Doctor of Philosophy in Mathematics
The TCU Doctor of Philosophy (PhD) degree in Mathematics is designed for students who desire to do original research in pure mathematics and who desire to teach at the college/university level. After each doctoral student acquires a strong mathematical foundation in algebra, real and complex analysis, and topology, that student concentrates on one of the research specialties of the TCU Mathematics faculty. These fields of mathematics include real and complex analysis, harmonic analysis, functional analysis, algebraic geometry, differential geometry, number theory, topology, global analysis, representation theory, operator algebras, and K-theory. Award-winning teachers, faculty expertise in a wide range of research areas, and abundant opportunities for one-to-one student and faculty interaction characterize our program.
Application Deadlines: Generally, the application deadline for the
fall semester of a given academic year is March 1. After that date, we
continue to consider applications until the assistantship positions are filled.
We do not consider applications for spring admission.
Click here to see the grad program flyer.
Application Process: It is strongly recommended that the student contact the
at the time of application. An application package consists of:
- a complete application form (available online at www.csegrad.tcu.edu),
- Graduate Student Financial Aid form, if any support is desired,
- one set of official transcripts from all college work including summer classes (in English),
- three or more recommendation letters,
- a non-refundable $60 application fee in the form of a personal check (drawn on U.S. bank), money order, or cashier's check made payable to TCU (this fee is waived for foreign nationals not residing in USA), and
- official GRE scores sent from ETS (General test is required, and the subject test is optional but recommended).
- International students only:
- official TOEFL scores sent from ETS,
- If you are seeking a student visa, please download, complete, and return the following forms:
-- International Student and Scholar Form (PDF)
-- Financial Statement for International Students (PDF)
(Both available at http://www.cse.tcu.edu/ at link above.)
See www.cse.tcu.edu/prospective.asp for more information. Mail all materials to:
College of Science & Engineering
Attn: Graduate Studies
TCU Box 298960
Fort Worth, TX 76129
Program Details
Admission Requirements: BA or BS in mathematics or 24 semester hours of mathematics, including courses in elementary calculus of one and several variables, linear algebra, abstract algebra, and real analysis. Students deficient in any area of preparation may be required to take the necessary course work during the first year of graduate study. Scores on the Graduate Record Examinations are used as an aid in the overall evaluation of the applicant's graduate potential.
The PhD program consists of coursework, examinations, and research, as specified below. In accordance with university policy, a grade point average 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. Also, only 5 courses may be taken at the 50000-level; other classes must be at the 60000-level or higher.
Core Coursework: The following courses are required:
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 of these course 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. There are four preliminary written exams:
Real Analysis Exam - based on MATH 50503 and 60513
Algebra Exam - based on MATH 50253 and 60263
Topology Exam - based on MATH 60313and 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 first semester of the third year. To see detailed syllabi and sample questions for the preliminary exams, click here.
Research-Specific Coursework: After passing the preliminary examinations, the student decides on his or her direction of research and thesis advisor. Based on the recommendation of the department, the dean appoints an advisory committee of at least three members, including the thesis advisor as chair. Possible areas of research specialization include real analysis, complex analysis, functional analysis, algebraic geometry, differential geometry, number theory, topology, global analysis, K-theory, operator algebras, and representation 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. The student advances to candidacy upon passing the qualifying examination.
Dissertation: Advancement 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.
For more information, contact
Ken Richardson
Director of Graduate Studies in Mathematics
TCU Box 298900
Fort Worth, TX 76129
817-257-6128