WRITING ABOUT MATHEMATICS

(including THEORETICAL PHYSICS*)

I. GENERAL PURPOSE

Mathematicians andtheoretical physicists write research articles which may contain theorems,proofs, and other investigations;short letters;lectures; grant proposals; letters of recommendation; committee reports and critiques; progress reports; internal memos; and public oral presentations. Writing should be clear, concise, and logical in creating convincing arguments. Audiences include fellow researchers, professors, students, government or business communities, or the general public. Mathematicians and theoretical physicists may also respond to editors and reviewers.

II. TYPES OF WRITING

1. Research Articles

  • Short, exact title
  • Abstract
  • Introduction

Opening attention grabber inform of a question

Succinct statement of mathematical problem

Explanation of how problem was approached

  • Statement of main result

Statement of answer in complete sentence

Statements of assumptions related to formulae used

  • Proof of theorem (if needed)

Logical demonstrations of connections between steps

Provisions of tables, graphs, and charts with concise labels

Definitions of variables

Explanations of how each formula used was derived

  • Citations of sources used to solve problem
  • Conclusion, summary, or implications
  • Acknowledgments
  • References

2. Short Letters (for Theoretical Physics) (brief, 1-4 page quick findings)

  • Title
  • Abstract
  • Body (combining introduction and acknowledgments)
  • 0-4 figures
  • References

III. TYPES OF EVIDENCE

  • Prerequisites—references identified in proofs as precedents
  • Proper use of terms and symbols
  • Proof itself, which is accurate, direct and calculable

IV.WRITING CONVENTIONS

  • Correct grammar and punctuation
  • Correct mathematics
  • For proofs over eight pages, divisions in numbered sections and numbered theorems used serially within each section
  • Active voice, first person plural (the writer and the reader), following standard grammatical rules of English
  • Symbols meaningful, simple, and direct, with no contractions
  • Abstracts are written in passive voice, with no notation, tables, or symbols.

V. CITATION STYLE

Applied mathematicians may use one of several styles, depending on the collaborative discipline, such as mathematics biology or mathematics education. Whatever plan is used should be consistent.

Citation-sequence system: Each source is assigned a number, which identifies the source each time it is used, then listed numerically in the bibliography.

[32] S. Kihara, On the rank of the elliptical curves with a rational point of order 4, II, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), pp. 158-159.

[See the AMS website for abbreviations and examples:

For theoretical physicists, citations may be numbered or by lead author’s last name et al. using the American Institute of Physics Style Manual. Some journals use superscripts rather than brackets for each citation. Also note that the article title is unnamed and the issue is in bold.

If numbered, the reference in the text is [32] and the reference work at the end of the paper appears like this:

[32] S. Kilhara, Proc. Japan Acad. Ser. A Math. Sci. 80, 158-159 (2004).

If the author’s last name is used, the reference in the paper looks like this— [Kilhara et al, 2004)—and the reference list entry looks like this:

Kilhara, S. Carroll, E.J., Heagy, J. F., and Milton, J. R., “Fundamentals of chaos

systems and concepts,” Proc. Japan Acad. Ser. A Math. Sci. 80, 158-159

(2004).

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SOURCES

American Institute of Physics (2016). Preparing your manuscript.Retrieved from

Gillman, Leonard. (1987). Writing Mathematics Well: A Manual for Authors. The Mathematical Association of America.

Penrose, Ann M. and Katz, Steven B. (2010). Writing in the Sciences: Exploring Conventions in Scientific Discourse. 3rd. ed. Pearson.

* For Applied Physics, see also Writing about Science