A Guide to Writing Mathematics [pdf]
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A Guide to Writing Mathematics [pdf]
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Re: A Guide to Writing Mathematics [pdf]
#2This is a sensible guide, by Kevin P. Lee, aimed at undergraduates taking math classes.
A similar guide, aimed at people writing research papers, is “How to Write Mathematics” by Paul Halmos (1970) [1].
They both start from a similar assumption:
Lee: “When you write a paper in a math class, your goal will be to communicate mathematical reasoning and ideas clearly to another person. The writing done in a math class is very similar to the writing done for other classes. You are probably already used to writing papers in other subjects like psychology, history, and literature. You can follow many of the same guidelines in a mathematics paper as you would in a paper written about these other subjects.”
Halmos: “The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea.”
[1] https://www.mathematik.uni-marburg.de/~agricola/material/hal...
Re: A Guide to Writing Mathematics [pdf]
#3I don't know if anyone else experienced something similar in physics, but it was not until I read the textbooks of David Griffiths (his books on E&M and quantum especially), that either of these subjects became clear to me.
I think the reason is that his writing was like a clear 1-on-1 tutorial session, with many of the "writing mathematics" practices described in the article here. It had a conversational style as if it was someone trying to explain but in written words. I recall phrases like "now look at the expression we have here, what does it tell us?" Or, "what follows is a somewhat long derivation, but you will find the effort of working through it pays off".
Most other textbooks read like stilted reference manuals by comparison, with "exercises left to the reader".
Re: A Guide to Writing Mathematics [pdf]
#4This is a sensible guide, by Kevin P. Lee, aimed at undergraduates taking math classes. A similar guide, aimed at people writing research papers, is “How to Write Mathematics” by Paul Halmos (1970) [1]. They both start from a similar assumption: Lee: “When you write a paper in a math class, your goal will be to communicate mathematical reasoning and ideas clearly to another person. The writing done in a math class is…
I'm going to read through the guide linked in the post, but I don't have time (Or really the desire) to read through the guide aimed at people writing research papers.
Do you have TL;DR for the difference between aimed at undergraduates vs research papers in terms of writing?
Re: A Guide to Writing Mathematics [pdf]
#5There is also “Mathematical Writing” by Knuth: https://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematic...
Re: A Guide to Writing Mathematics [pdf]
#6This is a sensible guide, by Kevin P. Lee, aimed at undergraduates taking math classes. A similar guide, aimed at people writing research papers, is “How to Write Mathematics” by Paul Halmos (1970) [1]. They both start from a similar assumption: Lee: “When you write a paper in a math class, your goal will be to communicate mathematical reasoning and ideas clearly to another person. The writing done in a math class is…
I'm going to read through the guide linked in the post, but I don't have time (Or really the desire) to read through the guide aimed at people writing research papers. Do you have TL;DR for the difference between aimed at undergraduates vs research papers in terms of writing?
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Re: A Guide to Writing Mathematics [pdf]
#7I don't know if anyone else experienced something similar in physics, but it was not until I read the textbooks of David Griffiths (his books on E&M and quantum especially), that either of these subjects became clear to me. I think the reason is that his writing was like a clear 1-on-1 tutorial session, with many of the "writing mathematics" practices described in the article here. It had a conversational style as if…
It has been a while since I read Griffiths. If I recall I liked his style for E&M, but the quantum mechanics book was far too discursive, full of unnecessary jokes and cutesy phrases that muddled the discussion instead of aiding understanding. I remember being frequently confused about when Griffiths was making a physical argument versus a mathematical argument when deriving results.
My professor didn’t use Griffiths for the exercises, so I actually sold my copy back to the bookstore and bought a used copy of Shankar’s book: it is certainly drier, but I think it’s much more clear and precise.
Re: A Guide to Writing Mathematics [pdf]
#8This is a sensible guide, by Kevin P. Lee, aimed at undergraduates taking math classes. A similar guide, aimed at people writing research papers, is “How to Write Mathematics” by Paul Halmos (1970) [1]. They both start from a similar assumption: Lee: “When you write a paper in a math class, your goal will be to communicate mathematical reasoning and ideas clearly to another person. The writing done in a math class is…
As a math major at UCD, I never saw Lee's essay, so I'm guessing it's from the past few years.
I did read Halmos's, though. It was helpful for me because I was starting from a very programming centric frame of mind and I was surprised at how "conversational" math writing was. Reading it helped me start to learn how to express ideas precisely and clearly without a strict code-like structure.
Re: A Guide to Writing Mathematics [pdf]
#9What's not in the paper but I find quite annoying in scientific articles is excessively loaded notation. Some variables get to have like 4 or 5 subscripts and equations become unreadable.
I really appreciate when papers get to say at some point "for the sake of clarity, let drop this or that notation" that are not that relevant to the key ideas. Usually it's in the good quality papers.
Re: A Guide to Writing Mathematics [pdf]
#10More of a rant, but since I began to implement algorithms from various papers for my PhD, my aversion to mathematical notation grows steadily. More often than not it's imprecise and hard to reproduce.