201 Mathematics and Statistics Building

Box 41042, Lubbock, TX 79409-1042

T 806.742.2566 | F 806.742.1112

www.math.ttu.edu

This department supervises the following degree and certificate programs:

- Bachelor of Arts in Mathematics
- Bachelor of Science in Mathematics
- Master of Arts in Mathematics
- Master of Science in Mathematics
- Master of Science in Statistics
- Doctor of Philosophy in Mathematics
- Graduate Certificate in Mathematics

Dual Degree Program

- Bachelor of Science in Mathematics/Bachelor of Science in Computer Science

A Bachelor of Arts or Bachelor of Science in Mathematics with a minor in actuarial science has been offered since 2008. In addition, the department supervises programs leading to minors in mathematics and to teacher certification in mathematics at the middle and secondary school levels.

The academic background of undergraduate students pursuing a degree in mathematics is extremely diverse. Because of this diversity, semester-by-semester schedules for undergraduate degree plans are formulated individually for each student on a case-by-case basis.

Specific listings of General Degree Requirements for each undergraduate program, based
on disciplines and number of corresponding credit hours, can be found on the website

www.math.ttu.edu/Undergraduate/undergrad_program.shtml.

The mathematics curriculum is designed to allow flexibility in choosing elective courses so that students can prepare to enter the industrial job market, graduate or professional school, or a teaching career. Recent Texas Tech mathematics graduates have been employed by companies in aerospace (NASA, defense), electronics (computers, telecommunications), engineering, finance (banks, brokerage, insurance), government (federal agencies, offices, laboratories), petroleum (geophysical, oil), security, entertainment, and education. Some graduates have entered law school or medical school, while many have pursued graduate degrees at various universities.

Highly motivated students are strongly encouraged to pursue an accelerated bachelor's-to-master's program. The department offers honors-level courses in collaboration with the Honors College. The upper-division curriculum includes customized special topics classes and fosters individual undergraduate research projects under supervision of faculty members.

The 120-hour curriculum established for the B.A. degree is designed to provide the foundation for a liberal education through a well-rounded study of the humanities and fine arts; the physical, biological, and social sciences; and mathematics. It also provides the factual basis and insights requisite for specialized study and professional work in these fields.

** Requirements**. Twenty-five semester hours of upper-level math courses are required. These course
requirements may be broadly divided into four components:

- Calculus: MATH 1451, 1452, 2450
- Foundation: MATH 2360, 3310, 3354, 3360, 4350
- Depth (take one of the four): MATH 4343, 4351, 4354, 4360
- Breadth (take minimum of 10 hours not used on above lists): MATH 3342, 3430, 4000, 4310, 4312, 4330, 4331, 4342, 4343, 4351, 4354, 4356, 4360, 4362, 4363

Total MATH hours must be at least 37, with at least half of the upper-division (3000- and 4000-level) courses taken at Texas Tech.

The Bachelor of Arts in Mathematics requires a minimum of 40 semester hours of junior and senior work. Not more than 42 semester hours in one subject may be counted nor more than 8 hours in applied music and/or music ensemble except for students offering music as a major or minor. Not more than 6 hours in personal fitness and wellness courses may be counted as electives nor more than 24 hours in the technical or professional subjects or agriculture, business administration, engineering, and/or human sciences.

** Minor**. A minimum of 9 semester hours above the level of Calculus III is required for a
minor, 6 hours of which must be upper-division coursework. The minor is subject to
the requirements of and must be approved by the department that supervises the minor.

** Elective Courses**. Additional courses sufficient to bring the total to 120 semester hours must be taken.

The 120-hour B.S. degree permits a greater degree of specialization than that afforded by the B.A. degree.

* Requirements*. Twenty-seven semester hours of upper-level math courses are required. The mathematics
requirements are similar to those for the B.A. degree, but two additional advanced
math courses are required. These course requirements may be broadly divided into four
components:

- Calculus: MATH 1451, 1452, 2450
- Foundation: MATH 2360, 3310, 3354, 3360, 4350
- Depth (take two of the four): MATH 4343, 4351, 4354, 4360
- Breadth (take a minimum of 9 hours not used in the above lists): MATH 3342, 3430, 4000, 4310, 4312, 4330, 4331, 4342, 4343, 4351, 4354, 4356, 4360, 4362, 4363

Total MATH hours must be at least 39, with at least half of the upper-division (3000- and 4000-level) courses taken at Texas Tech.

** Minor**. Candidates for the B.S. degree must choose their minor from the following: actuarial
science, atmospheric science, biology, chemistry, chemical engineering, civil engineering,
computer science, economics, electrical engineering, kinesiology, geology, geophysics, industrial engineering, mechanical engineering, microbiology,
petroleum engineering, physics, sport management, or zoology. A minor must include 18 semester hours, 6 of which must be advanced.
In particular, an engineering minor must consist of 18 semester hours in only one
department. Courses counted for the minor must be approved by the department supervising
the minor.

** Electives**. Additional courses must be taken which, together with the required courses, are
sufficient to total 120 semester hours. The inventory of courses that can be used
to fulfill various requirements changes every year as some courses are deleted and
others added. Students should consult the department's Director of Undergraduate Programs
if they have any questions about a particular course and the general degree requirements.
For the minor in actuarial sciences, refer to www.math.ttu.edu/Undergraduate/Minors/actuary.shtml.

Additional Requirements

* Residency Requirement.* For the minor and major in mathematics, at least one half of the upper-level mathematics
courses must be taken in the Department of Mathematics and Statistics at Texas Tech
University. This residency requirement will be waived by the department only in very
exceptional circumstances.

** Teacher Education**. The Department of Mathematics and Statistics cooperates with the College of Education
in offering plans for teacher certification in mathematics at both the middle and
secondary school levels. A student must have a grade of C or better in each mathematics
course counted toward middle- or secondary-education certification.

The courses offered in mathematics for students intending to prepare themselves for middle school teaching are MATH 1320, 2370, 2371, 3370, 3371, 3372, 4370, and 4371.

The student preparing to teach in the secondary school may select mathematics as a
teaching field and complete the program for teacher certification in mathematics.
Students planning to become high school teachers should minor in secondary education.
They will be required to take EDSE 4000 for their student teaching experience. The
university is implementing a new teacher education program that includes a full year
of student teaching (two semesters of the senior year) for students beginning their
teacher education program in spring 2013 or later. Students wishing to obtain teacher
certification should consult with the department's undergraduate advisor and see a
College of Education advisor to complete a certification plan.

The minimum requirements for the teaching field in mathematics at the secondary level
are as follows:

- MATH 1451, 1452, 2450, 2360, 3310, and 4331
- One of MATH 2300, 3342, or 4342
- One of MATH 3430, 4330, or 4371

** Mathematics Placement**. Placement for students into entry-level mathematics courses (0301–2345) is based
on either appropriate previous prerequisite collegiate mathematics credit or the results
of the departmentally administered Mathematics Placement Examination (MPE). Students
matriculating to the university in a fall semester are typically expected to take
the online MPE prior to attending their summer new student orientation. Students matriculating
to the university in a spring semester or a summer term are expected to take the placement
examination during the open registration periods prior to the start of the semester
or term. Students without appropriate prerequisite collegiate mathematics credit will
be placed into entry-level courses based on the results of the MPE. Students may retake
the MPE if necessary. Students who have scored at least 610 (660 for 1451) on the
SATM or at least 26 (29 for 1451) on the ACTM may enroll in any entry-level mathematics
course independent of whether they have the appropriate previous prerequisite collegiate
mathematics credit or the appropriate MPE score. However, students are encouraged
to take the MPE during an orientation session to provide them with a current assessment
of their mathematics skills for advisement purposes.

**NOTE**: A satisfactory score on the placement exam or satisfactory completion of TSI requirements
is required for entrance to all above courses. Texas Success Initiative (TSI) students
who have not passed the mathematics section of the TSI test may not enroll in MATH
1320 or 1321 until they have successfully completed their prescribed program of TSI
mathematics skills development. See course listings for descriptions and prerequisites
for the courses listed above.

Undergraduate mathematics majors may apply for admission to the master's degree program during their junior year so they can begin taking graduate courses during their senior year. The 150-hour accelerated bachelor's-to-master's degree program can result in a B.A./M.A., B.A./M.S., or B.S./M.S. depending on the needs of the student. The combined bachelor's and master's degrees in mathematics differ only in the final two years; the first three years are the same as the standard B.A. or B.S. in Mathematics program. See either the graduate or undergraduate advisor for details.

Semester-by-semester degree plans for accelerated degrees can be found on the department's website.

The Department of Mathematics and Statistics participates with the Department of Computer
Science to offer a 162-hour dual degree program in mathematics and computer science.
This is a five-year program that culminates in a B.S. in Mathematics with a minor
in computer science from the College of Arts and Sciences and a B.S. in Computer Science
from the College of Engineering. Students should consult with an academic advisor
in each college and may declare either as their primary college. See the Department of Computer Science catalog section for curriculum information.

Students seeking an advanced degree in mathematics or statistics should consult with the Graduate Director of the department before enrolling in any courses. The department offers a number of graduate courses that are suitable for students who wish to complete a minor in mathematics or statistics.

Master's Programs

The requirements listed below are in addition to the University and Graduate School requirements found in the Catalog of the Graduate School. A student must fill out a degree plan after the end of the first long semester and before the start of their second long semester in the program. Each student's program of study and committee must be approved by the Director of Graduate Studies in the Department of Mathematics and Statistics. With regard to all of the programs below, it is expected that the student's final oral defense of his/her thesis or report will be open to all who wish to attend, with scheduling to reflect this.

* M.A. Degree in Mathematics (Thesis Option). * This degree is offered primarily for those students who wish to teach mathematics
at the secondary level or at a junior/community college. This is an online program
consisting of 30 hours of graduate work, including 6 hours of credit for the master's
thesis.

This plan calls for 24 hours of course work and at least 6 hours of the thesis course (MATH 6000). Of the 24 hours of course work, 18 must be in mathematics. Of the 6 sequences listed below, the student must complete at least two or the equivalent:

- Analysis (MATH 5366/5367)
- Algebra (MATH 5368/5369)
- Topology (MATH 5371/5372)
- Geometry (MATH 5375/5376)
- Applied Mathematics (MATH 5377/5378)
- Computer Literacy and Programing (MATH 5364/5365)

This degree is offered primarily for those students who wish to teach mathematics
at the secondary level or at a junior/community college. This is an online program
consisting of 36 hours of graduate work that includes 3 hours of credit for a departmental
report.

M.A. Degree in Mathematics (Non-Thesis Option).

This plan calls for 33 hours of course work and 3 hours of work on a departmental report (MATH 6310). Of the 33 hours of course work at least 24 hours must be in mathematics. Of the 6 sequences listed below, the student must complete at least three or the equivalent:

- Analysis (MATH 5366/5367)
- Algebra (MATH 5368/5369)
- Topology (MATH 5371/5372)
- Geometry (MATH 5375/5376)
- Applied Mathematics (MATH 5377/5378)
- Computer Literacy and Programing (MATH 5364/5365)

This program consists of 30 hours of graduate work, including 6 hours of credit for
the master's thesis.

M.S. Degree in Mathematics (Thesis Option).

This plan calls for 24 hours of course work and at least 6 hours of the thesis course (MATH 6000). Of the 24 hours of course work, 18 must be in mathematics and must include one sequence in a core area. The core areas are:

- Algebra
- Ordinary Differential Equations / Partial Differential Equations
- Complex Analysis
- Probability and Statistics
- Real Analysis
- Topology
- Numerical Analysis
- Applied Statistics

In the area of Real Analysis, 5318-5319 is not considered to be a core sequence; likewise in the area of Applied Mathematics, 5310-5311 is not considered to be a core sequence.

This program consists of 36 hours of graduate work that includes 3 hours of credit
for a departmental report.

M.S. Degree in Mathematics (Non-Thesis Option).

This program calls for 33 hours of course work and 3 hours of work on a departmental report (MATH 6310). Of the 33 hours of course work, 24 must be in mathematics and must include two sequences from the core areaa. The core areas are:

- Algebra
- Ordinary Differential Equations / Partial Differential Equations
- Complex Analysis
- Probability and Statistics
- Real Analysis
- Topology
- Numerical Analysis
- Applied Statistics

In the area of Real Analysis, 5318-5319 is not considered to be a core sequence; likewise in the area of Applied Mathematics, 5310-5311 is not considered to be a core sequence.

This program consists of 36 hours of graduate work that includes 6 hours of credit
for the master's thesis.

M.S. Degree in Statistics (Thesis Option).

- 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

Additionally, two of the following courses must be included:

STAT 5372 Nonparametric Statistical Inference

STAT 5375 Statistical Multivariate Analysis

STAT 5377 Statistical Sampling Theory

STAT 5378 Stochastic Processes

STAT 5379 Time Series Analysis

STAT 5386 Statistical Computing and Simulation - Six hours of mathematics to be selected with the approval of the Director of Graduate Studies and the Statistics Coordinator.
- One of the following two options (to be selected with the approval of the Director
of Graduate Studies)

a. Three hours in an area other Statistics, e.g. Mathematics, Animal Science, Computer Science, Biology, Economics, Engineering, Psychology, or Sociology. This option requires approval of the Graduate Advisor from the selected area.

b. Three additional hours in Statistics (to be selected from the Department of Mathematics and Statistics offerings). - Students who have the potential to be accepted in the PhD program and who have the agreement of an advisor may choose the thesis option.
- All Statistics courses for the M.S. Degree in Statistics must be taken from the Statistics offerings in the Department of Mathematics and Statistics.

This program consists of 36 hours of graduate work that includes 3 hours of credit
for a departmental report.

M.S. Degree in Statistics (Non-Thesis Option).

- 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

Additionally, two of the following courses must be included:

STAT 5372 Nonparametric Statistical Inference

STAT 5375 Statistical Multivariate Analysis

STAT 5377 Statistical Sampling Theory

STAT 5378 Stochastic Processes

STAT 5379 Time Series Analysis

STAT 5386 Statistical Computing and Simulation - Six hours of mathematics to be selected with the approval of the Director of Graduate Studies and the Statistics Coordinator.
- One of the following two options (to be selected with the approval of the Director
of Graduate Studies)

a. Three hours in an area other Statistics, e.g. Mathematics, Animal Science, Computer Science, Biology, Economics, Engineering, Psychology, or Sociology. This option requires approval of the Graduate Advisor from the selected area.

b. Three additional hours in Statistics (to be selected from the Department of Mathematics and Statistics offerings). - Three additional hours to be selected from requirements 1. or 3. above.
- All Statistics courses for the M.S. Degree in Statistics must be taken from the Statistics offerings in the Department of Mathematics and Statistics.

The doctoral program offers concentrations in four areas of study: applied mathematics, pure mathematics, statistics, and mathematics education. The program consists of 60 hours of graduate coursework and 12 hours of doctoral dissertation. The program requirements listed below (under Guidelines for Areas of Concentration) are in addition to the University and Graduate School requirements found in the Catalog of the Graduate School. Specific questions concerning 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 his/her second long semester and before the start of his/her third long semester in the program.

Each doctoral student will complete the preliminary examination requirements as early
as possible during graduate training. The examinations are administered annually in
May and August. *See Details for Preliminary Examinations below*. In addition, each doctoral student must pass a qualifying examination in a specialty
area and complete the doctoral dissertation. *See Details for Qualifying Examinations below*.

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 5326-5327)
- Complex Analysis (MATH 5320-5321)
- Ordinary Differential Equations (MATH 5330) and Partial Differential Equations (MATH 5332)
- Numerical Analysis (MATH 5334-5335)
- Real Analysis (MATH 5322-5323)
- Topology (MATH 5324-5325)
- Probability and Statistics (STAT 5328-5329)
- 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**

I. Category A: Graduate students with a Master’s degree in Math or Stat.

II. Category B: Graduate students who are not in Category A.

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

**Prelim requirements:** Students have to pass three 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.

**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 subject 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.

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 Program Director.

- All of the following three sequences:

MATH 5322-5323 Functions of a Real Variable I and II

MATH 5330 Ordinary Differential Equations I and MATH 5332 Partial Differential Equations I

MATH 5334-5335 Numerical Analysis I and II - At least one of the following sequences:

MATH 5320-5321 Functions of a Complex Variable I and II

STAT 5328-5329 Intermediate Mathematical Statistics I and II - At least six courses, different from the courses used in part 2, chosen from:

MATH 5312-5313 Control Theory I and II

MATH 5320-5321 Functions of a Complex Variable I and II

MATH 5324-5325 Topology I and II

MATH 5326-5327 Modern Algebra I and II

MATH 5331 Ordinary Differential Equations II

MATH 5333 Partial Differential Equations II

MATH 5340-5341 Functional Analysis I and II

MATH 5354-5355 Biomathematics I and II

MATH 5382-5383 Advanced Probability I and II

STAT 5328-5329 Intermediate Mathematical Statistics I and II

STAT 5378 Stochastic Processes

STAT 5379 Time Series Analysis - At least six additional courses which are usually related to the student's dissertation area. These courses may be listed under MATH 5342-5343 or MATH 5344-5345.
- Twelve hours of MATH 8000

- All of the following four sequences:

MATH 5320-5321 Functions of a Complex Variable I and II

MATH 5322-5323 Functions of a Real Variable I and II

MATH 5324-5325 Topology I and II

MATH 5326-5327 Modern Algebra I and II - 36 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.
- Twelve hours of MATH 8000

- All of the following 13 courses:

MATH 5322-5323 Functions of a Real variable I and II

MATH 5382-5383 Advanced Probability I and II

STAT 5328-5329 Intermediate Mathematical Statistics I and II

STAT 5370 Decision Theory

STAT 5371 Regression Analysis

STAT 5372 Nonparametric Statistical Inference

STAT 5373 Design of Experiments

STAT 5374 Theory of Linear Statistical Models

STAT 5375 Statistical Multivariate Analysis

STAT 5379 Time series analysis - 21 additional hours 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 5302-5303 and STAT 5384-5385). 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.
- At least 12 hours of MATH 8000.

- All of the following sequences:

STAT 5328-5239 Intermediate Mathematical Statistics I and II

EPSY 5379-5385 Introduction to Educational Research and Foundations of Educational Research

EPSY 5356-6303 Educational Measurement

EPSY 6304-6305 Qualitative Research Methods - At least three of the following sequences:

MATH 5320-5321 Functions of a Complex Variable I and II

MATH 5322-5323 Functions of a Real Variable I and II

MATH 5324-5325 Topology I and II

MATH 5326-5327 Modern Algebra I and II

MATH 5330-5332 Ordinary Differential Equations I and Partial Differential Equations I

MATH 5334-5335 Numerical Analysis I and II - 18 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.
- Twelve hours of MATH 8000.

- The guidelines for areas of concentration are meant to be an outlines of minimal requirements. The individual student is encouraged to supplement specified requirements with as much advanced work as possible. Specific course requirement may be waived at the request of the student's dissertation advisor with the consent of the Graduate Advisor.
- Course Notes: Courses Math 531x except Math 5312 and Math 5313, all Math536x courses except Math 5362, and all Math 537x will not count toward a doctoral degree. The student should check with the Graduate Advisor to see whether or not a specific course will count toward their degree.

**Foreign Language:**Any foreign language requirement will be at the discretion of the student's dissertation advisor**Seminars:**Advanced topics seminars which contribute to the student's overall mathematical background will be offered each semester. It is expected that each student will participate in seminar work in his/her area of specialty.**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.
**Dissertation Defense:**A final public oral examination over the student's dissertation topics is required of every candidate for the doctorate.- A student who passes a prelim exam before enrolling in the corresponding course/sequence is exempted from taking/completing the sequence. This does not however mean that the student will get credit on a transcript for that core sequence. The rules 2b and 3a for transfer credit would apply.

The Graduate Certificate in Mathematics is an online 18-hourcertificate designed for anyone with a bachelor's degree (that included coursework in linear algebra) who wants to increase mastery of mathematics, particularly in-service teachers who desire to teach dual credit in high school or teach at a junior college. Students may choose six courses from among MATH 5364 through 5378.

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. A core course/sequence from a Master's degree granting institution will not transfer.

b. 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 degree granting institution may
transfer towards a Ph.D. degree.

a. A core course/sequence from a Ph.D. degree granting institution may transfer if the student has passed the corresponding prelim exam at TTU.

b. No courses from a Master's degree granting 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.

* Horn Professor*: L. Allen, J. Conover