Weinan E

Teaching: Graduate curriculum in applied mathematics

This set of courses is designed for graduate students in applied mathematics whose primary interest is in the modeling and analysis of scientific problems. There is a total of five coursess. The first four courses have been developed and are now either regular courses at Princeton or Peking University or regular courses in the summer school at Peking University.

1. Applied Partial Differential Equations
   Provides an overview of the PDEs that are often encountered in applied mathematics, as well as an introduction of analytical, asymptotic and qualitative methods. Emphasis is put on the qualitative properties of the solutions to these PDEs.
2. Introduction to Atomistic Modeling
   A systematic introduction to simulation methods in computational sciences, including quantum mechanics, molecular dynamics, Monte Carlo, Brownian dynamics and continuum methods.
3. Applied Stochastic Analysis
   An introduction to stochastic analysis and stochastic methods. The material is selected for the particular needs of applied mathematicians. It does not assume background in probability theory or stochastic processes, yet it leads to fairly advanced topics such as rare events.
4. A Mathematical Introduction to Aspects of Physics
   Provides the necessary scientific background, including fundamental principles of physics, atomic structures and chemical kinetics.
5. An Introduction to Mathematical Physics
   An introduction to the mathematical problems that arise in these areas, in particular the modeling from atomistic to continuum scales.