Written and Oral Presentation
MATH-GA.2840-004, 3 Points, Wednesdays 11:00-12:50PM, 1302
Warren Weaver Hall
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
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.
of writing for the mathematical sciences" by Nicholas J
Higham, published by SIAM, any edition, strongly
Academic Writing" by Helen Sword (available to NYU members
format free of charge),
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
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.
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.
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:
- A short video lesson "How Big is
Infinity?" by TedEd.
- A lecture on TED on the "Mathematics
of origami. Watch on your own and comment on Piazza.
- A mathematical conference lecture on a very technical topic of
- A 5
minute talk on the rise of multicellular life related to
Attenborough style. Comment on Piazza.
"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
Take a look at Bloom's
taxonomy interpreted for Mathematics by Lindsey Shorser, and
Does Active Learning Mean For Mathematicians?" by Braun et
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:
- Topic: Limits (non-rigorous introduction)
Audience: Calculus 1 students (undergraduates, first-year, a mix
- Topic: Limits (rigorous definition)
Audience: Intro to Math Analysis students (undergraduates,
juniors, mostly math majors)
- 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)
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
(2/28) First student presentation on the topic of the "Fast
Multipole Method" (see draft on Overleaf).
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:
(3/7) Student presentation on "Optimal experimental design
for Bayesian inverse problems" (see draft on Overleaf).
- The Introduction and Outlook of an article by Prof. Miranda
Holmes-Cerfon on "Sticky-sphere
- 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.
- 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.
- Look at the section headings / table of contents in this preprint
on Langevin simulations.
(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)
We will discuss some simple tips to improve your writing style /
(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)