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Department of Mathematics
Main Departmental Office
General Academic Building, 418
P.O. Box 5116
Denton, TX 76203-0116
(817) 565-2155
John E. Allen, Chair
Graduate Faculty: Allen, Anghel, Appling, Arvola, Bator, Brand, Brozovic, Castro, DeLatte, Douglass, Hagan, Hill, Iaia, Jackson, Kallman, Kung, Lewis, Maher, Mauldin, Michler, Monticino, Neuberger, Urbanski, Vaughn, Vest, Warchall, Zamboni.
The department offers programs leading to the following degrees:
- · Master of Science,
- · Master of Arts, and
- · Doctor of Philosophy.
Opportunities for supervised research are available in algebra, integration theory, differential equations, numerical analysis, probability and statistics, topology, descriptive set theory, vector measures, operator theory and group representations, combinatorics, Banach spaces, image processing, logic and foundations, chaos and dynamical systems.
Students who graduate with degrees in mathematics are flexible and adaptable in the workplace and readily obtain jobs with high-technology companies and in business, industry, government and education. Salaries and working conditions match those of engineers and computer scientists.
The library collection in the mathematical sciences is one of the nation's finest, with more than 17,000 volumes. Students and faculty have access to the mainframe computers by way of terminals in the department. Each faculty and graduate student office is equipped with a desktop PC and printer.
Research
Faculty and students actively pursue both basic and applied research in mathematics. Current research activity includes applied areas in mathematics of Fourier spectroscopy, engineering optimization, image processing and experimental design. In addition, research interest is in probabilistic analysis of dynamical systems, numerical analysis, partial differential equations and combinatorics. Basic research areas include analysis and functional analysis, algebra, topology, vector measures, Banach spaces, operator theory and group representation.
Research is currently supported by grants from the National Science Foundation, Los Alamos Scientific Laboratories, Oak Ridge National Laboratories, the Air Force Armament Laboratory, the state of Texas, the Naval Surface Warfare Agency and the National Security Agency.
Scholarships and Financial Support
Graduate students usually support their study by working as teaching fellows for the department. Stipends paid for teaching fellows are among the highest in the country.
Work also is available for teaching assistants and math lab tutors, and the department has funds available for research assistants.
Contact the department chair for complete details and for information about financial support.
Admission Requirements
Application for admission to the Toulouse School of Graduate Studies is made through the office of the dean of the School of Graduate Studies. The applicant should have the equivalent of an undergraduate major in mathematics at this institution. Deficiencies in this respect will be evaluated and must be remedied as a condition of final admission. A score of 1100 (verbal plus quantitative) on the GRE is required.
Degree Programs
The Department of Mathematics offers graduate programs leading to the following degrees:
Master of Arts (MA)
The Master of Arts degree in mathematics is designed primarily for those students who plan to pursue the PhD degree and who plan careers in college teaching, business or industry. The program consists of 24 hours of approved course work (numbered 5000 or above) and a thesis carrying 6 hours of credit. The student in this program normally will take five of these six courses: MATH 5310, 5320, 5520, 5530, 5610 and 5620. A minor of 6 semester hours may be elected by the student with consent of the department. The final oral examination is scheduled after completion of the thesis.
Candidates for the MA degree must demonstrate proficiency in a foreign language (normally French, German, Spanish or Russian). See the Admission section of this catalog for further details.
Master of Science
The Master of Science degree with a major in mathematics is designed for those students who wish to develop a high level of competence in mathematical theory and technique in order to apply this knowledge in fields outside mathematics. The program consists of 36 hours of approved course work, including a minor of 9 hours in a field outside mathematics. The student normally will take five of these six courses: MATH 5310, 5320, 5520, 5530, 5610 and 5620.
A thesis is optional. Normally the minor of 9 hours must be in a field in which the student has a background at least equivalent to an undergraduate minor. Recommended minor areas include biology, chemistry, computer sciences and physics.
Candidates must demonstrate a proficiency in computer programming equivalent to that acquired in a 6-hour introductory course. The final examination normally will be scheduled during the final semester of the student's course work.
Doctor of Philosophy
The Doctor of Philosophy degree is awarded for superior accomplishment, the attainment of a high level of scholarship and the demonstrated ability, through independent study and research, to carry out an original investigation and present the results of such investigation.
Course Requirements
Until the student has selected a major professor, a provisional committee will assist in planning the doctoral program. The program will be designed to provide the student with competence in several major areas of mathematics and to provide for intensive study and research in the area of specialization. The student will be expected to complete approximately 90 hours of graduate work in mathematics beyond the bachelor's degree, of which about half should be in courses numbered above 6000. Included in this work, the student will be expected to take (or previously have taken the equivalent of) the following core sequences: MATH 5310-5320, 5410-5420, 5520-5530 and 5610-5620. In addition the student is required to take at least two 6000-level courses in each of the areas of algebra, analysis and topology.
Foreign Language Requirement
PhD candidates must demonstrate proficiency in two foreign languages approved by the department (normally chosen from French, German, Spanish and Russian). See the General Information section of this catalog for additional information.
Qualifying Examinations and Admission to Candidacy
Before enrolling in the dissertation seminar, the student must pass a qualifying examination over two areas chosen from algebra, topology, real analysis and complex analysis. Students are required to begin qualifying examinations as soon as two of the core sequences have been completed. The doctoral advisory committee is appointed upon successful completion of the qualifying examinations. It is the policy of the Department of Mathematics that the major professor has sole discretion to decide if an outside member will be on the dissertation committees of their students.
Dissertation and Final Examination
The candidate must submit a dissertation exhibiting independent research on a topic approved by the doctoral committee. After the completion of the dissertation, a final comprehensive oral examination will be given, which will be primarily a defense of the dissertation.
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