Mathematical Writing Autumn 2023

Lecturer: Emmanuel Kowalski

Lectures

Wednesdays, 12 to 14 in HG G.3

There will be regular writing exercises assigned, which will determine the final grade. There is no separate exam at the end of the semester.

Summary

The goal of this course is to present and give guidelines and suggestions for good mathematical writing, both in general stylistic terms and in concrete technical manner through an introduction to LaTeX. It is also an introduction to the mathematical community, and especially to the research community.

Forum

A DMATH forum is available for discussion and to ask/answer questions about the course, see here.

Office hours

Starting on November 1, I will offer office hours on Wednesdays, 15:00 to 16:00 (or other times) by appointment. These are intended for individual feedback discussion of the writing exercises (or any other question related to the class). Please send an email to kowalski@math.ethz.ch if you are interested. It is expected that each discussion will be about 30 minutes long, but this will be adjusted with experience. The meetings will be in my office, HG G 64.1.

Writing exercises

The information on the writing exercises can also be found on the forum.
The document should be sent by email to kowalski@math.ethz.ch, with the indication [Math. Writing] in the subject line. The important part is the LaTeX source code, but it is fine to also send the PDF.
Although the preferred language is English, the exercises can be also sent in German or French.

Due date	Goal
4.10.2023	Take a theorem from Analysis I or Linear Algebra I (or from the analogous course for students not in DMATH), and write a LaTeX document of at most two pages containing the statement (in a suitable Theorem environnment) and discussion and/or proof and/or examples and/or applications.
11.10.2023	Download this LaTeX file, and adapt it to give a text which is corrected, readable, and more pleasant to the eye. This shouldn't take more than one page.
25.10.2023 (new deadline)	Borrow a book from the mathematical library, and write about it (at most two pages; one page or even less is fine). This should include basic information (author, title, etc), and you should try to describe what it is about (for instance, with some definitions followed by some statements of theorems proved in the book). This exercise is as much about reading as about writing.
8.11.2023	Take one of the results from the following list. Research its history, background, developments, and write a short report (at most two pages), with bibliography, etc. In particular, you must identify the original source. You should use Mathscinet and zBmath to track references and related material. Note: (1) if you are interested in a theorem which is not on the list, send me an email to ask if it is suitable. (2) the star numbers on the list give a rough indication of the amount of background involved in understanding the statements (in particular, it is not a reflection of the depth or difficulty of the results).
15.11.2023	Download the paper of Erdös and Szemerédi and write a report containing at least 15 writing problems, in your opinion (spelling, grammar, typography, bad notation, unclear statements, etc).
6.12.2023	Write a short beamer presentation (about 5 to 10 slides) on a mathematical topic of your choice. This should be accompanied with a short separate document (about one page) explaining what your target audience is, what the goals of the presentation are, and what kinds of things you would say when presenting the slides.

Summary of the lectures

We indicate here the topics discussed in each lecture, with various links to useful references and examples.

Day	Content
20.9.2023	First hour: Introduction to the lecture. Question: which mathematicians do you know? Have you heard of So-and-So? Which theorems have you heard about outside of the basic classes? Have you heard of Such-and-Such statement? Presentation of the arXiv preprint server; a quick look at some random preprints. Second hour: Introduction to LaTeX: using amsart as base package, using theorem styles, labels and references to keep track of numbering of theorems and equations. Sections and subsections. Sample file: LaTeX file (with explanatory comments).
27.9.2023	First hour: Some useful websites for students and mathematicians: Stack Exchange, MathOverflow, Mathscinet (from within ETH only), zBmath, the Mathematical Genealogy website, MacTutor. Second hour: More basic useful LaTeX commands and typography hints. Sample file: LaTeX file (with explanatory comments).
4.10.2023	First hour: More specialized websites useful for specific fields of research: Online Encyclopedia of Integer Sequences, L-functions and modular forms database. General Feedback about the first writing exercise. Second hour: More technical LaTeX feedback from the first writing exercise. More useful LaTeX commands. Sample file: LaTeX file (with explanatory comments).
11.10.2023	First hour: Feedback about second writing exercise. Presentation of a "corrected" version; LaTeX file for the corrected version as presented, LaTeX file for the corrected version, after further corrections in class (with some comments in the source). Second hour: More useful LaTeX commands; bibliography without using BibTeX. Sample file: LaTeX file (with explanatory comments).
18.10.2023	First hour: Discussion of papers and books, and of the next writing exercise. Second hour: LaTeX formatting guidelines for longer projects. Bibliography with BibTeX, and recomendations for citations. Sample file: LaTeX file (with explanatory comments), and auxiliary file, bibliography file and picture.
25.10.2023	First hour: General guidelines about mathematical writing. Second hour: Some LaTeX options to typeset tables, listings and (commutative) diagrams. Sample file: guidelines and LaTeX file for the second hour (with explanatory comments).
1.11.2023	First hour: Some feedback about the third writing exercise and more guidelines about mathematical writing. Presentation of the fifth writing exercise. Second hour: Introduction to the beamer package. Sample files: guidelines; the beamer sample; auxiliary files: first, second, third, fourth, fifth.
8.11.2023	First hour: Continuation of discussion of guidelines. Second hour: Examples of mathematical styles. Sample files: guidelines (updated).
15.11.2023	First hour: Feedback on fourth writing exercise, including bibliography issues. Second hour: More examples of mathematical styles. Sample files: LaTeX file for BibTeX issues, accompanying bib file.
22.11.2023	First hour: Feedback on fifth writing exercise. Second hour: Guidelines; Serre's lecture on How to write mathematics badly. Sample files: guidelines (updated).
29.11.2023	Mathematics and computers; examples with Magma. Theorem provers (examples with Lean). Sample files and links: Introduction to Magma. Link to sagemath homepage; V. Voevodsky's 2014 slides; K. Buzzard's 2020 slides and Bernays Lectures; the Lean system; the Liquid Tensor Experiment; T. Bloom's Unit Fractions theorem; A. Chambert-Loir's alternating group paper; S. Morel's talk and lean project.
6.12.2023	No lecture
13.12.2023	Feedback on the sixth writing exercise and beamer talks on general. Discussion of suggestions on preparation for writing a semesterarbeit or a Bachelor Thesis or similar texts.
20.12.2023	Discussion of suggestions on preparation for writing a semesterarbeit or a Bachelor Thesis or similar texts. Written text: guidelines.