General Information

Math Department > Graduate Studies > General Information

Degree Programs

The Department of Mathematical Sciences offers several graduate degree programs, one of which has more than one option. The basic requirements for the various degrees are set forth in the Graduate Catalogue.

Master of Science in Mathematics (General Option)

This option is intended for students who plan to be collegiate teachers of mathematics, continue advanced study in mathematics, or obtain a broad background for preparation as a non-teaching professional mathematician. Three semester hours each of linear and abstract algebra and three semester hours in advanced calculus are prerequisites for this program; however, a student may be admitted with deficiencies, normally not to exceed six semester hours.

The candidate must complete a minimum of 32 semester hours of graduate work. Specific courses are chosen in consultation with the Graduate Advisor and are subject to approval by the Graduate Committee. Students may include up to nine semester hours of graduate work outside the Department. A thesis is optional.

In addition to this semester hour requirement, a candidate for this degree (and all Master's degrees) must pass a comprehensive examination, have a cumulative grade point average of at least 3.0, and meet a thirty-week residence requirement. See the Graduate Catalogue for a more detailed exposition.

The comprehensive examination consists of four two-hour examinations, normally taken near the end of the last semester of residence. The examination subjects and the courses normally taken to prepare for them are listed below:

  1. abstract algebra--MATH 5123 and MATH 5133
  2. topology--MATH 5703 and MATH 5713
  3. analysis--choose one of the following options:
    • real analysis (MATH 5503 and MATH 5513);
    • complex analysis (MATH 5523 and MATH 5533);
    • or a combination (MATH 5503 and MATH 5523)
  4. option--based on an approved six-hour sequence at the graduate level in mathematics or a closely related field (e.g. MATH 4353-4363, MATH 5303-5313, STAT 5103-5113).

Master of Science in Mathematics (Computational Option)

This option is intended for students who plan to specialize in computational and applied mathematics in preparation for advanced study or employment in an inter-disciplinary or computationally intensive environment.

The candidate must complete a minimum of 32 semester hours of approved graduate work. Students must include at least six but not more than twelve semester hours of graduate work in courses outside of mathematics. Statistics courses may be used to fulfill the outside requirement. A thesis is optional. The candidate who does not elect to write a thesis must complete MATH 4153 or an approved substitute.

The comprehensive examination subjects and the courses normally taken to prepare for them are listed below:

  1. numerical analysis--MATH 4353 and MATH 4363
  2. applied mathematics--two of several courses including but not limited to MATH 5303 and MATH 5313
  3. analysis or algebra--see general option for courses
  4. outside area--an approved six-hour sequence of graduate level work in an area outside mathematics (e.g., statistics, computer science, physics, or engineering).

Master of Science in Statistics

This degree program is intended to provide training for either a professional career in statistics or a step toward a doctorate in statistics. The emphasis is in applied and computational statistics. The program is designed to accommodate students with undergraduate degrees either in mathematics or in areas other than mathematics. The prospective student should have completed at least ten semester hours of calculus. Calculus through at least one semester of advanced calculus will be considered a deficiency towards this degree.

The candidate should consult the Graduate Catalogue under "Statistics" for specific course requirements. A suggested outline of course work may be obtained from the Statistics Graduate Student Advisor, Professor Laurie Meaux. The comprehensive examination consists of a total of eight hours of examinations over a wide range of subjects. It is normally scheduled concurrently with the comprehensive examination in mathematics.

Master of Arts in Mathematics with a Secondary Mathematics Major

This degree program is designed for secondary school teachers of mathematics. It requires 30 semester hours of graduate work.

The candidate's program must include MATH 5123 and one of the mathematics courses 5133, 5303, 5313, 5503, 5523, or 5703. As many as twelve semester hours of credit toward this degree may be mathematics courses designed especially for secondary teachers or graduate courses in education. Students not already certified are responsible for determining that all state certification requirements are fulfilled. As with all degree programs, specific course selections are subject to the approval of the Graduate Advisor in consultation with the Graduate Committee.

The comprehensive examination consists of four two-hour examinations. The subject areas and courses normally taken to prepare for them are listed below:

  1. advanced calculus --MATH 4513
  2. algebra--MATH 5123
  3. geometry--MATH 4783
  4. option--three to six hours of graduate level mathematics or statistics, subject to approval by Graduate Committee.

Doctor of Philosophy in Mathematics

This is a research degree which maintains a balance between thesis research and achieving a breadth of knowledge in the mathematical sciences. The basic requirement for this degree is the preparation of a dissertation which demonstrates the candidate's ability to do independent, original, and significant work in the mathematical sciences. To become a candidate for this degree, the student must pass a comprehensive examination in the mathematical sciences. The student should carefully consult the Graduate Catalogue for a discussion of the somewhat numerous requirements pertaining to this degree.

The comprehensive examination consists of three four-hour examinations (except for the general examination for the statistics option which is an eight hour examination) offered each August during the week preceding the beginning of the Fall semester and each January during the week preceding the beginning of Spring semester. This examination must be taken by all students in the graduate program who are one semester beyond the completion of the requirements for an M.S. degree or have filed a Declaration of Intent to pursue the Ph.D. Degree. In some cases, a student may be excused from the examination by the Graduate Committee. The comprehensive examination serves as both a qualifying and a candidacy examination. It has three possible results: fail, pass at the qualifying level, or pass at the candidacy level. A student is allowed at most three attempts to pass the examination at the candidacy level, except that at least a qualifying level pass must be attained on one of the first two attempts. Each of the three examinations has two possible results: pass or fail. If a student receives a pass, then that particular examination need not be retaken on any future attempts to achieve an overall pass.

The Ph.D. degree is offered in two options--mathematics and statistics. They differ in the structure of the comprehensive examinations and, of course, in the thesis area expected of the candidate.

The comprehensive examination for the mathematics option consists of 3 of the following exams:

  • Reals I and Complex I (RC)
  • Reals I and Reals II (R)
  • Complex I and Complex II (C)
  • ODE and PDE (DE)
  • Algebra I and Algebra II (A)
  • Topology I and Topology II (T)

To be selected by the student in such a way that (i) at least one of (A) or (T) is taken, and (ii) (RC) is not taken with either (R) or (C). The Ph.D. examinations are not restricted to the content of the specific courses; however, the courses listed under the M.S. comprehensive examinations are good preparation for these examinations. Syllabi for the examinations, as well as copies of past examinations, are available from the graduate secretary.

The Ph.D. statistics option comprehensive examination consists of three four-hour examinations in the following areas:

  1. probability and statistical inference
  2. general
  3. analysis

The probability examination is based on Stochastic Processes (STAT 5343) and Probability Theory. Students are introduced to the subject of inference in Statistical Inference (STAT 5113), but the inference examination is not limited to specific courses. The inference examination covers the ideas of estimation, hypothesis testing, and decision theory, among others. Either six hours of real variables or three hours of real variables and three hours of complex variables are acceptable for the analysis examination. The general examination covers statistical methods, including knowledge of statistical packages, and applied mathematics, including numerical analysis (MATH 4353 and MATH 4363). This degree option should be pursued in close consultation with the statistics faculty.

Disclaimer

This is an unofficial and informal document designed to address the questions most often asked by graduate students. While we intend for it to be as accurate as possible, we can not guarantee that this document reflects official University policy. The student should refer to the Graduate Catalogue and other publications of the Graduate School and the University for official and authoritative statements regarding the issues addressed here.