Written and Oral Presentation

MATH-GA.2840-004, 3 Points, Wednesdays 11:00-12:50PM, 1302 Warren Weaver Hall
Co-instructors: Aleksandar Donev and Mutiara Sondjaja


In addition to this page, where we will post lecture notes and links to external material, we will use Piazza for communication and to quickly give feedback to each other on various samples of writing.


This course will provide graduate students preparing for teaching and research careers with several skills and tools for more effective professional oral and written presentation. It will also provide a platform for supervised teaching practice. Students from all fields of mathematics are welcome, both pure and applied. The first part of the course, taught primarily by Prof. Mutiara Sondjaja, will focus on teaching pedagogy and effective class management. The second part of the course, co-taught with Prof. Aleks Donev, will focus on scientific writing, from abstracts to complete papers. Students will practice both by writing a review article or lecture notes on a topic from their field of study, aimed at their peers and not at specialists. They will deliver lectures to the class on the chosen topic and get feedback from the instructors and other students. The use of LaTex or tools based on LaTex such as LyX or sharelatex/Overleaf will be strongly encouraged. We will also have some guest lectures from professional writers and career service professionals, and will provide, as time permits, help with basic job search skills like writing CVs, teaching and research statements, and cover letters. Students will be encouraged to help each other and learn from peers.


  1. "Handbook of writing for the mathematical sciences" by Nicholas J Higham, published by SIAM, any edition, strongly recommended. 
  2. "Stylish Academic Writing" by Helen Sword (available to NYU members in electronic format free of charge),
  3. "The Elements of Style" by Strunk and White, which we recommend for non-native speakers, or those wishing to refresh their English writing skills. It is available free in electronic form at a number of online locations (use google).


Each of you will be required to write a set of "lecture notes" in LaTex. It is essential that you setup a working LaTex environment (for OS X use MACTex and consider installing homebrew) on the computing system you wish to use for this course (the Linux-based CIMS networked computers have everything you need and more). First-time LaTex users (but also others!) should consider using the WYSIWYG Latex frontend / word processor LyX to start. Students that prefer to work directly with LaTex should take a look at some latex-specific editors, such as the free and portable TeXMaker (installed on Courant's linux network). More experienced users could use a programming editor that is latex-aware, such as atom-latex or LaTeXTools-sublime.

If you want to make presentations in PowerPoint or keynote and include equations, try LatexIt (comes with MACTex on OS X systems).

To co-edit and comment on this as a group, we will use Overleaf, and/or maybe github+TeX editor of choice.

Lecture Notes

(1/24) Basic oral presentation skills

Writing a talk is covered in Chapter 9 in the textbook by Higham. Also look at these tips on the David Attenborough style of scientific presentation from Will Ratcliff. Watch it in action in this 5-minute lecture from Ratcliff.


  1. A short video lesson "How Big is Infinity?" by TedEd.
  2. A lecture on TED on the "Mathematics of origami. Watch on your own and comment on Piazza.
  3. A mathematical conference lecture on a very technical topic of Operads (algebraic geometry).
  4. A 5 minute talk on the rise of multicellular life related to the David Attenborough style. Comment on Piazza.
Elevator statements are discussed on page 154 in Chapter 13 (The Big Picture) of the book Stylish Academic Writing. Here is what Sword has to say about it:
"Condensing a complex research project into a pithy abstract is no simple task, to be sure. An even greater challenge is to boil that abstract down into an “elevator statement”: the seemingly off-the-cuff but in fact brilliantly polished single-sentence sum- mary that you offer to the colleague who turns to you in the elevator at an academic conference and asks, “So what are you working on?” You have just a minute or two to respond: the time that it takes for the elevator to arrive at its destination floor...The secret ingredient of an effective elevator statement—or, for that matter, of a persuasive abstract, article, or book—is a strong thesis or argument. Both words are frequently heard in the freshman composition classroom but seldom in the research laboratory. However, identical principles apply in both venues: writers who put forth a bold, defensible claim are much more likely to generate engaging, persuasive prose than those who of- fer bland statements of fact with which no one could possibly disagree. In the sciences and social sciences, a strong thesis fol- lows naturally from a compelling research question..."

Homework: Prepare a 2-3min elevator talk. Choose your topic (e.g., your own research, field of math) and audience. Try one more specialized and one less specialized audience (e.g., a colleague and a neighbor). Present in class and put it on Piazza for comment.

(1/31 and 2/7) Tips for Teaching: Active Learning

Take a look at Bloom's taxonomy interpreted for Mathematics by Lindsey Shorser, and "What Does Active Learning Mean For Mathematicians?" by Braun et al.

Gain inspiration for teaching from the book The Joy of Teaching by Peter Filene (available to you in PDF format).

Think about the advantages and disadvantages of using slides versus a blackboard, for lectures/seminars/talks, within your field of mathematics.

We will also conduct micro-teaching (15min per group) exercises. Each group will give a 15 minute lecture on one of these topics:

  1. Topic: Limits (non-rigorous introduction)
    Audience: Calculus 1 students (undergraduates, first-year, a mix of non-majors)

  2. Topic: Limits (rigorous definition)
    Audience: Intro to Math Analysis students (undergraduates, juniors, mostly math majors)

  3. Topic: Introduction to rigorous proofs, with focus on introducing proof by induction
    Audience: Students taking something like Discrete Math (undergraduates, sophomores, math/CS/education majors)

(2/14 and 2/28) Computer Tools: LaTex

We will discuss computer tools for mathematical writing in class but see Tools above for links. Also get the AMS Short Math Guide for LaTex.

(2/21) Guest workshop on academic writing

Robert Diyanni and Anton Borst from the NYU Center for the Advancement of Teaching will give a guest workshop on academic writing. The center is available to you for assistance with writing or presenting. They also offer engaging and effective workshops that you should consider attending.

(2/28) First student presentation on the topic of the "Fast Multipole Method" (see draft on Overleaf).

(3/7 and 3/28) Structure of a paper

We will begin going through some fundamentals of good scientific writing, starting from the structure of a paper. We will use the following two review articles as examples:

  1. The Introduction and Outlook of an article by Prof. Miranda Holmes-Cerfon on "Sticky-sphere clusters."
  2. First two pages of this "Introduction to Regularity Structures" by Martin Hairer. Observe the structure of the introduction and what different paragraphs do, and write down some notes.
  3. First two pages of the complete article "A theory of regularity structures" by Martin Hairier, published in Invent. Math. 2014 (Hairer won the Fields Medal for this work). Also take a look at the structure of the article and Section 1 in particular and take some notes of what you notice.
  4. Look at the section headings / table of contents in this preprint on Langevin simulations.
(3/7) Student presentation on "Optimal experimental design for Bayesian inverse problems" (see draft on Overleaf).

(3/14) Spring break!
(3/21) Snow day!

(3/28) Student presentation on "Wave-Vortex Decomposition of one-dimensional track data" (see draft on Overleaf)

(4/4, 4/11, 4/18 and 4/25) Tips for better writing

We will discuss some simple tips to improve your writing style / English usage.

(4/4) Student presentation on "Polar Amplification and Heat Fluxes in the Atmosphere" (see draft on Overleaf)

(4/11) Student presentation on "The Markov Chain Monte Carlo Method" (see draft on Overleaf)

(4/18) Student presentation on "Reinforcement Learning" (see draft on Overleaf)

(4/25) Student presentation on "Mathematical theory for Go endgames" (see draft on Overleaf)