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- MASTER'S DEGREE IN MATHEMATICS
The Department of Mathematics offers the Master"s Degree in
Mathematics in each of the four options discussed below. The
requirements listed below are in addition to the University and
Graduate School requirements found in the Catalog of the Graduate
School. Each student"s program of study and committee must be
approved by the Director of Graduate Studies in the Department of
Mathematics. The requirements listed here are to be regarded as
minimal and the student should give very careful consideration to
the selection of the particular option which is best suited to his or her
needs. Work completed with a grade less than `B" will not be
accepted on a degree plan for any graduate degree in mathematics or
statistics.
Option: A
This option is a 30 hour plan leading to the degree of Master of Science. 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: 1) Algebra, 2) Applied Mathematics, 3) Complex Analysis, 4) Probability and Statistics, 5) Real Analysis, 6) Topology. In the case of Real Analysis, Math 5318-5319 is not considered to be a core sequence for purposes of Option A; likewise with Math 5310-5311 in the area of Applied Mathematics. A minor of 6 hours in an approved area outside of mathematics is permitted. A thesis defense is required.Option: B
This option is a 36 hour plan leading to the degree of Master of Science. 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 areas listed in part A. A third core area is strongly recommended. A minor of 9 hours in an approved area outside mathematics is permitted. A presentation of the report and a final comprehensive examination is required.Option: C
This option is a 36 hour plan leading to the degree of Master of Science in Mathematics, and is designed for students desiring an emphasis in computer science. The plan calls for 18-21 hours of course work in mathematics, 12-15 hours of course work in computer science, and 3 hours of departmental report (MATH 6310). Of the 18-21 hours of mathematics course work, at least two sequences from the following list must be included:- MATH 5318-5319 (Intermediate Analysis);
- MATH 5320-5321 (Complex Analysis);
- MATH 5322-5323 (Real Analysis);
- MATH 5324-5325 (Topology);
- MATH 5326-5327 (Modern Algebra);
- STAT 5328-5329 (Intermediate Mathematical Statistics);
- MATH 5330-5332 (Ordinary and Partial Differential Equations);
- MATH 5334-5335 (Numerical Analysis).
The 12 to 15 hours of computer science course work constitute adjunct requirements (i.e., special requirements by the Department of Mathematics). These required courses must be taken from the graduate offerings in Computer Science and/or Information Systems and Quantitative Science (ISQS) in the Business College with the approval of the Director of Graduate Studies in the Department of Mathematics. The approved ISQS courses are 5338, 5341, 6337, 6339, 7338, and 7340. CS 5301 is not approved for Program credit; all other 5000-level CS courses may be used, with permission from the Graduate Advisor. A presentation of the report and a final comprehensive examination is required for completion of the program.
It is anticipated that a substantial number of students having mathematics degrees but no background in computer science will wish to enter this program. Such students will be required to take undergraduate leveling courses, as deemed appropriate in their individual cases, for undergraduate credit only; no such leveling work will be credited toward satisfying the above requirements.
Option: D
This option is a 36 hour plan leading to the Master of Arts degree. This option is designed for persons who are teaching (or plan to teach) mathematics at the secondary, community college or junior college level. 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 and statistics. Many of these courses will be selected from the MATH 5360-5361 block of courses. These consist of 6 sequences of two courses each:- Analysis
- Algebra
- Computer Literacy
- Geometry
- Modeling and Applications
- Probability and Statistics
The student must take both courses in at least 2 of these sequences. In addition, courses may be taken in any combination from the remaining sequences. A minor of 9 hours in an approved area outside mathematics is permitted. Normally, work in the student"s second field of certification or work towards the Professional Teacher"s Certificate will be an acceptable minor area. A presentation of the report and final comprehensive examination is required.
With regard to all of the above programs, it is expected that the student"s final oral defense of his or her thesis or report will be open to all who wish to attend, with scheduling to reflect this.
- MASTER'S DEGREE IN STATISTICS
In order to enter the program of study leading to a Master of Science
Degree in Statistics the applicant must meet the requirements of the
Graduate School and of the Department of Mathematics. In addition
the applicant must satisfy the following undergraduate requirements:
a) differential and integral calculus, (Calculus I, II, III),
b) linear algebra,
c) FORTRAN or some other high-level computer language.The requirements b) and c) may be satisfied after admission into the program, but must be satisfied before the second year of study begins.
The degree requirements are:
- Completion of STAT 5328-5329, Intermediate Mathematical
Statistics; STAT 5373, Design of Experiments; STAT 5374, Theory of
Linear Statistical Models; and STAT 5375,
Statistical Multivariate Analysis. In addition, the completion of
any two courses from the following list:
- STAT 5372 Nonparametric Statistical Inference
- STAT 5377 Statistical Sampling Theory
- STAT 5378 Stochastic Processes
- STAT 5379 Advanced Stochastic Processes
- STAT 5386 Statistical Computing and Simulation, I
- A six hours Mathematics to be selected with the approval
of the Director of Graduate Studies and the statistics coordinator.
Those students aspiring for a Ph.D. (statistics emphasis) should
take Math 5318-5319 sequence during their first year of
graduate studies.
- 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 than Statistics, e.g., Mathematics, Animal Science, Biology, Economics, Engineering, Psychology, or Sociology. This option requires approval of the appropriate graduate advisor from the selected area.
b) Three additional hours in Statistics (to be selected from the Mathematics Department offerings).
- Either a six-hour Master"s Thesis or a three-hour Master"s Report with an additional three hour course to be selected from requirement 1 or 3 above. A thesis defense or a final comprehensive examination for the report is required.
NOTE: All statistics courses for the M.S. degree must be taken from the statistics offerings in the Department of Mathematics.
- Completion of STAT 5328-5329, Intermediate Mathematical
Statistics; STAT 5373, Design of Experiments; STAT 5374, Theory of
Linear Statistical Models; and STAT 5375,
Statistical Multivariate Analysis. In addition, the completion of
any two courses from the following list:
- DOCTORAL PROGRAM
The following represents an outline of the Mathematics Department
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 interpretation
of these policies should be directed to the Graduate Advisor.
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 three broad specialty areas:Overall policy guidelines have been established by the Mathematics Department 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 seven 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)
and Partial Differential Equations (MATH 5332)
4. Numerical Analysis (MATH 5334-5335)
5. Real Analysis (MATH 5322-5323)
6. Probability and Statistics (STAT 5328-5329)
7. Topology (MATH 5324-5325)
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. The student must pass a total of three different examinations in four consecutive administrations of the Preliminary Examinations. This includes a requirement that at least one of the examinations must be in either Algebra, Complex Analysis, Real Analysis, or Topology. A grade of P (pass) or F (fail) will be given in each examination.
Any student who in four consecutive administrations of the Preliminary Examinations does not successfully complete the Doctoral Preliminary Examinations may not continue in the Doctoral Program in the Department of Mathematics 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. The Qualifying Examination will, in general, 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.Colloquium
Doctoral candidates are expected to present a departmental colloquium prior to graduation.Foreign Language Requirement
Any foreign language requirement will be at the discretion of the student's dissertation advisor.Area Programs
The following listing of area programs is meant to be an outline of minimal requirements. The individual student is encouraged to supplement these requirements with as much advanced work as possible. The student's dissertation advisor may require additional course work beyond the courses listed in the particular program.As usual any statement concerning required courses must be interpreted to mean "having equivalent knowledge." Also any specific course requirement may be waived at the request of the student's Doctoral Advisory Committee and with the consent of the Graduate Advisor provided the student is unable to schedule that particular course.
Advanced topics seminars will be offered each semester which will contribute to the student's overall mathematical background. It is expected that each student will participate in seminar work in his/her area of specialty as time and interest permit.
Note that Math 5316, Math 5318-5319 will not be counted as hours toward the doctoral degree.
Applied Mathematics
- All of the following three sequences:
- MATH 5322-5323 Functions of a Real Variable I and II
- MATH 5330, MATH 5332 Ordinary Differential Equations I and
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
- 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 5371 Intermediate Probability Theory
- MATH 5382 Advanced Probability I
- STAT 5328-5329 Intermediate Mathematical Statistics I and II
- STAT 5378 Stochastic Processes.
- At least seven additional courses(usually related to the student's
dissertation area). These courses may be listed under MATH 5342-5343 or MATH 53444-5345.
- Twelve hours of MATH 8000.
Pure Mathematics
- 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.
- One additional 6-hour sequence in Mathematics. Functional Analysis
MATH 5340-5341 is recommended. With the approval of the student's
Doctoral Advisory Committee and the Graduate Advisor another
sequence may be acceptable.
- Four additional courses providing breadth in training. These will
normally come from the following courses:
- STAT 5328-5329 Intermediate Mathematical Statistics I and II
- MATH 5330 Ordinary Differential Equations I
- MATH 5332 Partial Differential Equations I
- MATH 5334-5335 Numerical Analysis I and II.
With the approval of the student's Doctoral Advisory Committee and the Graduate Advisor some other courses may be acceptable.
- At least six additional courses to be determined by the student's
Doctoral Advisory Committee and the Graduate Advisor.
- Twelve hours of MATH 8000.
Statistics
- All of the following sixteen courses:
- MATH 5322-5323 Functions of a Real Variable I and II
- MATH 5371 Intermediate Probability Theory
- MATH 5382 Advanced Probability I
- STAT 5328-5239 Intermediate Mathematical Statistics I and II
- STAT 5370 Decision Theory
- STAT 5372 Nonparametric Statistical Inference
- STAT 5373 Design of Experiments
- STAT 5374 Theory of Linear Statistical Models
- STAT 5375 Statistical Multivariate Analysis
- STAT 5376 Advanced Statistical Methods
- STAT 5377 Statistical Sampling Theory
- STAT 5378 Stochastic Processes
- STAT 5379 Time Series Analysis
- STAT 5380 Advanced Mathematical Statistics I.
- At least two of the following sequences:
- MATH 5320-5321 Functions of a Complex Variable I and II
- MATH 5330-5332 Ordinary Differential Equations I and Partial Differential Equations I
- MATH 5334-5335 Numerical Analysis I and II.
- Twelve hours of STAT 8000
Final Examination
A final public oral examination over the student's dissertation topics is required of every candidate for the doctorate.EACH DOCTORAL STUDENT SHOULD BECOME FAMILIAR WITH THE UNIVERSITY AND DEPARTMENTAL REQUIREMENTS FOR THE DOCTORAL DEGREE.
Comments | Updated: 21 Nov 2002 | Webmaster - All of the following three sequences: