Mathematics PhD Degree Requirements

The PhD Program consists of coursework, examinations, and research, as specified below. In accordance with University policy, a GPA of at least 2.75 must be maintained with no more than two grades of "C+" or lower being utilized in satisfying the degree requirement.

Core Coursework (27 hours):

Coursework for the PhD must include the following nine core courses:

MATH 50253 Abstract Algebra I

MATH 60263 Abstract Algebra II

MATH 50503 Real Analysis I

MATH 60513 Real Analysis II

MATH 60223 Applied Linear Algebra

MATH 60313 Topology

MATH 60323 Algebraic Topology I

MATH 60413 Advanced Complex Analysis

MATH 60523 Measure Theory

Any or all of these courses may be waived for more advanced students by departmental permission.

Preliminary Examinations

The program requires substantial training in algebra, real analysis, topology, and complex analysis. The student must pass three of the following four preliminary written exams:

  • Real Analysis Exam (based on MATH 50503 and 60513)
  • Algebra Exam (based on MATH 30224, 50253 and 60263)
  • Topology Exam (based on MATH 60313 and 60323)
  • Complex Analysis Exam (based on MATH 50403 and 60413)

The student must pass the Real Analysis Exam, the Algebra Exam, and either the Topology Exam or the Complex Analysis Exam. These exams are administered twice each year and must be passed by the end of the sixth semester.

Research-Specific Coursework

After passing the preliminary examinations, the student decides on his/her direction of research and thesis adviser. Based on the recommendation of the department, the dean appoints an advisory committee of at least three members, including the thesis adviser as chair.

Possible areas of research specialization include real analysis, complex analysis, functional analysis, algebraic geometry, differential geometry, number theory, topology, global analysis and K-theory.

Students must also take at least one semester of three hours of MATH 80880 Graduate Student Seminar, providing training in the oral presentation of research-level mathematics.

Qualifying Examination

The student and advisory committee agree on a detailed plan of study to prepare the student for mathematical research. They decide on a syllabus of qualifying topics; after due preparation, the student takes the oral qualifying exam on these topics, administered by the advisory committee. In accordance with University requirements, the exam can only be taken after passing the preliminary examinations and not before the second semester of the second year. If the exam is not passed, at most one re-examination is allowed.

Admission to Candidacy

The student advances to candidacy after passing the qualifying examination.

Research

The student performs research in his/her area of specialization, which leads to a dissertation, if successful.

Dissertation (at least 12 hours)

Admission to candidacy is the prerequisite to enrollment in dissertation research, consisting of an original research project directed by a graduate faculty member at TCU. Six hours of MATH 90980 Dissertation and six hours of MATH 90990 Dissertation are required. According to University policy, the time allowed to complete the dissertation is at most six years after advancement to candidacy. Also in accordance with University rules, the student must submit an Intent to Graduate form at the beginning of the last semester, for which there is a non-refundable fee. At the completion of the dissertation, a final oral examination is required, which is open to the public.





Texas Christian University
© Copyright 2007. All Rights Reserved.
Disclaimer