Ph.D. students in computational and applied mathematics at Rice University should take the following introductory courses in their first year — except for CAAM 600, which is taken in the spring semester of the second year.

### Introductory Courses

- CAAM 501: Analysis I
- CAAM 519: Computational Science I
- CAAM 553: Advanced Numerical Analysis I
- CAAM 554: Iterative Methods for Systems of Equations and Unconstrained Optimization
- CAAM 571: Linear and Integer Programming
- CAAM 600: Thesis Writing

In addition to the Introductory PhD Courses, CAAM PhD students are required to complete a minimum of one course each from the three Areas A, B, C specified below, and one 1 elective 3-credit lecture course.

As always, these requirements are in addition to the general university requirements specified in the General Announcements.

### Area A — (Courses with emphasis on Foundations and Theory)

CAAM 523: Partial Differential Equations I

CAAM 540: Applied Functional Analysis

CAAM 552: Foundations of Finite Element Methods

CAAM 558: Intro to Partial Differential Equation Based Simulation and Optimization

CAAM 560: Optimization Theory

CAAM 570: Graph Theory

CAAM/STAT 581: Mathematical Probability I

CAAM/STAT 583: Introduction to Random Processes and Applications

500 level MATH courses with advisor approval

### Area B — (Courses with emphasis on Algorithms and Computation)

CAAM 520: Computational Science II

CAAM 536: Numerical Methods for PDEs

CAAM 542: Discontinuous Galerkin Methods for Solving Engineering Problems

CAAM 551: Numerical Linear Algebra

CAAM 564: Numerical Optimization

CAAM 565: Convex Optimization

CAAM 574: Combinatorial Optimization

CAAM 585: Stochastic Optimization

CAAM 640: Optimization with Simulation Constraints

### Area C — (Courses with emphasis on Modeling and Applications)

CAAM 535: Modeling Mathematical Physics

CAAM 567: Signal Recovery: Theory and Simulation

CAAM 583: Introduction to Random Processes and Applications

CAAM 615: Theoretical Neuroscience: From Cells to Learning Systems

STAT 502: Neural Machine Learning I

STAT 503: Topics in Methods and Data Analysis

STAT 514: Introduction to Biostatistics

STAT 519: Statistical Inference

500 level courses offered in the schools of Natural Sciences and Engineering with advisor approval

### Course Descriptions

Descriptions of all CAAM courses can be found in General Announcements.

### Graduate Handbook

The CAAM graduate handbook contains detailed information about exams, funding, required and recommended courses, and regulations and rules for the various degree programs.