Advanced Topics in Numerical Analysis

G63.2011.002 (math) / G22.22960.001 (computer science)

Monte Carlo Methods

Warren Weeaver Hall, room 512, Thursdays, 5 - 7 pm
Courant Institute of Mathematical Sciences,
New York University
Fall Semester, 2010


Jonathan Goodman ,
212-998-3326, room 529 Warren Weaver Hall
office hours: 4 to 6 pm Tuesdays or by appointment

Course description

Monte Carlo methods are computational methods that use random numbers. They are central to many parts of computational science such as phase transitions in statistical physics, electronic structure in computational chemistry and materials science, mechanisms for chemical reactions, etc. Emerging applications include uncertainty quantification and reliability, Bayesian statistics, and nonlinear filtering. There is a strong relationship between theoretical analysis and development of novel algorithms. This is an introduction to Monte Carlo methods with an emphasis on areas of active interest, both from a practical and a theoretical point of view. We focus on four related active research areas: finding good samplers, theoretical analysis of their convergence rates, rare event simulation, filtering and optimization. See the syllabus for for more details and a tentative course outline.

Download syllabus


This is an advanced graduate class. The mathematical background includes measure theoretic robability, basics of partial differential equations, and eigenvalues eigenvectors of self adjoint operators. The assignments will involve scientific programming and visualization in some language.

Assignments and grading

There will be regular assingments and possibly a final project. There is no final exam. Some requirements may be waived for advanced graduates involved in thesis research. See instructor at the first class meeting.


There is a message board on the course Blackboard page. If you register for the class, you automatically have access to the message board. Others should email the instructor for access.