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I am currently writing a book in mathematics. I have written a few pages and often stumble upon the question "is this good pedagogy" or is this "good typography". The chances of my work getting published is slim, but I am using it for a personal collection of notes and ideas in addition to learning writing a longer text. Below is an excerpt from my notes

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An older version of my notes can be found here.As now the notes are dividied into a somewhat strict pattern with lemmas, propositions, corollary with theorems reserved for the main purpose of each section. I have a ton of questions about layout, design how formal to be in my writing, and how spiced up I should make the text. I see modern calculus books like to divide the text into blocks (a different color for theorems, proofs etc) while published articles tend to keep a much more minimalistic presence. I just do not know if I am on a good path, or if I need to do some fundamental changes.

To summarize

  • What are the do's and dont when writing longer notes (mainly aimed at undergrads).

  • Are there any books or literature on writing longer academic texts?

closed as too broad by David Richerby, Wrzlprmft, Enthusiastic Engineer, Peter Jansson, earthling Dec 28 '14 at 23:32

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    My first thought was "why does he spell those Danish words incorrectly?" :) My next (more serious) thought was that using \mapsto felt odd given the wording (I felt that it ought to be an = given the word sette). But this might be overly specific to the example. – Tobias Kildetoft Dec 28 '14 at 17:51
  • From a quick glance at your file, you seem to be doing a lot of things right -- I would be pleased reading a book written like that about algebraic combinatorics :) A random observation on design: "figur (2.3)" should be "figur 2.3", as parenthesized reference numbers usually are understood to refer to formulas and nothing else. My pet peeve with mathematical writing is the failure to separate the introduction-for-readers from the introduction-for-reviewers (the former being high-faluting and obscure, the latter elementary and readable), but seeing that you don't yet have an introduction... – darij grinberg Dec 28 '14 at 19:20
  • Your first question is too broad and also too opinion-based for this platform in my opinion. Your second question is fine and I strongly suggest to restrict your question to this. – Wrzlprmft Dec 28 '14 at 21:48
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There are many books and online resources on mathematical writing. These range from style guides that deal with issues from type setting to copy editing to books that talk about mathematical writing at a somewhat higher level. Here are a few of my favorite sources:

Nicholas J. Higham. Handbook of Writing for the Mathematical Sciences. SIAM 1998. http://www.worldcat.org/title/handbook-of-writing-for-the-mathematical-sciences/oclc/697886419

Steven G. Krantz. A primer of mathematical writing : being a disquisition on having your ideas recorded, typeset, published, read, and appreciated. American Mathematical Society, 1997. http://www.worldcat.org/title/primer-of-mathematical-writing-being-a-disquisition-on-having-your-ideas-recorded-typeset-published-read-and-appreciated/oclc/797735421

SIAM Style Manual for Journals and Books. http://www.siam.org/journals/pdf/stylemanual.pdf

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In general, my advice would be

  1. look at other books or lecture notes and copy the things you like, change the things you don't;
  2. get feedback from your target audience;
  3. don't overthink it for your first draft: you can (and likely will have to) edit it multiple times anyway.

But mostly I want to recommend Paul Halmos classical essay, How to write mathematics, L’Enseignement Mathématique, Vol.16 (1970).

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