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 Examinations  Qualifying Examination  Foreign Language Requirement  Transfer 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 5320MATH 5321, MATH 5322MATH 5323, MATH 5324MATH 5325, MATH 5340MATH 5341.
Group B: MATH 5330 and MATH 5332, MATH 5334MATH 5335, STAT 5328STAT 5329, STAT 5373STAT
5374.
 At last two other courses (not necessarily in a sequence) chosen from Group A and
Group B.
2. Additional coursework: Thirtysix 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 5320MATH 5321, MATH 5322MATH 5323, MATH
5324MATH 5325, MATH 5326MATH 5327.
2. Thirtysix 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
1. All of the following 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
2. Four courses from the following stastical courses
• 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
3. 27 additional hours of statistics courses (excluding STAT 5302 & 5303 and STAT 5384
& 5385), mathematics courses relevant to the student's area of research, or courses
offered outside the department relevant to the student's area of research. These courses
must be approved by the student's dissertation advisor and Director of Graduate Studies.
4. 12 hours of MATH 8000
Mathematical Finance
1. All of the following eight 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
2. At least 4 of the following courses:
MATH 5382  Advanced Probability I
MATH 6354  Numerical Partial Differential Equations in Finance
MATH 6355  Numerical Methods with Applications to Financial Data
MATH 6356  Software Engineering with Financial Applications
MATH 6357  Stochastic Processes and Applications to Mathematical Finance
MATH 5399  Special Topics in Mathematical Finance
STAT 5371  Regression Analysis
STAT 5380  Advanced Statistical Methods I
STAT 5386  Statistical Computation and Simulation
STAT 6352  Bayesian Methods and Application to Financial Data
3. Twentyfour 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 (excluding STAT 53025303 and STAT 53845385)
relevant to the student's area of research or courses offered outside the department
relevant to the student's area of research.
4. Twelve hours of MATH 8000
Mathematics Education
1. Foundational coursework (24 hours):
a) STAT 5328STAT 5329 Intermediate Mathematical Statistics I and II
b) At least two sequences from the following, including at least one sequence from Group A and one sequence from Group B:
Group A
MATH 5320 and MATH 5321 Functions of a Complex Variable I and II
MATH 5320 and MATH 5321 Functions of a Real Variable I and II
MATH 5320 and MATH 5321 Topology I and II
MATH 5320 and MATH 5321 Modern Algebra I and II
MATH 5320 and MATH 5321 Functional Analysis I and II
Group B
MATH 5330 and MATH 5332 Ordinary Differential Equations I and Partial Differential
Equations I
MATH 5334 and MATH 5335 Numerical Analysis I and II
STAT 5373 and MATH 5374 Design of Experiments and Theory of Linear Statistical Models
c) At least 2 other courses (not necessarily in a sequence) chosen from Group A & Group B
2. Additional coursework (36 hours): 36 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. (It is assumed that these courses will include
a significant number of graduate Education courses chosen in consultation with the
student's dissertation advisor.)
3. Twelve hours of MATH 8000
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:
 Algebra (MATH 53265327)
 Complex Analysis (MATH 53205321)
 Ordinary Differential Equations (MATH 5330)/Partial Differential Equations (MATH 5332)
 Numerical Analysis (MATH 53345335)
 Real Analysis (MATH 53225323)
 Topology (MATH 53245325)
 Probability and Statistics (STAT 53285329)
 Applied Statistics (STAT 53735374)
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:
 Category A: Graduate students with a Master's degree in Math or Stat.
 Category B: Graduate students who are not in Category A.
 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.
 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:
 One course (3 credit hours) may transfer towards a grad certificate provided there is an equivalent TTU course.
 Two courses (6 credit hours) may transfer towards a Master's degree, provided there
is an equivalent TTU course.
 A core course/sequence from a Master's degreegranting institution will not transfer.
 Students can be exempted from a core course/sequence by passing the corresponding Ph.D. prelim exam at TTU.
 Up to 10 courses (30 credit hours) from a doctoral degreegranting institution may
transfer towards a Ph. D. degree.
 A course/sequence from a Ph.D. degreegranting institution may transfer if the student has passed the corresponding prelim exam at TTU.
 No courses from a Master's degreegranting institution will be granted transfer credit.
 No course or credit from an undergraduate program will be allowed to transfer toward a graduate degree or certificate.
Department of Mathematics & Statistics

Address
Texas Tech University, 1108 Memorial Circle, Lubbock, TX 794091042 
Phone
806.742.2566 
Email
math.dept@ttu.edu