The program will admit a small number of exceptionally qualified students. Each student will be assigned to a member of the steering committee to plan and approve a course of study.

By the end of their second year, students will choose a thesis advisor from CAM and two additional thesis committee members. A student may propose an advisor who is not a member of CAM, with approval of the steering committee, in which case the additional members of the thesis committee will be from CAM.

The course requirements of the Ph.D. in Computational and Applied Mathematics are fairly low, consistent with the goal of involving students in original research early in their graduate careers. Together with an assigned advisor, students will select courses from core sequences and a diverse set of possible electives. Example topics include traditional areas such as partial differential equations, numerical analysis, and dynamical systems, as well as modern signal processing, machine learning, data collection and processing, optimization, stochastic modeling and analysis, and the statistical analysis of high dimensional data. Students will complete preliminary examinations in two chosen areas, typically in their second year of study. The track will be highly interdisciplinary, with many students interacting with at least one scientific domain.

Students are required to take nine quarter courses over the first two years, according to a plan designed in consultation with the advisor. This allows students to take preparatory courses as needed. Courses are chosen from a selected set of courses in computational, statistical, and mathematical foundations. Students are also required to take at least one graduate level course in a scientific domain such as chemistry, genetics, geophysical sciences, molecular biology, neuroscience, and physics. Examples of each group of courses is provided below.

*Computational and Statistical Foundations*- Computer Science
- CMSC 37000 Algorithms
- TTIC 31080 Approximation Algorithms
- Optimization
- Stat 30900 Matrix Computation
- Stat 31015 Convex Optimization
- Statistics and Machine Learning
- Stat 37710 Machine Learning
- Stat 37400 Nonparametric Inference
- Stat 37500 Pattern Recognition
- Stat 37750 Compressed Sensing
*Mathematical Foundations*- Analysis and Differential Equations
- Math 312 Analysis I
- Math 313 Analysis II
- Math PDE Analysis
- Mathematical Computation
- Stat 37760 Modern signal processing
- Stat 31095 Numerical ODEs
- Stat 31100 Numerical PDEs
- Dynamical Systems
- Applied dynamical systems I/II
- Advanced topics in dynamical systems
*Applications and Domain Science*- Stat 35410 Computational Biology
- Stat 42510 Computational Neuroscience
- Chem 36800 Advanced Computational Chemistry
- TTIC 31040 Introduction to Computer Vision

As two example nine-course sequences, a student with a machine learning focus might take

- Stat 30900 Matrix Computation
- Stat 31015 Convex Optimization
- Stat 37710 Machine Learning
- CMSC 37000 Algorithms
- Stat 37500 Pattern Recognition
- Math 312 Analysis I
- Stat 37760 Modern signal processing
- Stat 31095 Numerical ODEs
- TTIC 31040 Introduction to Computer Vision

- Stat 30900 Matrix Computation
- Stat 31015 Convex Optimization
- Math 312 Analysis I
- Math 313 Analysis II
- Stat 37760 Modern signal processing
- Math PDE Analysis
- Stat 31095 Numerical ODEs
- Stat 31100 Numerical PDEs
- Chem 36800 Advanced Computational Chemistry