Co-instructors:

piazza.com/nyu/spring2018/mathga2840004

- "Handbook of writing for the mathematical sciences" by Nicholas J Higham, published by SIAM, any edition, strongly recommended.
- "Stylish Academic Writing" by Helen Sword (available to NYU members in electronic format free of charge),
- "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).

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.

- "
**A Brief Introduction to the Fast Multipole Method**" by Jason Kaye - "
**Optimal experimental design for Bayesian inverse problems**" by Karina Koval - "
**Markov Chain Monte Carlo: The Metropolis-Hastings Algorithm**" by Anthony Trubiano - "
**Geostrophic and Quasi-Geostrophic Balances**" by Qiyu Xiao - "
**A Mathematical Introduction to Reinforcement Learning**" by Xintian Han

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.

Examples/assignments:

- 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 Operads (algebraic geometry).
- A 5 minute talk on the rise of multicellular life related to the David 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:

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:

- Topic: Limits (non-rigorous introduction)

Audience: Calculus 1 students (undergraduates, first-year, a mix of non-majors)

- 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.

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).

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:

- The Introduction and Outlook of an article by Prof. Miranda Holmes-Cerfon on "Sticky-sphere clusters."
- 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.

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

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