ProgramDoctoral
Ph.D. Programs
The Department of Mathematics and Statistics maintains policies for the Ph.D. program that supplement the general requirements of Texas Tech University and the Graduate School. Students should consult the Graduate Advisor regarding interpretation and application of these policies. Doctoral students must file an official degree plan after completing their second long semester and before beginning their third long semester in the program.
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Areas of Specialization
The Department of Mathematics and Statistics offers multiple areas of specialization within the Ph.D. program, allowing students to pursue advanced study and research aligned with their academic and professional goals. These tracks reflect the full scope of modern mathematical and statistical sciences and provide the rigorous training necessary for doctoral-level research.
Students select a specialization in consultation with the Graduate Advisor and their Doctoral Advisory Committee. Each specialization includes foundational sequences, advanced coursework, and research preparation tailored to expectations within the discipline.
- Foundational coursework (24 hours):
- Three sequences from the following, with at least one sequence from Group A and at
least one from Group B.
Group A:
- MATH 5320 & 5321 – Complex Analysis I & II
- MATH 5322 & 5323 – Real Analysis I & II
- MATH 5324 & 5325 – Topology I & II
- MATH 5340 & 5341 – Functional Analysis I & II
Group B:
- MATH 5330 & 5331 – Ordinary Differential Equations I & II
- MATH 5334 & 5335 – Numerical Analysis I & II
- STAT 5328 & 5329 – Intermediate Mathematical Statistics I & II
- STAT 5373 & 5374 – Applied Statistics (Design of Experiments & Linear Models)
- At least two additional courses (not necessarily a sequence) chosen from Group A or Group B.
- Three sequences from the following, with at least one sequence from Group A and at
least one from Group B.
- Additional coursework (36 hours): Courses selected with approval from the student’s dissertation advisor and the Director of Graduate Studies. These may include departmental courses relevant to the student’s research area or approved courses outside the department.
- Dissertation: Twelve hours of MATH 8000 – Doctoral Dissertation.
- Completion of all four core sequences:
- MATH 5320 & 5321 – Complex Analysis I & II
- MATH 5322 & 5323 – Real Analysis I & II
- MATH 5324 & 5325 – Topology I & II
- MATH 5326 & 5327 – Modern Algebra I & II
- Additional coursework (36 hours): Selected with approval from the student’s dissertation advisor and the Director of Graduate Studies. These may include departmental or relevant external courses aligned with the student’s research area.
- Dissertation: Twelve hours of MATH 8000 – Doctoral Dissertation.
- Required courses:
- STAT 5328 – Intermediate Mathematical Statistics I
- STAT 5329 – Intermediate Mathematical Statistics II
- STAT 5371 – Regression Analysis
- STAT 5373 – Design of Experiments
- STAT 5374 – Theory of Linear Statistical Models
- STAT 5380 – Advanced Mathematical Statistics I
- MATH 5382 – Advanced Probability
- Four electives chosen from:
- STAT 5326 – Biostatistics
- STAT 5370 – Decision Theory (Bayesian Statistics)
- STAT 5372 – Nonparametric Statistical Inference
- STAT 5375 – Statistical Multivariate Analysis
- STAT 5378 – Stochastic Processes
- STAT 5379 – Time Series Analysis
- STAT 5386 – Statistical Computing and Simulation
- Additional coursework (27 hours): Approved coursework (excluding STAT 5302–5303 and STAT 5384–5385). These may include statistics, mathematics, or relevant external courses with approval from the student’s dissertation advisor and the Director of Graduate Studies.
- Dissertation: Twelve hours of MATH 8000 – Doctoral Dissertation.
- Required courses:
- MATH 5322 – Functions of a Real Variable I
- MATH 5323 – Functions of a Real Variable II
- MATH 6351 – Quantitative Methods with Applications to Financial Data
- MATH 6353 – Stochastic Calculus with Applications to Financial Derivatives
- STAT 5328 – Intermediate Mathematical Statistics I
- STAT 5329 – Intermediate Mathematical Statistics II
- STAT 6351 – Applied Time Series
- FIN 5328 – Options and Futures
- At least four of the following:
- MATH 5382 – Advanced Probability I
- MATH 6354 – Numerical PDEs in Finance
- MATH 6355 – Numerical Methods for Financial Data
- MATH 6356 – Software Engineering for Financial Applications
- MATH 6357 – Stochastic Processes in Mathematical Finance
- MATH 5399 – Special Topics in Mathematical Finance
- STAT 5371 – Regression Analysis
- STAT 5380 – Advanced Mathematical Statistics I
- STAT 5386 – Statistical Computation and Simulation
- STAT 6352 – Bayesian Methods for Financial Data
- Additional coursework (24 hours): Selected with approval from the student’s dissertation advisor and the Director of Graduate Studies. These may include courses within the department (excluding STAT 5302–5303 and STAT 5384–5385) or relevant external courses.
- Dissertation: Twelve hours of MATH 8000 – Doctoral Dissertation.
- Foundational coursework (24 hours):
- STAT 5328 & 5329 – Intermediate Mathematical Statistics I and II
- At least two sequences from the following, including one from Group A and one from
Group B:
Group A:
- MATH 5320 & 5321 – Functions of a Complex Variable I & II
- MATH 5322 & 5323 – Functions of a Real Variable I & II
- MATH 5324 & 5325 – Topology I & II
- MATH 5326 & 5327 – Modern Algebra I & II
- MATH 5340 & 5341 – Functional Analysis I & II
Group B:
- MATH 5330 & 5332 – Ordinary Differential Equations I & Partial Differential Equations I
- MATH 5334 & 5335 – Numerical Analysis I & II
- STAT 5373 & 5374 – Design of Experiments & Theory of Linear Statistical Models
- At least two additional courses selected from Group A or Group B.
- Additional coursework (36 hours): Courses selected with approval from the student’s dissertation advisor and the Director of Graduate Studies. These may include departmental or approved Education courses relevant to the student’s research interests.
- Dissertation: Twelve hours of MATH 8000 – Doctoral Dissertation.
The Department of Mathematics and Statistics establishes overall policy guidelines for the specialty areas above.
Preliminary Examinations
The Doctoral Preliminary Examinations are administered twice each year (May and August) and are offered in the subject areas associated with the department’s core graduate course sequences:
- MATH 5326 & 5327 – Algebra
- MATH 5320 & 5321 – Complex Analysis
- MATH 5330 & 5331 – Ordinary Differential Equations
- MATH 5332 & 5333 – Partial Differential Equations
- MATH 5334 & 5335 – Numerical Analysis
- MATH 5322 & 5323 – Real Analysis
- MATH 5324 & 5325 – Topology
- STAT 5328 & 5329 – Probability and Statistics
- STAT 5373 & 5374 – Applied Statistics
- MATH 6351 & 6353 – Financial Mathematics
Each examination is four hours in length and evaluates a student’s understanding of foundational concepts within the chosen area. These examinations are not equivalent to final course exams; rather, they are developed by faculty committees in coordination with the Graduate Committee and are guided by the official Preliminary Examination Topics List available from the Graduate Advisor.
Students must notify the Graduate Advisor at least three weeks prior to an examination date, specifying which exams they intend to take. Up to three exams may be attempted in a single administration, and each exam is graded Pass (P) or Fail (F).
Definitions:
- Category A: Students who hold a master’s degree in Mathematics or Statistics.
- Category B: Students who do not meet the Category A criteria.
- An attempt: Occurs when a student views the contents of an exam while it is being administered.
- Preliminary Examination Requirement: Students must pass three examinations in different subject areas.
At least one passed examination must be in the pure mathematics group (Algebra, Complex Analysis, Real Analysis, or Topology). Students in the statistics concentration must pass the Probability and Statistics preliminary exam.
Important Note: Registering for an examination but not attending does not count as an attempt.
Preliminary Examination Policy:
- Category A students must complete the preliminary examination requirement by the beginning of their third academic year.
- Category B students must complete the requirement by the beginning of their fourth academic year.
- Students may attempt up to 12 preliminary exams in total.
- No more than three attempts are permitted in any one exam area.
- The academic year officially begins with the Fall semester.
Students who do not successfully complete the Preliminary Examination requirement within the timelines and limits described above may not continue in the Ph.D. program in the Department of Mathematics and Statistics.
Qualifying Examination
Each doctoral student must successfully complete a Qualifying Examination that evaluates mastery of advanced material beyond the scope of the Preliminary Examinations. The examination typically follows the structure and expectations outlined in the Texas Tech University Graduate Catalog and is intended to assess the student’s readiness for doctoral-level research.
Any deviation from the standard Qualifying Examination format must be approved in advance by both the student’s Doctoral Advisory Committee and the Graduate Advisor.
Foreign Language Requirement
The requirement of a foreign language for the Ph.D. is determined by the student’s dissertation advisor. This decision is based on the scholarly needs of the student’s research area and may vary by specialization.
Important Information for All Ph.D. Students
- Preliminary Examination Eligibility: Only students who have completed all Preliminary Examination requirements may enroll in MATH 8000. Students should consult the instructor of record during the year the examinations are administered to obtain the current list of approved topics.
- Dissertation Requirement: Every doctoral candidate must produce a dissertation that represents a significant and original contribution to the discipline. The dissertation requirement is independent of other program requirements, and strong performance in coursework or exams does not guarantee dissertation approval.
- Program Requirements and Deadlines: Students are responsible for becoming familiar with all university and departmental policies, procedures, and deadlines related to doctoral study.
- Final Examination: All doctoral candidates must complete a final public oral examination (the dissertation defense) covering their dissertation research.
- Course Sequence Exemptions: A student who passes a Preliminary Examination without having taken the associated course sequence in the department is exempt from that specific sequence requirement. However, unless approved transfer credit has been accepted by both the department and the Graduate School, the student must still complete the required number of foundational sequences and courses for their concentration.
Transfer of Courses
Graduate coursework completed at other accredited institutions may be transferred toward degree requirements with the approval of the Graduate Advisor. Transfer policies vary by credential and degree level:
- Graduate Certificate: Up to one course (3 credit hours) may be transferred, provided an equivalent course exists at Texas Tech University.
- Master’s Degree: Up to two courses (6 credit hours) may be transferred if equivalent TTU courses exist.
- Core courses or sequences from a master’s-degree-granting institution will not transfer.
- Students may be exempted from a core course or sequence by passing the corresponding TTU Ph.D. prelim exam.
- Ph.D. Degree: Up to ten courses (30 credit hours) may be transferred from a doctoral degree–granting
institution.
- A course or sequence may transfer only if the student has passed the related TTU preliminary exam.
- No courses from a master’s-degree-granting institution are eligible for Ph.D. transfer credit.
- Undergraduate Courses: No coursework from an undergraduate program may be transferred toward any graduate degree or certificate.
Next Steps
Ready to move forward or need clarification on eligibility and course selection? Connect with an advisor to discuss admission requirements, course planning, and timelines.
Department of Mathematics & Statistics
-
Address
Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409-1042 -
Phone
806.742.2566 -
Email
math.dept@ttu.edu