Advanced Topics in Numerical Methods

Monte Carlo Methods

MATH-GA.2011-001 and CSCI-GA.2945-‚Äč001

Courant Institute of Mathematical Sciences,
New York University
Fall Semester, 2020
Wednesdays, 5:10 to 7pm, at first purely remote, but possiby later in blended form in room 1302, Warren Weaver Hall

Instructor: Jonathan Goodman, his web page, email: goodman@cims.nyu.edu
phone: 212-998-3326, office: 529 Warren Weaver Hall
office hours: 10 am to 12 pm Tuesdays on zoom or by appointment
(email for a time)

Course description

A graduate class on Monte Carlo methods. It is a combination of basic material and more advanced topics. The basic material includes sampling methods and error bars, variance reduction method (importance sampling, control variates), rejection and Markov chain Monte Carlo (MCMC). Advanced topics subject to change, but probably include

Depending on student interest and time, other possible topics include There will be much theoretical material, but everything will be illustrated in practical applications from diverse fields.

Prerequisites:

The ability to write computational programs, preferably in Python. A basic course in probability that includes multi-variate densities and the multi-variate central limit theorem. A good background in linear algrbra and multi-variate calculus. Preferably a course on scientific computing or numerical analyis.

Assignments and work flow

This COVID impacted class will be mostly remote with some in person class time depending on student interest and how things go at NYU this September. The following learning and workflow schedule follows math department recommendations for graduate courses this fall.

Group final project

Students will work in small gruoups (up to 4 members, or permission of the instructor) to do a research project that explores some aspect of Montey Carlo. Each group will prepare a "written" (PDF file) writeup of their project and make a presentation to the class. Project organization (group formation, topic selection, etc.) will begin after week 4.

Web sites:

There are two web sites for the class, a public site (this one) and an NYU Classes site for the class. Educational materials will be posted on the public site. The weekly quizzes and homework upload mechanism is on the NYU Classes site. The Classes site also will have a communication forum and access to your entries in the gradebook.

Assignments, exams, grading:

The final course grade will be determined by a weighted sum of scores for quizes (5%), assignments (65%), and the final project (30%). I try to use the gradea A, A-, B+ and B, with lower grades only for people who "earn" them by failing to do much of the assigned work. Students who make a good faith effort should not expect a grade below B. Please contact me immediately if the material or the assignments are unmanageable, particularly if you are weak in some of the prerequisites.

Communication:

Please use the Forum page of the NYU Classes site for this course for all content related communication, including questions about assignments, lectures, or notes. Feel free to contact the instructor directly about other issues such as appointments, missed classes, late assignments, grading issues, etc. The instructor and TA will check the message board frequently. Look there for important course announcements, in particular corrections to assignments.

Academic integrity

Please review the academic integrity policies of the math department and the Graduate School of Arts and Sciences. The policies for this course are