Program Overview

Ph.D. Program Overview

The CSME Ph.D. Program at UCSD is a campus-wide interdisciplinary training program designed to train the next generation of scientists, mathematicians, and engineers in the use of modern tools of computational science. The CSME Doctoral Program is integrated into the existing doctoral programs of a number of core participating departments. The CSME Doctoral Program leads to a normal Ph.D. in the field of the specific participating department, with an additional credential of "Specialization in Computational Science". A "Specialization" is a formal University of California mechanism that allows a graduate student pursuing a Ph.D. in the UC System to obtain the Doctoral equivalent of a minor in a particular area of specialization.

Ph.D. Program Structure

The CSME Ph.D. program involves modification of the standard graduate degree requirements in the core participating departments to allow students to complete additional requirements to earn a computational science specialization to their doctoral degree. The overall CSME Graduate Program is administered by the Center for Computational Mathematics within the UCSD Mathematics Department, but in all other respects the core participating departments are completely equal partners in the design, development, management, and evolution of the CSME Graduate Program.

Ph.D. Program Admission

Prospective students must apply to the Ph.D. program of a participating home department, be admitted to that department and then be admitted to the specialization through the CSME Program. The participating academic departments which allow their doctoral students to specialize in computational science through the CSME doctoral program are listed on the CSME Overview webpage.

Ph.D. Program Structure and Requirements

Requirements consist of those of the doctoral program in the admitting home department as well as the CSME proficiency, qualifying and elective course requirements as outlined below. Requirements and policies relating to the home department can be found in the General Catalog under that department's name.

• The specialization requires that students complete all home department requirements for the Ph.D. along with satisfying the CSME proficiency, qualifying and elective requirements.
• CSME Proficiency must be satisfied by the end of the first year.
• The CSME Qualifying Exams must be passed by the end of the second year or, on petition, by the end of the third year.
• The CSME qualifying exams can be attempted repeatedly but no more than once per quarter per subject.
• The regular qualifying exams in the home department and the CSME qualifying exams must all be passed before the student is permitted to take the candidacy (senate) exam.
• Two CSME electives outside the home department must be taken.
• The two CSME electives can be taken at any time before defending the thesis.
• One of the CSME electives may be taken Pass/Fail; the other must be taken for a letter grade.
• Full-time students are required to register for a minimum of twelve (12) units every quarter. Eight (8) of these twelve (12) units must be graduate-level CSME Program courses taken for a letter grade.

Proficiency Requirements

All Ph.D. students participating in the CSME doctoral program must demonstrate advanced undergraduate level proficiency in numerical analysis and in computer algorithms and data structures. Proficiency may be demonstrated by taking UCSD's courses in both subjects while enrolled in the graduate program:

1. Numerical Methods (MATH 174/274 or MAE 290A)
2. Data Structures and Algorithms (CSE 100/101) Alternatively, proficiency in the material contained in these courses may be satisfied by having previously taken these or equivalent courses at other institutions, or through other evidence of sufficient knowledge of this material.

Qualifying Requirements

In addition to the home department doctoral program qualifying exam requirements, Ph.D. students participating in the CSME doctoral program must pass the final exams in all three qualifying exam courses listed below. The three qualifying exam courses have been selected to provide a general broad set of tools in computational science.

1. MATH 275 or MAE 290B (Numerical PDE)
2. PHYS 244 or CSE 260 (Parallel Computing)
3. Course to be selected from LIST A

LIST A: CSME Qualifying Exam Courses

The LIST A set of courses is a fairly small collection of computational science and applied mathematics courses that represents core knowledge in modern computational science.

1. MATH 270A, B or C (Numerical Analysis; Not permitted for Math Students, who typically take MATH 270ABC as a normal mathematics qual course)
2. MATH 271A, B or C (Numerical Optimization)
3. MATH 272A, B or C (Numerical Partial Differential Equations)
4. MATH 273A, B or C (Advanced Techniques in Computational Mathematics)
5. MAE 223 (Computational Fluid Dynamics)
6. MAE 232 / SE 276A, B or C (Computational Solid Mechanics)
7. MAE 280A or B (Linear Systems Theory)
8. MAE 294 / SIO 203A, B or C (Introduction to Applied Mathematics)
9. PHYS 221 AB (Nonlinear dynamics)
10. PHYS 243 (Stochastic Methods)
11. SE 233 (Computational and Technical Aspects of Finite Element Methods)
12. CHEM 285 (Introduction to Computational Chemistry)
13. (Additional Courses To Be Determined by Executive Committee or Allowed by Petition)

Elective Requirements

To encourage CSME Ph.D. students to both broaden themselves in an area of science or engineering as well as to obtain more specialized training in specific areas of computational science, students will be required to take and pass two elective courses, both of which must be outside of their home department, the first of which must be taken for a letter grade, and the second of which may be taken pass/fail.

LIST B: Elective Graduate Courses in Mathematics, Science, and Engineering

The LIST B set of courses is a slowly expanding collection of computational science, science, and applied mathematics courses that encourages CSME doctoral students to increase their breadth across disciplines, and also gives students the opportunity to achieve substantial depth in a particular secondary discipline.

1. Any course appearing on List A above
2. PHYS 241 (Computational Physics I)
3. PHYS 242 (Computational Physics II)
4. MAE 222 (Flow Control)
5. MAE 261 (Cardiovascular Fluid Mechanics)
6. SE 277 (Error Control in Finite Element Methods)
7. SE 278A (Computational Fluid Dynamics)
8. SE 278B (Computational Fluid-Structure Interaction)
9. CHEM 215 (Modeling Biological Macromolecules)
10. BGGN 260 (Neurodynamics)
11. ECE 272 (Dynamical Systems under Uncertainty)
12. CSE 250A or B (Principles of Artificial Intelligence)
13. MATH 210A, B or C (Mathematical Methods in Physics and Engineering)
14. MATH 282A or B (Applied Statistics)
15. MATH 231A, B, or C (Partial Differential Equations)
16. (Additional Courses To Be Determined by Executive Committee or Allowed by Petition)

Thesis/Dissertation

Ph.D. students participating in the CSME doctoral program must complete a dissertation which meets all requirements for the regular Ph.D. in the home department. In addition, it is expected that the Ph.D. dissertation will be interdisciplinary in nature and involve some aspect of computational science.

Final Examination

Ph.D. students participating in the CSME doctoral program must meet the regular final examination requirements of the home department.

Time Limits and other Requirements for the Ph.D.

All requirements for the Ph.D. in the home department are enforced for CSME Ph.D. students, unless the specific department has modified the internal structure of their Ph.D. program to allow for CSME participation.