本科高年级Foundations计划中
Mathematical writing
Writing mathematics that others can read and check: structure, definitions before use, notation, examples, LaTeX, and honest statements of what has and has not been proved.
math.found.mathematical-writing
本主题的课程尚未编写。下面的提纲是课程地图的一部分，尚未经过审校。
前置知识
10 项必需的前置知识（一直追溯到底）
你将学会
- Rewrite a correct but unclear proof so that its structure, assumptions and key steps are explicit.
- Typeset definitions, theorems and proofs in LaTeX with consistent notation.
- Write a short expository note that states precisely which results are proved, which are cited and which are conjectured.
定义
- A theorem is a principal result, a lemma an auxiliary result, and a corollary a result that follows quickly from another.
- Exposition is writing whose purpose is explanation rather than the announcement of new results.
定理
- Every symbol should be defined before it is used, and every cited result should be identifiable by the reader.
- A proof is written for a reader who will check it against the stated hypotheses.
常见误解
- Thinking a shorter proof is always a clearer one.
- Using 'standard' notation without defining it.
- Leaving the status of a claim (proved, cited or conjectured) for the reader to guess.
通向
可选发现
- Formalising published mathematics Formalisation blueprints link each informal statement to its formal counterpart, which forces precision in writing.
学习路径
延伸阅读
- Donald E. Knuth, Tracy Larrabee and Paul M. Roberts, Mathematical Writing (1989)
- Nicholas J. Higham, Handbook of Writing for the Mathematical Sciences
- Paul R. Halmos, How to Write Mathematics (1970)