Mathematics Major, PhD

Credit Hours Required

Minimum of 72 graduate credit hours beyond the Bachelor’s or
Minimum of 48 graduate credit hours beyond the Master’s

Required Courses

• These requirements must be completed no later than the start of the student’s seventh year (as a mathematics graduate student at UT).
• Demonstrate competency in advanced calculus and linear algebra by either a satisfactory performance on a diagnostic examination or by passing the appropriate 400-level course with a grade of B or better by the end of the student’s first year of graduate school. The appropriate course for advanced calculus is the MATH 447-MATH 448 sequence and for linear algebra MATH 457-MATH 458 sequence or MATH 453.
• A student must pass written examinations on mathematical ecology (MATH 581-MATH 582) and one of the following year-long sequences –

• Analysis

• MATH 545 - Real Analysis and
• MATH 546 - Complex Analysis

• Computational and Applied Mathematics

• MATH 571 - Numerical Analysis I and
• MATH 572 - Numerical Analysis II

• Differential Equations

• MATH 535 - Partial Differential Equations I and
• MATH 536 - Partial Differential Equations II

• Stochastics

• MATH 523 - Probability I and
• MATH 524 - Probability II
• A student must pass one examination by the middle of their third year and both examinations by the middle of their fourth year.

• Take at least two different one-semester research seminars

• MATH 519 - Seminar in Applied Mathematics
• MATH 529 - Seminar in Stochastics
• MATH 539 - Seminar in Differential Equations
• MATH 549 - Seminar in Analysis
• MATH 559 - Seminar in Algebra
• MATH 569 - Seminar in Topology and Geometry
• MATH 579 - Seminar in Numerical Mathematics
• MATH 589 - Seminar in Mathematical Biology
• MATH 619 - Seminar in Applied Mathematics
• MATH 629 - Seminar in Stochastics
• MATH 639 - Seminar in Differential Equations
• MATH 649 - Seminar in Analysis
• MATH 659 - Seminar in Algebra
• MATH 669 - Seminar in Topology and Geometry
• MATH 679 - Seminar in Numerical Mathematics
• MATH 689 - Concentration in Mathematical Biology
• Pass an examination in the field of specialization after requirements in first three bullets have been met.
• This examination will be given by a committee appointed by the department head.
• A student may take this specialty examination no more than two times.
• Pass a one-year, 600-level sequence in mathematics outside the student’s area of specialization. The sequence selected to fulfill this requirement must be approved by the department head and the student’s doctoral committee.
• In addition to the two year-long sequences chosen for the preliminary examinations, a student must take the following:
  1) a 600-level sequence outside the student’s area of specialization;
  2) Six additional one-semester 500-600 level courses. Two of those courses may be from the area of biology (courses from the Department of Ecology and Evolutionary Biology, College of Veterinary Medicine or Public Health) approved by their advisor,
• These six courses must include:
  a. A one year-long mathematics sequence in a third area (i.e. an area different from those represented in the two preliminary examinations); and
  b. At least one mathematics course in a fourth area (this fourth area must be distinct from the two preliminary exam areas, but may coincide with the area of the sequence used to satisfy (1).
• Students must earn a grade of B- (B minus) or better in each of these six courses.
• MATH 600 - Doctoral Research and Dissertation (24 credit hours)

Non-Course Requirements

• Pass an oral defense and complete a written dissertation.