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I am a freshly graduated Ph.D. I want to improve further my mathematical writing (in English, if this matters).

I am looking for books/resource that address good mathematical writing. I can find some books, for example, A Primer of Mathematical Writing by the AMS. But I wonder if there are any other new books or resources.

  • You do not have to. Wait how your first question turns out, and learn from it to improve the further questions. (I retracted my close vote, by the way.) Also, I think we can clear up the comments now. – Wrzlprmft Dec 20 '15 at 13:13
  • As this is a resource request whose answers will be a list, I've made it community wiki. (That doesn't necessarily mean it's on-topic - the community may still decide to close this question, as often happens with "big list" questions) – ff524 Dec 20 '15 at 22:34
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I recommend the paper (series of class notes) Mathematical Writing, 1989, written by Donald Knuth ("Art of Programming" author, among other things), Tracy Larrabee and Paul M. Roberts.

Here is a description from Stanford:

This booklet records the class on Mathematical Writing led by Don Knuth at Stanford in 1987. Among the 31 lectures are guest appearances by Herb Wilf, Jeff Ullman, Leslie Lamport, Nils Nilsson, Mary-Claire van Leunen, Rosalie Stemer, and Paul Halmos.

We saw many examples of "before" and "after" from manuscripts in progress. We learned how to avoid excessive subscripts and superscripts. We discussed the documentation of algorithms, computer programs, and user manuals. We considered the process of refereeing and editing. We studied how to make effective diagrams and tables, and how to find appropriate quotations to spice up a text. Some of the material duplicated topics that would be discussed in writing classes offered by the English department, but the vast majority of the lectures were devoted to issues that are specific to mathematics and/or computer science.

It is helpful not just for mathematicians but scientists and technical communicators of all sorts.

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Knuth, mentioned in another answer, is trustworthy and a good author. The book mentioned by the OP maybe be useful to beginners, but I don't agree with many of Krantz's (the author) opinions about writing. In general, people have various opinions and tastes about writing, so it's good to see a spectrum of opinions and determine what approach fits for you in a particular situation. And now that you've started thinking about these things, read mathematics critically so you can build up examples of what you think works well and what doesn't.

Anyway, some other references are:

Terry Tao's advice on writing, which includes many links to pieces written by other authors

Milne's tips for authors, which includes a reference to Krantz's book and an essay of Hersh)

It might also not be a bad idea to read general advice about writing (not just mathematical/technical writing).

  • Also, while not specifically about writing, Rota's 10 lessons touch on a couple aspects of writing. – Kimball Dec 21 '15 at 13:28
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Coursera has a specialization called Reasoning, Data Analysis, and Writing Specialization I recommend watching the first three weeks of Think Again: How to Reason and Argue. You can consider the course English Composition I as well. There are other MOOCs dealing with your topics as well. Search coursetalk.com to find some MOOCs.

  • After reading the description, I must say I am sceptical that this course has much value for someone who already has a PhD and is specifically looking to improve their mathematical writing skills. – Tobias Kildetoft Dec 22 '15 at 10:46
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These two books are spot-on and I'm surprised they haven't been mentioned yet.

Handbook of Writing for the Mathematical Sciences, Nicholas J. Higham, SIAM, https://www.siam.org/books/ot63/.

Writing Mathematical Papers in English, Jerzy Trzeciak, EMS Publishing, http://www.ems-ph.org/books/book.php?proj_nr=34.

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I have come across good book for Mathematical writing with the titleWrite Maths right by Prof. Radhakrishna.

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Can you elaborate what type of writing?

For example, Joseph Mazur brings forward Euclid in the Rainforest, which includes mathematical concepts but is also in part biographical and simply an enjoyable read.

I am not sure if you mean tools such as Mathematica or LaTeX for symbiology ?

Or perhaps something like SHARELaTeX at https://www.sharelatex.com/learn/Mathematical_fonts ?

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