The University of Texas at Austin offers the Doctor of Philosophy (PhD) degree with a major in Computational Science, Engineering, and Mathematics (CSEM). We seek students who are committed to excellence, desire expertise in multiple disciplines, and are willing to take on new challenges while working alongside faculty involved in research at the forefront of computational science. CSEM doctoral students complete advanced coursework in applied mathematics, computer science, and in fields representing the application area. Graduates of the CSEM PhD Program have made significant contributions to research, academia, and technology.
Within this graduate studies program, each student must develop a program of study and research in Computational Science, Engineering, and Mathematics that includes a substantial component from each of the three CSEM concentration areas:
Area A
Applied mathematics
Area A encompasses the mathematical theory and foundations underlying the scientific models and computational science addressed in the overall research effort. It may involve, for example, functional analysis, partial differential equations, differential geometry, probability, data science, optimization, and approximation theory.
Area B
Numerical Analysis and Scientific Computation
Area B encompasses all areas of algorithms and computational simulation, as well as their development, verification, and analysis. It often covers, for example, issues of numerical stability and approximation, scientific programming, visualization, parallel computation, software design, and high performance computing.
Area C
Mathematical Modeling & Applications
Area C encompasses the scientific principles of the natural, engineered, social, or other system that motivates the research and aims to foster some scientific or societal goal through computational modeling and simulation. With the assistance of a CSEM faculty member, all students are expected to develop a concentration of coursework in a well-defined discipline of science, engineering, medicine, economics or the social sciences. Examples include physics, chemistry, biology, geology, biomedicine, all disciplines of engineering, and other areas of science and medicine that form the basis for developing mathematical and computational models.
CSEM has two degree options. Upon entering the program, each student must select an option.
Every student is required to have a faculty dissertation advisor (or co-advisors). The primary advisor must be chosen from the CSEM Graduate Studies Committee (GSC). The student must select an advisor willing to serve as a mentor, supervise the dissertation, and give advice on coursework. A dissertation advisor need not be selected until the end of the second long semester of the student's studies. Prior to the selection of a dissertation advisor, the CSEM Graduate Advisor will appoint a faculty mentor who, along with the Graduate Advisor, will advise the student on coursework and progress in the program.
The student's overall cumulative grade point average must be 3.25 (B) or better. The student must satisfactorily complete requirements in the three CSEM concentration areas A, B, and C. These requirements include 12 hours of approved graduate level coursework in each area, taken for a grade. The student must achieve a grade point average of 3.25 (B) or better in those courses. Moreover, in one of Areas A, B, or C, the student must achieve a grade point average of 3.5 (B+/A-) or better. The student must complete all required coursework by the end of the seventh long semester.
Note: specific course numbers are subject to change
Summary of requirements
During the first full academic year of the program, the student must complete the following first year sequence, depending on the degree option.
Course requirements: First year sequence
CAM option
CSE option
Area A
CSE 386C Methods of Applied Mathematics I (Fall)
and
CSE 386D Methods of Applied Mathematics II (Spring)
CSE 386M Functional Analysis in Theoretical Mechanics (Fall)
and
CSE 386L Mathematical Methods in Science and Engineering (Spring)
Area B
CSE 383C Numerical Analysis: Linear Algebra (Fall)
and one of the following
– CSE 383L Numerical Analysis: Differential Equations (Spring)
– CSE 382M Foundational Techniques of Machine Learning and Data Sciences (Spring)
Same requirements as CAM option
Area C
CSE 389C Introduction to Mathematical Modeling in Science and Engineering I (Fall)
and
CSE 389D Introduction to Mathematical Modeling in Science and Engineering II (Spring)
Same requirements as CAM option
CAM option
Area A
CSE 386C Methods of Applied Mathematics I (Fall)
and
CSE 386D Methods of Applied Mathematics II (Spring)
Area B
CSE 383C Numerical Analysis: Linear Algebra (Fall)
and one of the following
– CSE 383L Numerical Analysis: Differential Equations (Spring)
– CSE 382M Foundational Techniques of Machine Learning and Data Sciences (Spring)
Area C
CSE 389C Introduction to Mathematical Modeling in Science and Engineering I (Fall)
and
CSE 389D Introduction to Mathematical Modeling in Science and Engineering II (Spring)
CSE option
Area A
CSE 386M Functional Analysis in Theoretical Mechanics (Fall)
and
CSE 386L Mathematical Methods in Science and Engineering (Spring)
Area B
Same requirements as CAM option
Area C
Same requirements as CAM option
After completing the first-year sequence, students must complete the following additional coursework by the end of the seventh long semester:
At the end of the first full academic year, the student is required to demonstrate a graduate level proficiency in CSEM Areas A, B, and C by taking and passing a written preliminary examination in each area. These exams cover the subject material of the first year courses taken by the student.
A student failing any of the preliminary exams will be required by the examining committee to do one of the following:
The student and dissertation advisor must recommend to the Graduate Advisor a dissertation committee to pose the qualifying exam and evaluate the dissertation. The dissertation committee must consist of the advisor and at least four additional faculty members. The committee must include at least one CSEM Graduate Studies Committee faculty member representing Area A, a second representing Area B, and a third representing Area C, not including the student's advisor. Moreover, at least three of the committee members must represent distinct UT departments through positive time appointment. The Graduate Advisor must approve the composition of the committee. Minimum committee requirements summarized below:
Before the end of the sixth long semester, the student must propose research for their PhD dissertation.
The student must write a concise abstract of the dissertation proposal. The abstract must address how each of the three CSEM Concentration Areas A, B, and C will be addressed in, and form an integral part of, the proposed research (Abstract Guidelines). The student must meet with each member of his or her dissertation committee to discuss the abstract, the expertise the committee member will contribute to the dissertation, and the background knowledge expected of the student, as well as the types of questions that might be asked at the proposal presentation (see Dissertation Proposal Presentation section below.) The abstract must be signed by each member of the committee. Before the dissertation proposal presentation may be scheduled, this abstract must be submitted to and approved by the Graduate Studies Subcommittee (GSSC.) Submit the abstract in pdf format to the Graduate Coordinator who will make it available to the GSSC for review.
The student must write his or her dissertation proposal and submit it to each member of the dissertation committee, and to the Graduate Coordinator. The format of the proposal must conform to the CSEM PhD Proposal Requirements.
Approximately two weeks after submission of the written dissertation proposal, the student is required to give a private, oral presentation of the proposal to his or her dissertation committee. The presentation itself should be about 45 minutes in length. The committee will then examine the student to explore details of the proposal and to test his or her general background knowledge relevant to the proposed research, including the ability to integrate ideas from Areas A, B, and C. The committee will expect somewhat greater depth and breadth in Area A as opposed to Area C for students in the CAM option, and the opposite for students in the CSE option.
Once you have scheduled the proposal presentation, you must notify the Graduate Coordinator of the date, time, and room number.
The student's performance is satisfactory if the committee agrees, with at most one dissenting vote, that the student developed a sufficiently rich, original and interdisciplinary research program and demonstrated competence to complete the proposed research. In the event of an unsatisfactory performance, the committee is charged with explaining to the student the reasons that his or her performance was not satisfactory. The committee may impose requirements on the student, such as requiring changes to the proposal, additional coursework, and/or another presentation to be given within one year.
The Candidacy Checklist outlines the steps for entering candidacy, from the formation of the dissertation committee to the submission of the candidacy application to the Graduate School.
After completing all coursework, preliminary examination, and proposal requirements, the student must submit a Graduate School application for candidacy. The CSEM Graduate Coordinator will send instructions for submitting the application once the student's advisor has confirmed that student has passed the proposal.
Generally, by the end of the tenth long semester, and definitely before the end of the fourteenth long semester, students must prepare a written dissertation of the results of their research and provide a copy to each member of their PhD dissertation committee and to the Graduate Coordinator. This dissertation must be presented in a seminar of about 45 minutes that is open to the public, and it must be announced publicly to CSEM faculty and students within the Oden Institute. Immediately after the presentation, the student will meet privately with the dissertation committee to face questions and orally defend the work. The dissertation committee will judge whether the dissertation and the oral defense are acceptable.
Both the dissertation and the oral defense must follow appropriate Graduate School requirements and procedures found on the Deadlines and Submission Instructions page.
Each student is expected to regularly attend regularly Oden Institute sponsored seminars. The GSSC will set the number required each semester.
Each student is required to submit an annual progress report of coursework, research activities, and financial support. Students not making satisfactory progress to the degree will be given specific requirements that must be met to return to good standing in the program.
Students failing to satisfy the requirements of the program in a timely manner will be put on probation by the GSSC, and their progress will be monitored closely. The student will remain on probation until satisfactory progress is achieved. A student may remain on probation for a maximum of two long semesters. A student who has been on probation for a total of two long semesters and is found to be out of compliance with the timely requirements of the program will not be allowed to continue in the program.
Students may appeal to or petition the CSEM GSSC for waiver or alteration of any CSEM requirement, except for waiver of an exam or waiver of a Graduate School degree requirement. Written appeals or petitions should be submitted to the GSSC through either the Graduate Advisor or the CSEM Graduate Studies Committee Chair.
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