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Ph.D. Program

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Doctor of Philosophy in Mathematics

The TCU Doctor of Philosophy (Ph.D.) 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 professors, faculty expertise in a wide range of research areas, and abundant opportunities for one-to-one student-to-faculty interaction characterize our program.

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.

Application Deadlines: The application deadline for the fall semester of a given academic year is January 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.

Click here to see a Prezi presentation about our graduate program.

Application Process: It is recommended that the student contact the graduate director at the time of application, in case there are any questions about the program or the application procedure. The application is now for the most part online, and the student should click here to start the online application. Realize that you will need to submit the following with your online application:

  1. A completed online application
  2. Three letters of recommendation (the online application will prompt you for information regarding your references.)
  3. Transcripts of all colleges attended (upload unofficial copies via the online application. If you are admitted to the program a single copy of all official transcripts will be required – see address below) [When applicable, student needs to submit English translations of transcripts. We do not provide this service.]
  4. Personal Statement of Purpose (upload via the the online application. Essay – 1,000 words or less, that describes your motivation and goals for graduate study, career ambitions, and the specific ways TCU may fit those.)
  5. General GRE scores (input scores in Testing Information section in the online application, then request ETS to send official scores to TCU Graduate Studies, institutional code 6820). [The TCU Requirement for GRE is a minimum score of 300 (new scale) or 1000 (old scale). However, Mathematics applicants who are accepted typically have higher GRE scores.]
  6. Application fee of $60 (payment via online application.)
  7. If desired, request financial aid (tuition waivers and stipends) within the online application.
  8. Additional items for international applicants only:
    • TOEFL scores (input scores in Testing Information section in the online application, then request ETS to send official scores to TCU Graduate Studies, institutional code 6820) It is also possible to use IELTS scores instead; in that case, please fill in the information on the online application and then request that official scores are sent directly to TCU. [TCU requires the following minimum scores: IELTS – 6.5; TOEFL (IBT) – 80; TOEFL (PBT) – 550; TOEFL (CBT) – 213 .]
    • For U.S. permanent resident: Please confirm that you are a permanent resident of the United States by emailing a scanned copy of your green card to
    • If you are not a permanent resident, please email the completed International Student and Scholar Form to
    • Admitted students will also be required to provide proof of financial support by filling out and returning the Financial Statement for International Students to Students on full Teaching Assistantships do not have to use this form.
    • For additional information for international students refer to the International Student Services (ISS) web pages (

Please use the address below for mailing of any hard copies of documents (e.g. transcripts sent from your institutions). Please also feel free to contact us regarding any questions you may have about the application process.

Dr. Magnus Rittby, Senior Associate Dean (
TCU College of Science & Engineering
Attn: Graduate Studies
TCU Box 298960
Fort Worth, TX 76129

TCU is committed to providing a positive learning and working environment free from discrimination and harassment. In support of this commitment, TCU prohibits discrimination and harassment on the basis of age, race, color, religion, sex, sexual orientation, gender, gender identity, gender expression, national origin, ethnic origin, disability, genetic information, covered veteran status, and any other basis protected by law. Inquiries about TCU’s policies and compliance with Title IX, The Age Discrimination Act of 1975, or the aspects of TCU’s equal opportunity or affirmative action programs should be directed to:

Dr. Darron Turner
Chief Inclusion Officer and Title IX Coordinator
TCU Box 297090
Jarvis Hall 228
Fort Worth, Texas 76129

Program Details

The Ph.D. program consists of coursework, examinations and research, as specified below. In accordance with TCU 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 five 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 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. The department maintains exam syllabi and practice problems to help students prepare for the exams.

Research-Specific Coursework: After passing the preliminary examinations, the student decides on his or 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, 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 may 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 TCU policy, the time allowed to complete the dissertation is at most six years after advancement to candidacy. Also in accordance with TCU 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