How to Read Mathematics
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How to Read Mathematics
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Re: How to Read Mathematics
#2A very nice article.
>A particular notorious example is the use of “It follows easily that” and equivalent constructs. It means something like this:
>One can now check that the next statement is true with a certain amount of essentially mechanical, though perhaps laborious, checking. I, the author, could do it, but it would use up a large amount of space and perhaps not accomplish much, since it'd be best for you to go ahead and do the computation to clarify for yourself what's going on here. I promise that no new ideas are involved, though of course you might need to think a little in order to find just the right combination of good ideas to apply.
Even knowing this ahead of time, this kind of thing can be maddening. Namely, when the meaning of the assertion is be sensitive to little sign changes, index shifts and the like these are quite likely to end up in the computation.
Re: How to Read Mathematics
#3The article is by Shai Simonson, one of the instructors at ArsDigita University (http://aduni.org/).
This was part of the reading material for ADU Course 0: "Mathematics for Computer Science" (http://aduni.org/courses/math/index.php?view=cw), but unfortunately the video lectures aren't available, whereas they are available for all the other courses.
Re: How to Read Mathematics
#4What a boring text!
M.Sc.in applied Mathematics
Re: How to Read Mathematics
#5I took a history of mathematics course at the University of Virginia. One of the I interesting things I learned was that people used to write out equations as sentences before symbolic notation was invented. And so you would realize that a single moderately large equation (such as the quadratic equation) might be equivalent to a full paragraph or more of text. So if you ever get discouraged at how long it takes you to read mathematics, remember that equations can be as information-dense as entire paragraphs, or even more so, and just because it is presented in a spatially compact format doesn't necessarily mean that it shouldn't take you at least as long as a text paragraph to read and comprehend.
Re: How to Read Mathematics
#6During college, in order to plan my time, I used to measure my studying time on more mathematically intense texts. I took 30-60mins per page on average. It is a hard read, at least for me, but intensely gratifying too.
Re: How to Read Mathematics
#7I took a history of mathematics course at the University of Virginia. One of the I interesting things I learned was that people used to write out equations as sentences before symbolic notation was invented. And so you would realize that a single moderately large equation (such as the quadratic equation) might be equivalent to a full paragraph or more of text. So if you ever get discouraged at how long it takes you t…
Happen to remember the text you used?
Re: How to Read Mathematics
#8The article is by Shai Simonson, one of the instructors at ArsDigita University ( http://aduni.org/ ). This was part of the reading material for ADU Course 0: "Mathematics for Computer Science" ( http://aduni.org/courses/math/index.php?view=cw ), but unfortunately the video lectures aren't available, whereas they are available for all the other courses.
Shai is an incredible teacher; his video lectures on theory of computation were a major part of what made me understand the beauty of CS theory (automata, CFG's etc). It was sad to see that they had to shut down ADU; but I guess it was an unsustainable model; if I recall correctly, there was absolutely no tuition charged to the students.
Re: How to Read Mathematics
#9A very nice article. >A particular notorious example is the use of “It follows easily that” and equivalent constructs. It means something like this: >One can now check that the next statement is true with a certain amount of essentially mechanical, though perhaps laborious, checking. I, the author, could do it, but it would use up a large amount of space and perhaps not accomplish much, since it'd be best for you to…
My Basic Concepts of Mathematics teacher was notorious for getting about halfway through a problem before announcing "and from here it's trivial to show...". One day he walks into class one day and addressed us:
"I've been told by the head of the department that I can no longer say 'it's trivial'. You have to understand when I say 'it's trivial', I just mean that I can do it"
Re: How to Read Mathematics
#10Great article. I think it can very well extend to reading code as well, which may seem daunting at first.