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Scientific Computation Ph.D.

The Mathematics Department offers an interdisciplinary doctorate in Scientific Computation in cooperation with the Laboratory for Scientific Computation (LaSC) and several Departments in the College of Engineering. Students seeking the Mathematics/Scientific Computation degree are students in the Mathematics Department and proceed to the degree in the same three stages as the Math Ph.D, but they should also make contact with LaSC as soon as it is decided that they will seek this degree. LaSC will appoint a committee to counsel and supervise the student.

Stage 1

To pass the Qualifying Review, students in the Mathematics/Scientific Computation degree program must:

  1. Pass the Qualifying Review in one of the three core areas of Algebra, Analysis and Geometry/Topology.
  2. Pass a written exam in numerical analysis to be given by the faculty of LaSC. The material for this exam is covered in Math 571 and 572.
  3. Either pass the Qualifying Review in a second of the three core areas of Algebra, Analysis and Geometry/Topology, or pass two additional core courses, each with a grade of B or higher, chosen from two of the four core areas of Algebra, Analysis, Applied Analysis and Geometry/Topology, but excluding Math 572 which has already been used in 2.

As is the case for other Mathematics students one of the two written exams must be passed by the start of the fourth term, it is expected that the entire Review will be completed by the end of the fourth term and must be completed by the start of the sixth term. Normally financial aid is not committed beyond the second year until the Qualifying Review has been passed.

Stage 2

At this stage the student should have a LaSC Advisory Committee and should in reasonable time select a member of the Mathematics Department faculty, also a member of LaSC, to serve as his or her supervisor and chair of the Advisory Committee.

Requirements for Candidacy in Mathematics/Scientific Computation

Admission to Candidacy in this program is contingent upon completing the following requirements:

  1. Knowledge of at least five Mathematics courses at the level 500 or above in addition to those used to satisfy the Qualifying Review, and including at least one additional course in numerical analysis, chosen so as to meet the criterion in "The course requirement'' on page 4. One of the five could be a core course not used to meet the Qualifying Review requirements.
  2. Knowledge of at least three graduate courses in scientific computation or applications offered by associated Departments. (This requirement also fulfills the Cognate requirement).
  3. Passing the Departmental Reading Exam in one of the following three languages: French, German, Russian.
  4. Passing the oral Preliminary Exam, which will be administered by two mathematicians and two additional faculty from LaSC selected with the approval of both LaSC and the Chair of the Doctoral Committee. The student will be examined on a detailed list of subjects in scientific computation and related areas prepared by the student in consultation with the Advisor.

Stage 3

Post Candidate Course Requirement

After entering Candidacy a student is required to take one advanced course in mathematics, scientific computation, or applications for credit during each of the next two semesters in residence.

Thesis Advisor/Thesis Topic

The Thesis Advisor is chosen by the student with the approval of LaSC and the Doctoral Committee of the Mathematics Department. The thesis will be on some aspect of scientific computation and will be directed by the Advisor and a committee appointed by LaSC and the Doctoral Committee which will usually serve as the Dissertation Exam Committee.