mathematics
#5I disagree with 'do not read too fast':
Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.
Re: How to Read Mathematics
#6I disagree with 'do not read too fast': Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.
So basically take a couple days to understand the material rather than going all in all at once?
Re: How to Read Mathematics
#7Good advice. Here is my advice for reading research papers.
http://muratbuffalo.blogspot.com/2013/07/how-i-read-research...
Re: How to Read Mathematics
#8I disagree with 'do not read too fast': Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.
Just... no. If you actually have to understand it (rather than, say, peer-review it), then make a honest attempt to understand it right from the beginning. For instance, suppose it takes you 30 minutes to skim through a chapter of a math book. Then you've wasted 30 minutes you could've spent understanding the chapter's first section.
Re: How to Read Mathematics
#9I disagree with 'do not read too fast': Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.
Just... no. If you actually have to understand it (rather than, say, peer-review it), then make a honest attempt to understand it right from the beginning. For instance, suppose it takes you 30 minutes to skim through a chapter of a math book. Then you've wasted 30 minutes you could've spent understanding the chapter's first section.
What if everyone learns differently?
Re: How to Read Mathematics
#10I disagree with 'do not read too fast': Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.
Just... no. If you actually have to understand it (rather than, say, peer-review it), then make a honest attempt to understand it right from the beginning. For instance, suppose it takes you 30 minutes to skim through a chapter of a math book. Then you've wasted 30 minutes you could've spent understanding the chapter's first section.
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