Texas Tech University

Ph.D. Programs

The following represents an outline of the Department of Mathematics and Statistics policies concerning the doctoral program. These policies are supplemental to the general Texas Tech University policies as outlined in the official catalogs of the university. Specific questions concerning the interpretation of these policies should be directed to the Graduate Advisor. A student in the doctoral program must fill out a degree plan after the end of their second long semester and before the start of their third long semester in the program.

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Areas of Specialization Preliminary ExaminationsQualifying ExaminationForeign Language RequirementTransfer of Courses

Areas of Specialization

Each doctorate in mathematics at Texas Tech University will be based on the doctoral candidate's choice of an area of specialization from the following four broad specialty areas:

Applied Mathematics

1. Foundational coursework (24 hours):

- Three sequences from the following, with at least one sequence from Group A and at least one sequence from Group B.

Group A: MATH 5320-MATH 5321, MATH 5322-MATH 5323, MATH 5324-MATH 5325, MATH 5340-MATH 5341.

Group B: MATH 5330 and MATH 5332, MATH 5334-MATH 5335, STAT 5328-STAT 5329, STAT 5373-STAT 5374.

- At last two other courses (not necessarily in a sequence) chosen from Group A and Group B.

2. Additional coursework: Thirty-six additional hours selected with the approval of the student's dissertation advisor and the director of graduate studies. These may include courses offered by the Department of Mathematics and Statistics relevant to the student's area of research or courses offered outside the department relevant to the student's area of research.

3. Twelve hours of MATH 8000

Pure Mathematics

1. All of the following four sequences: MATH 5320-MATH 5321, MATH 5322-MATH 5323, MATH 5324-MATH 5325, MATH 5326-MATH 5327.

2. Thirty-six additional hours selected with the approval of the student's dissertation advisor and the director of graduate studies. These may be courses offered by the Department of Mathematics and Statistics relevant to the student's area of research or courses offered outside the Department of Mathematics and Statistics relevant to the student's area of research.

3. Twelve hours of MATH 8000.

Statistics

The following seven courses are referred to as “Required Courses” and are required for all students:

STAT 5328, STAT 5329, STAT 5371, STAT 5373, STAT 5374, STAT 5386, MATH 5382.

The following eight courses are referred to as “Elective Courses” and may be taken for the master's degree, but all must be taken for the doctoral degree.

STAT 5326, STAT 5370, STAT 5372, STAT 5375, STAT 5376, STAT 5378, STAT 5379, STAT 5380.

1. All seven of the required STAT courses listed above. Additionally all eight of the STAT elective courses from the list above.

2. Fifteen additional hours of courses selected with the approval of the student's dissertation advisor, the director of graduate studies, and the statistics coordinator. These may be statistics courses offered by the Department of Mathematics and Statistics (excluding STAT 5302-3 and STAT 5384-5), mathematics courses relevant to the student's area of research, or courses offered outside the Department of Mathematics and Statistics relevant to the student's area of research.

3. At least twelve hours of MATH 8000 for a doctoral dissertation.

Overall policy guidelines have been established by the Department of Mathematics and Statistics with respect to work within these specialty areas.

Preliminary Examinations

The Doctoral Preliminary Examinations will be administered twice each year (in May and in August) and are offered in the eight areas corresponding to the following graduate core courses:

  1. Algebra (MATH 5326-5327)
  2. Complex Analysis (MATH 5320-5321)
  3. Ordinary Differential Equations (MATH 5330)/Partial Differential Equations (MATH 5332)
  4. Numerical Analysis (MATH 5334-5335)
  5. Real Analysis (MATH 5322-5323)
  6. Topology (MATH 5324-5325)
  7. Probability and Statistics (STAT 5328-5329)
  8. Applied Statistics (STAT 5373-5374)

Each examination is four hours long with content based on important fundamental concepts in the area. Students should NOT infer that the Preliminary Examination is equivalent to a Final Examination over the respective core area. Rather, each examination is developed by a committee of faculty in the respective core area in consultation with the Graduate Committee. The topics over which a student can be tested are listed in the Preliminary Examination Topics List which is available from the Graduate Advisor.

At least three weeks prior to taking a Preliminary Examination the student must inform the Graduate Advisor which examinations he/she wishes to take. Up to three different examinations can be taken in each administration of the Preliminary examinations. A grade of P (pass) or F (fail) will be given in each examination. The policy is below.

Definitions:

  1. Category A: Graduate students with a Master's degree in Math or Stat.
  2. Category B: Graduate students who are not in Category A.
  3. An attempt: A student is said to have attempted an exam when they have seen the contents of an exam while it is being administered.
  4. Prelim requirements: Students have to pass 3 exams in different subject areas. One subject area must be from the "pure mathematics" group: Algebra, Complex analysis, Real analysis, or Topology. Students in statistics concentration must pass the Probability and Statistics exam.

Remark: Signing up for an exam and not showing up does not constitute an attempt.

Policy: Students in Category A are required to finish the prelim requirements for their concentration by the beginning of their third academic year. Category B students are required to finish the prelim requirements for their concentration by the beginning of their fourth academic year. All students are allowed a maximum of 12 attempts with a maximum of three attempts per area. Note that an academic year starts with the Fall semester.

Any student who does not successfully complete the Doctoral Preliminary Examinations according to the policy stated above may not continue in the Doctoral Program in the Department of Mathematics and Statistics at Texas Tech University.

Qualifying Examination

Each doctoral student will be required to pass a Qualifying Examination on advanced topics beyond those covered in the Preliminary Examinations. In general, the Qualifying Examination will follow the format established by the Texas Tech University Graduate Catalog. Any exceptions to this format must be agreed upon by both the student's Doctoral Advisory Committee and the Graduate Advisor.

Foreign Language Requirement

Any foreign language requirement will be at the discretion of the student's dissertation advisor.

Note to all Ph.D. Students:

  • Preliminary Examination: Only those students who have passed the preliminary examination requirement are eligible to take MATH 8000. The students should check with the instructor of record in the year the preliminary exams are administered to find out the exact list of topics for the prelim exam.
  • Dissertation: A dissertation is required of every candidate for the doctoral degree. This requirement is separate and apart from other requirements in the doctoral program. Consequently, successful performance in other areas does not necessarily guarantee the acceptance of a dissertation. The dissertation should embody a significant contribution to new information to the subject.
  • Each doctoral student should become familiar with the university and departmental requirements and deadlines for the doctoral degree.
  • Final Examination: A final public oral examination over the student's dissertation topics is required of every candidate for the doctorate.
  • If a student passes a prelim without having taken the corresponding course sequence in our department, he or she is exempt from that specific sequence requirement. However, unless the student has appropriate transfer credit accepted by the department and the Graduate School, he or she must still complete the required number of foundational sequences and courses for his or her concentration. See Rules 2b and 3a below for information on transfer credit.

Transfer of Courses

With the permission of the graduate advisor:

  1. One course (3 credit hours) may transfer towards a grad certificate provided there is an equivalent TTU course.
  2. Two courses (6 credit hours) may transfer towards a Master's degree, provided there is an equivalent TTU course.
    1. A core course/sequence from a Master's degree-granting institution will not transfer.
    2. Students can be exempted from a core course/sequence by passing the corresponding Ph.D. prelim exam at TTU.
  3. Up to 10 courses (30 credit hours) from a doctoral degree-granting institution may transfer towards a Ph. D. degree. 
    1. A course/sequence from a Ph.D. degree-granting institution may transfer if the student has passed the corresponding prelim exam at TTU. 
    2. No courses from a Master's degree-granting institution will be granted transfer credit.
  4. No course or credit from an undergraduate program will be allowed to transfer toward a graduate degree or certificate.

Department of Mathematics & Statistics