How to Read Mathematics
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How to Read Mathematics
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Re: How to Read Mathematics
#2I had never really thought of mathematics having its own language, but the parallels to learning a second language (after childhood) are interesting.
Re: How to Read Mathematics
#3I remember back in school that doing the math was not really a problem, but actually reading the textbooks was. I was the same way with programming when I started, where I could write but not read the language, but I'm suprised that I got through 4 years of university math without really being able to read the proofs that explained it.
Re: How to Read Mathematics
#4Re: How to Read Mathematics
#5The big ones: Watch out for proof by contrapositive and contradiction. Until you really get used to proving things by assuming bits of them are false it throws you off to see it used in textbooks and papers because most papers do not tell you they are using them.
Re: How to Read Mathematics
#6http://news.ycombinator.com/item?id=1576969 http://news.ycombinator.com/item?id=85743 http://news.ycombinator.com/item?id=583977 http://news.ycombinator.com/item?id=1509758
Of those, only the most recent one has any substantial comments, and even that is now 10 months old and can no longer be commented on:
Re: How to Read Mathematics
#7The big ones: Watch out for proof by contrapositive and contradiction. Until you really get used to proving things by assuming bits of them are false it throws you off to see it used in textbooks and papers because most papers do not tell you they are using them.
Could you cite an example?
Re: How to Read Mathematics
#8Line by line carefully. Never skip anything in hopes it will clear up later.
You may allow to yourself not to know with what intention author wrote the line but you should never allow yourself not to know why the author could write this line.
Re: How to Read Mathematics
#9I just had a reviewer criticize a report I wrote for containing "sentence fragments". The paper says things like, "Then x = y/2", which my reviewer interpreted as a one-word sentence ("Then"), followed by an equation. It made me realize how unnatural it is for some people to actively read mathematics-- for example, turning "=" into the verb "equals".
Re: How to Read Mathematics
#10Line by line carefully. Never skip anything in hopes it will clear up later. You may allow to yourself not to know with what intention author wrote the line but you should never allow yourself not to know why the author could write this line.
You can skip on first reading to get an overview of where the author wants to take you, but don't expect it will clear up later on its own. Read and re-read. Fill in all the little gaps, especially when a sentence begins with "Clearly" or "As we can easily see".