The PhD curriculum in the Department of Computational Applied Mathematics and Operations Research at Rice University is designed to provide PhD students with a strong foundation, but also give them the flexibility to build a course portfolio focusing on their research area. The PhD curriculum is divided into introductory courses, distribution courses from Areas A, B, C specified below, and electives. PhD students develop their specific curriculum in consultation with their faculty advisor.
PhD students in the Department of Computational Applied Mathematics and Operations Research should complete the majority of the following introductory courses by the end of their first year and complete all introductory courses by the end of their second year.
- 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
In addition to the Introductory PhD Courses, CMOR PhD students are required to complete a minimum of one (1) course each from the three Areas A, B, C specified below, and one (1) elective 3-credit lecture course.
Area A — (Courses with emphasis on Foundations and Theory)
CAAM 523: Partial Differential Equations I
CAAM 540: Applied Functional Analysis
CAAM 542: Discontinuous Galerkin Methods
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 586: Stochastic Simulation
CAAM 640: Optimization with Simulation Constraints
Area C — (Courses with emphasis on Modeling and Applications)
CAAM 535: Modeling Mathematical Physics
CAAM 555: Stochastic Control and Applications
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 and Other Requirements
Descriptions of all CAAM courses can be found in General Announcements.
The Department of Computational Applied Mathematics and Operations Research regularly reviews and refines its PhD curriculum and adjustments to the above courses and areas may be made. As always, these requirements are in addition to the general university requirements specified in the General Announcements.
The CMOR Graduate Handbook contains detailed information about exams, funding, required and recommended courses, and regulations and rules for the PhD degree program in the Department of Computational Applied Mathematics and operations Research.