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CSME/Mathematics Ph.D. Program Structure

This particular webpage on the CSME website provides information specifically for Mathematics Department doctoral students who wish to participate in the CSME Doctoral Program. The other participating CSME departments listed on the CSME Overview webpage maintain a webpage or document similar to this webpage which explains the particular details of their internal Ph.D. program, and how it is adjusted to allow a doctoral student in their specific department to participate in the CSME specialization. The overall design of the CSME Graduate Program, and the motivation for its development, is outlined on the CSME Overview webpage and also in the CSME Ph.D. proposal document, which can be found on the CSME Resources webpage. The detailed structure of the CSME Ph.D. Program can be found on the CSME Ph.D. Program webpage.

This page of information may be viewed as an example of how one participating department (in this case, the Mathematics Department) has adjusted the internal structure of its regular doctoral program to accommodate students wishing to participate in the CSME Ph.D. specialization; each department will likely approach such internal adjustments differently.

CSME/Mathematics Ph.D. Admissions Procedure

Admission to the CSME Program as a new incoming mathematics graduate student requires joint admission by both the mathematics department admissions committee and the CSME admissions committee. This is done through coordination between the two committees, without a separate application to the CSME Program. A student applying to the mathematics department who also wishes to apply to the CSME program simply chooses "Computational Science" in the "Current Area of Interest" section of his/her online application. Existing mathematics graduate students who wish to obtain the computational science specialization to their PhD through the CSME Program must also apply for admission into the CSME Program even though they have already been accepted into the mathematics department; admission to the program is then decided by the CSME admissions committee. Participation in the CSME Program will impact the choice of course work in the second year of your studies, so it is important to apply early in your graduate career at UCSD. The application process for existing mathematics doctoral students consists of a short email to the primary administrative contact for the CSME doctoral program, who also plays the role as the CSME/mathematics administrator. The contact information is given on the CSME Application and Admission webpage. The number of graduate student slots in the CSME Program available to each of the six participating departments is limited due to computing, space, and funding resources, and is also limited in order to maintain balance across the participating departments. Therefore, if you wish to participate in the CSME Program you are encouraged to apply early.

CSME/Mathematics Ph.D. Qualifying Examination Structure

The qualifying examination requirements for the PhD in the mathematics department for non-CSME mathematics graduate students is currently as follows. (See the Mathematics Department webpage for the most updated information.) Each graduate student must pass three written qualifying exams within a specified time period; the first exam is in real or complex analysis, the second exam is in algebra or applied algebra, and the third exam is in one of numerical analysis, topology, or statistics.

Mathematics graduate students who are participating in the CSME Program are released from one of the three exams in order to allow them to prepare for, and take, the common CSME qualifying examination. These mathematics/CSME graduate students will be required to take one exam in real analysis, a second exam in numerical analysis, and then the common CSME qualifying exam will play the role of the third exam. As described in more detail on the CSME Ph.D. Program webpage, the common CSME qualifying exam consists of the final exam in each of three quarter-length courses in three core areas of computational science.

Modifications to this default qualifying examination structure for mathematics/CSME graduate students is allowed under the following guidelines. With permission of the mathematics faculty serving on the CSME executive committee, the qualifying exam in complex analysis may be substituted for the real analysis exam; similarly, with permission of the mathematics faculty serving on the CSME executive committee, one of the other mathematics qualifying exams (excluding real and complex analysis) may be substituted for the numerical analysis exam. It is understood that such substitutions would have some research justification; a typical student would otherwise likely be best served by taking the default real analysis and numerical analysis exams.

All other requirements and timetables for the PhD in mathematics remain the same for students earning a PhD in mathematics and the specialization in computational science through the CSME Program.

CSME/Mathematics Ph.D. Core Sequences: Math 270ABC and Math 273ABC

When the mathematics department joined as one of the six core participating departments in creating the CSME program, it committed to designing and offering a project-oriented mathematics sequence (Math 273ABC) that would train CSME students in the core physical modeling, applied analysis, approximation theory, and computational algorithm tools that form the mathematical foundations of modern computational mathematics. This sequence would supplement the existing high-quality numerical analysis graduate courses that are offered by the mathematics department, and in particular would complement the existing Math 270ABC sequence that forms the basis for the Numerical Analysis Qualifying Exam for the Ph.D. in Mathematics. The detailed syllabi for Math 270ABC and other courses relevant to the CSME program can be found on the CCoM Courses Webpage.

CSME/Mathematics Ph.D. Specialization Transfer Policies

The current policies for transferring between the regular mathematics program and the mathematics/CSME program are as follows:

Continuing Students:

Current MA students who wish to enter the CSME PhD program must:

  1. Pass all CSME qualifying exams at an appropriate level.
  2. Have a faculty member willing to serve as PhD thesis advisor.
  3. Apply to the CSME executive committee for permission to enter the program.

Current MA students who wish to enter the non-CSME PhD program must:

  1. Pass all qualifying exams at an appropriate level.
  2. Have a faculty member willing to serve as PhD thesis advisor.
  3. Apply to the Qualifying Exams and Appeals Committee (QEAC) for permission to enter the program.

Current non-CSME PhD students who wish to transfer to the CSME PhD program must either:

  1. Apply to the CSME executive committee before the beginning of the second year of graduate study for permission to enter the program, -OR-
  2. Follow the procedures 1.-3. for MA students above.

Current CSME PhD students who wish to transfer to the non-CSME PhD program must either:

  1. Apply to QEAC before the beginning of the second year of graduate study for permission to enter the program, -OR-
  2. Follow the procedures 1.-3. for MA students above.

New Admissions:

Students applying to the PhD program in mathematics should state whether they are applying to the non-CSME program, or to the CSME program.