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When you write in a math class, you are expected to use correct grammar and spelling. Your writing should be clear and professional. Do not use any irregular abbreviations or shorthand forms which do not conform to standard writing conventions. Mathematics is written with sentences in paragraphs.
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Aug 18, 2020 · BASICS. Know your audience. This is the most important consideration for writers. Put yourself in your reader’s shoes. What background can we assume of the reader? What terminology should we define? What kind of “voice” do we want to project: casual or professional, serious or inviting, terse or loquacious?
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Writing a paper should be easy once you have something to write about. You should write done your results and proofs as clearly as possible. Try not to get bogged down by details, and consult your advisor to determine what details an expert should be able fill in themselves.
This booklet is about writing mathematics at university. At pre-university level a lot of mathematics involves writing down a sequence of equations, a number or function appears at the bottom of the page and you get a tick or a cross depending on whether you are right or wrong.
- How to Write a Clear Math Paper: Some 21st Century Tips
- How to Write a Clear Math Paper: Some 21st Century Tips
- Synopsis
- 1.1. What does it mean to be clear?
- 1.2. Being clear | how hard can that be?
- 1.3. Why be clear?
- 2.3. So why do we need this new guide then?
- 3.1. Structure of the paper
- 3.2. Title
- 3.5. Introduction
- 3.6. Foreword
- 3.7. Final Remarks
- 3.8. Acknowledgements
- 4.2. How to cite a single paper
- 4.4. Where to cite a paper?
- 6.1. You are never really done
- 6.3. Rewrite and republish
- Acknowledgements
Igor Pak UCLA Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons
Igor Pak Department of Mathematics, UCLA, Los Angeles, California, USA pak@math.ucla.edu
In this note we explain the importance of clarity and give other tips for mathe-matical writing. Some of it is mildly opinionated, but most is just common sense and experience. 1. Be clear! This is the golden rule, really. It's absolutely paramount. Let me explain.
This might seem like an obvious question, but it's not. Most people think it's about clarity in phrasing, that's all. For example, one should of course write
Well, it can be easy. But it can also be pretty hard, especially if you are an inexperienced writer. The trouble with being clear as a concept is that most people think it doesn't take time. They think one naturally becomes a better writer. Quite the opposite is true. Making your paper clearer takes time and a lot of e ort. You learn to do this fas...
Now that we framed it as a tradeo between your time and e ort, and that of the readers, this is no longer an obvious question and it deserves a full explanation. And the key observation is | being clear is not about you! You must think of the reader and how they will read your paper. Imagine a graduate student at a small university with poor Englis...
I don't have a concise answer for that. I think the world is changing too fast. With the ever increasing competition for jobs, publishing in top journals, etc., some of the old advice needs to be calibrated and adjusted for modern times. This is particularly true about typesetting in LATEX, which is universal and represents its own advantages and c...
Every newspaper writing guide, including the above mentioned [18], will ad-vise writing an article in a Matryoshka doll manner | start with a super brief summary, then make a longer summary, and only then, once the reader is hooked and interested in details, proceed to give a complete set of facts. Over the years, math articles developed a similar ...
This is super important. Read about how to write a good title every-where. Think about it a long time. Try di erent versions on your colleagues. Then think again. Your title shouldn't be too long, too short, too vague or generic (as in \On some problems in group theory"), but should be the rst approximation to contents of your paper. These are ofte...
This is the hardest section to write. It's probably the only part of your paper that will be read by all but a few most devoted readers. If you have a senior coauthor, ask her or him to write this. If you don't, ask a senior colleague to read it and comment on your draft. Start writing your paper by writing the rst draft of the Introduction, so you...
If the Introduction is relatively short (say, under three pages), you are proba-bly ok. But if you followed the rules above and it's still over four pages, that probably means your paper is quite long, you have too many results, and/or the paper spans several sub-areas of mathematics which all have plenty of relevant background. In this case you sh...
This is the least understood section, in my opinion. I feel that most people use it as a place to include a mix of open problems, examples, applica-tions, references, whatever is left not included in the main part of the paper. The result is always like a paella | sometimes good, but you never know what are you going to nd there. While the intentio...
Rota advises \Give lavish acknowledgments" and this is mostly correct. Let me expound on that a bit. You still need to make choices when you thank everyone. Make a short unnumbered section at the end of the paper, right before the References. It's ok to have it in a smaller font. Proceed in the order of increasing importance. First, thank everyone ...
The citation rules are almost as complicated as Chinese honori cs, with an added disadvantage of never being discussed anywhere. Below we go through the (incomplete) list of possible ways in the decreasing level of citation im-portance and/or proof reliability.7 \Roth proved Murakami's conjecture in [Roth]." Clear. \Roth proved Murakami's conjectur...
That's actually easy. Only the most relevant papers should be cited in the Introduction. The rest are cited in the Final Remarks. Nothing is cited in the main part of the paper. The reason is simple | there is no way to be fair, clear, and complete all at the same time when citing in the middle of the paper, and without breaking the ow of the argum...
When you nish writing the paper, let it stew for a week or so. Do something else in the meantime. Come back to it then and reread all of it with a fresh eye, looking for typos, bad wording, imprecise statements, etc. Don't put it on the arXiv right away, but instead put it on your website and email about it a few colleagues. Not only they might giv...
Finally, suppose you already wrote and published the paper. You think it's being ignored because it's unclear. Well, rewrite it. Simplify all the arguments, maybe generalize the main result a bit, nd some new examples or applications. And publish this new version, even if just on the arXiv. Rota advises publishing the same paper several times, and ...
I am grateful to Bruce Berndt, Skip Garibaldi, Steven Krantz, Bjorn Poonen and Adam She er, for useful remarks and help with the references. I am especially grateful to Laci Babai for teaching me to distinguish di erent types of references (all misunderstandings are mine, of course). After this paper was written, I was honored to be asked by MSRI t...
- Igor Pak
- 2018
Good mathematical writing takes practice; it is also necessary to know some basic rules. Perhaps the most important feature of good mathematical writing is the revision process: writing and rewriting. This guide discusses, with examples, the principles of mathematical writing. Contents.
Jan 31, 2018 · How to Write a Clear Math Paper: Some 21st Century Tips. Igor Pak, UCLA Follow. Abstract / Synopsis. In this note we explain the importance of clarity and give other tips for mathematical writing. Some of it is mildly opinionated, but most is just common sense and experience. DOI. 10.5642/jhummath.201801.14. Recommended Citation.
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