Capsule Description of the Department

The faculty of the Mathematics Department comprises 52 regular, full-time members and a varying number of emeritus, temporary or part-time members. Several individuals have joint appointments with other departments, such as Computer Sciences, Curriculum and Instruction, and General Business.

Approximately 160 graduate students are currently enrolled in degree programs in the Department. For the most part, recent recipients of Ph.D.s from the Department have found employment teaching in colleges and universities. Holders of Texas Master's Degrees in Mathematics represent a wide variety of professions, working as teachers at the primary, secondary or junior college level, statisticians, actuaries, and computer programmers, to name a few. Others have continued their educations at Texas or elsewhere in pursuit of doctorates.

In 1984 the University launched a major program to spur development in a few designated thrust areas of science and engineering, one of which was Mathematics. To serve as centerpiece for this effort, the administration created thirty-two handsomely endowed chair positions. The Department of Mathematics was awarded four of the chairs. Currently there are 6 chairs affiliated with the Department of Mathematics. These positions are currently filled by individuals of universally recognized distinction: Luis Caffarelli, Bjorn Engquist, Cameron Gordon, Panagiotis Souganidis, John Tate and Karen Uhlenbeck. The program of chairs has stimulated faculty recruitment at all levels.

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Computer Facilities

The Department of Mathematics maintains a state-of-the-art computer network to facilitate, research, and departmental administration. This is predominantly a UNIX-based system consisting of Linux PC's and servers, with a few Windows XP workstations and a number of Apple Macintosh systems. Every graduate student office contains at least one Linux PC. Within the department, there are five computer labs available for general use, including one 40-seat instructional laboratory for its undergraduate mathematics program. The department also operates a 46 node cluster for research computing. The department's web page (http://www.ma.utexas.edu) offers easy access and links to mathematics information, locally developed mathematical software, and our internationally recognized Mathematical Physics Electronic Journal (MPEJ) and preprint archive (mp_arc). The most important element of the departmental computer operation is the ready availability of innovative mathematical and instructional software and free computer resources that create an environment conducive to experimentation and exploration by faculty and students alike.

The Texas Advanced Computing Center (TACC) is a research center at the University of Texas at Austin (UT Austin) reporting to the Office of the Vice President for Research. TACC provides advanced computing resources & services to enable computationally-intensive research and conducts research & development to enhance the capabilities of these resources. TACC offers a number of high performance computing facilities including a world leading 500-teraflops system.

The Computational Visualization Center is available nearby for visualization of scientific and computational data, as well as virtual reality simulations.

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Colloquia, Lecture Series, Seminars

The Department has a regular weekly colloquium. It also hosts two Distinguished Lecturer Series, which yearly feature some of the world's outstanding mathematicians. As a rule, these individuals remain in residence in the Department for a week or longer, during which time they are available for interaction with local faculty and students. Speakers during the past year included Nate Brown (dynamical systems), Russel Caflisch (computational and applied mathematics), Demetri Christodoulou (partial differential equations), Peter Constantin (applied mathematics), Giovanni Gallavotti (mathematical physics), Fan Chung Graham (graph theory), David Harbater (algebra), Philip Holmes (applied mathematics), Carlos Kenig (analysis), Sergiu Klainerman (analysis), Serge Lang (algebra), Pierre-Louis Lions (applied mathematics), Peter Markowich (dynamical systems), Yasumasa Nishiura (computational and applied mathematics), Karl Rubin (number theory), Michael Thaddeus (mathematical physics) and a host of others. An Introduction to Research lecture series, to which speakers are invited because of their national reputations as fine expositors of mathematics, is aimed at and extremely popular among graduate students.

Various groups within the Department sponsor regular seminars for faculty and graduate students. Some of these are designed for students with a modest background in the field under study; others target students at a more advanced level. Naturally, the participants and the topics for the seminars change from year to year. In recent years there have been seminars in mathematical physics, topology, Banach spaces, harmonic analysis, complex analysis, partial differential equations, applied and computational mathematics, number theory, dynamical systems, differential geometry, gauge theory, numerical analysis, statistics, algebra, and algebraic geometry. It is expected that most of these will continue during the coming year.

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Pure and Applied Mathematics

The Department's internationally recognized and respected research groups in low-dimensional topology, differential geometry, Banach space theory, harmonic analysis, ring theory, number theory and dynamical systems bear witness to the fact that the traditional strength of Texas in the pure Mathematics persists. Many active seminars are available to students with interests in these core areas.

Recently, the Department of Mathematics has experienced a rapid growth in applied and computational mathematics. Now there is a international renowned group of faculty in partial differential equations, mathematics physics, numerical analysis, scientific computing, probability, and math finance. Many of our faculty members are also affiliated with the Institute for Computational Engineering and Sciences (ICES), which houses several active research centers.

The Department has research groups that are ranked in the top ten in the country both in pure an applied mathematics.

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Statistics

Statistics is the science and art of planning and modelling stochastic observations and making inferences from them. The theories and methods for doing this use a wide range of mathematics, including probability, analysis, numerical analysis, and computing. Much of the mathematics is applied through the medium of statistics to the physical and social sciences, medicine, business, engineering, and many other areas. Statistics is a relatively new field; however, because it has become so important, the National Science Foundation has reported that in the future statistics, along with computer sciences, will be one of the scientific fields with the highest employment demand.

The mathematics department regularly offers graduate courses in statistics and administers an interdisciplinary Master's in Statistics program.

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Graduate Programs

Ph.D. Program in Mathematics

Requirements for Ph.D. Degree in Mathematics
(Amended in Spring 2004; effective Fall 2004)

The steps in obtaining a Ph.D. degree in Mathematics are as follows:

1. passage of two preliminary examinations and demonstration of command of a third area of mathematics through a satisfactory performance in the prelim course sequence for that area;
2. selection of an area of specialization and appointment of an advisory committee;
3. passage of an oral candidacy exam in the area of specialization;
4. fulfillment of the foreign language requirement;
5. certification by the advisory committee of the candidate's knowledge of the chosen area and of the adequacy of the proposed program of coursework;
6. completion of any remaining Graduate School requirements and formal admission to Ph.D. candidacy;
7. completion of a dissertation;
8. passage of a final oral exam on the dissertation research.

A detailed description of each step follows.

1.  Preliminary Examinations

Preliminary examinations are offered in four areas: Algebra, Analysis, Applied Mathematics, Topology. A Ph.D. student must establish his or her competence in three of these areas either (1) by passing three of the associated prelim exams or (2) by passing two of the prelim exams and completing the prelim course sequence in a third area with a grade of at least B each semester or (3) by passing the prelim exam in one area, completing the prelim option discussed below in a second area, and completing the prelim course sequence in a third area with a grade of at least B each semester. Each preliminary exam is based upon the topics in a corresponding syllabus. It is intended that these topics be accessible to a student who has completed a designated two-semester core sequence of courses treating the examination area, although it is not necessarily the case that every one of these topics will actually be covered in the core courses.

Week-long preliminary examination periods occur twice yearly, typically just before the beginning of each fall and spring semester. Each preliminary exam is a written exam of at least three hours' duration. A student may attempt an exam in a particular area at most three times.

A student may select one area in which to bypass a written preliminary examination by exercising the prelim option. In order to be eligible for the prelim option the student must first complete the corresponding course sequence with a grade of "A" each semester. The student can then substitute for passage of the preliminary examination in the designated area a specific program of work that is proposed by the student, approved by the Graduate Advisor, and supervised by a member of the Graduate Studies Committee (GSC). This program of work consists of two post-prelim courses in the chosen area, at least one of which must be an organized course (i.e., not a reading course), along with the presentation of a fifty-minute lecture on some reasonably advanced topic in the area. The lecture is to be announced in the department calendar, and attendance is to be open to all mathematics faculty and graduate students. (The logical forum for such a lecture would be a regular department seminar in the specified area.) In order for a student to exercise this option, all of its provisions must be fulfilled by the end of the spring semester of the student's second year in the Ph.D. program. If a student has completed all other preliminary examination requirements by January of the second year and uses the prelim option in his or her dissertation area, the required lecture can, at the discretion of the student's Ph.D. supervisor, serve as part of the student's candidacy exam.

A student who wants to do interdisciplinary research (e.g., in mathematical biology) may replace the third area requirement with an examination (but not merely with a sequence of courses) that covers material primarily from the outside discipline (e.g., from biology). A syllabus for such an exam must be developed by the student in consultation with appropriate faculty members and submitted to the ASGSC (Administrative Subcommittee of the GSC) for approval. If the syllabus receives approval from the ASGSC, then the Chair of the GSC appoints a committee of three people to administer the exam. The exam may be either written or oral, whichever the examining committee deems appropriate.

A student who has taken graduate level courses or passed preliminary examinations at another university may petition the ASGSC for prelim relief in the relevant area(s). Such a request must include a syllabus for each such course (respectively, exam) and, in the case of an examination, verification by an appropriate authority from the outside institution that the student has passed it. A student who is admitted to the Ph.D. program immediately after completing a Master's degree in mathematics at this university will be awarded credit for passing the prelim in the subject area of the Master's thesis or report, provided that the program of coursework for the Master's degree includes the prelim sequence of courses in that area. This will be regarded as the equivalent of the prelim option discussed in a previous paragraph - hence, will exhaust that option.

In order to continue in the Ph.D. program, a student must have credit for passing at least one prelim exam by January of the second year and must complete all preliminary examination requirements by September of the third year. Failing to accomplish the former, a student will be barred from registering in the Ph.D. program for a third year; a student who manages the former but not the latter will be allowed to register for the third year and will be given a TA position (if a TA position is available, and the student is both eligible and qualified for it), but the third year will be the terminal year for the student in the Ph.D. program. An exception to this rule occurs in the case of a student who enters the Ph.D. program upon completion of a Master's degree in this department: such a student must complete all preliminary examination requirements by January of the second year in the Ph.D. program. Failure to accomplish this will result in the student's dismissal from the mathematics graduate program at the end of his or her second year in the Ph.D. program.

• Exam Syllabi
• A Sampling of Previous Exams

2.  Advisory Committee

After satisfying preliminary examination requirements, a student selects an area of specialization and obtains the agreement of a member of the GSC to supervise his or her doctoral dissertation. In consultation with the student and the prospective Ph.D. supervisor, the Graduate Advisor appoints a three-person committee, chaired by the proposed supervisor, that helps the student determine what additional coursework is necessary in order (a) to prepare for research in the chosen area, (b) to ensure a program of work that is sufficiently broad and deep, and (c) to meet formal Graduate School requirements. This committee also has the responsibility of administering the oral candidacy exam.

3.  Candidacy Exam

Within one year after a student has completed the preliminary examination process or by the end of the student's fifth long semester in residence, whichever is later, the advisory committee must administer to the student an oral examination in his or her chosen area of specialization. The style, coverage, and time of the exam is set by the advisory committee in consultation with the student. If the advisory committee deems that the student has failed the candidacy oral, it may recommend that the student be granted a second opportunity to pass the exam. Otherwise, the student will not be allowed to continue in the Ph.D. program. If the student fails a second candidacy exam, the student will be required to leave the Ph.D. program.

4. Foreign Language Requirement

A student must demonstrate a reading knowledge of French, German, or Russian at a level that would allow the student to translate for its essential technical content a mathematical text in the language. The requirement can be satisfied either by passing the 301 class in the language (e.g., French 301, French for Graduate Students in Other Departments ) or by passing a reading examination in the language administered by a designated member of the department faculty. This requirement is waived for any student who can document at least two years of formal training in the chosen language at the undergraduate level and for native speakers of the language.

5.  Certification

After a student has passed the candidacy exam and satisfied the foreign language requirement, the student's advisory committee decides whether his or her proposed research area of specialization, subject preparation, and program of coursework are satisfactory for admission to Ph.D. candidacy. If so, the advisory committee officially certifies to the GSC that the student is ready to apply for doctoral candidacy; if not, the advisory committee determines in consultation with the student how any remaining deficiencies should be addressed.

6.  Formal Admission to Ph.D. Candidacy

Upon receipt of the required certification from the advisory committee, the Chair of the GSC appoints a five-person Doctoral Committee -- this committee is proposed by the student, is chaired by his or her doctoral supervisor, and is subject to certain Graduate School requirements concerning its composition -- and makes a formal recommendation to the Office of Graduate Studies that the student be admitted to Ph.D. candidacy. A Ph.D. student must fulfill all requirements for admission to Ph.D. candidacy by the beginning of his or her fourth year in the doctoral program.

7.  Dissertation

The dissertation is the most important part of the Ph.D. program. It involves original research in mathematics by the student. The research topics covered in the dissertation are selected by the student in consultation with his or her supervising professor. A student is expected to complete the dissertation within three years of admission to Ph.D. candidacy. Information about the required format for the dissertation, which must be submitted electronically, can be obtained from the Office of Graduate Studies.

8.  Final Oral Examination

After a student has completed the dissertation and his or her supervisor is satisified with the work that it contains, a student is required to defend the dissertation in a final oral examination. This examination must be scheduled through the Office of Graduate Studies at least two weeks in advance of the exam date; the Doctoral Committee, which administers the final oral, must have a draft of the dissertation at least four weeks before the exam date. If the members of the Doctoral Committee are in unanimous agreement that the student has passed this exam (i.e., that the dissertation is acceptable), then subject to the submission of the dissertation and certain supporting paperwork to the Office of Graduate Studies, the student becomes eligible to receive the Ph.D. degree.

Remark:  An appeal for a waiver of or an exception to any of the foregoing regulations must be submitted, in writing and accompanied by documentation of the extenuating circumstances that underlie the appeal, to the Chair of the GSC. The ASGSC will be the final arbiter in all such matters.
 

M. A. Program in Mathematics The M. A. in Mathematics requires that the candidate complete a minimum of thirty semester credit hours of courses, including a thesis or a report. Of the thirty required hours, six to twelve must be taken in a minor area outside of mathematics. Students electing to write a thesis must complete at least twenty-four hours of course work and six hours of thesis work. Those electing to write a report in lieu of a thesis must complete a minimum of thirty hours of course work in addition to the report course. The Department course offerings enable an M. A. student to specialize in such areas as actuarial studies, algebra, analysis, general applied mathematics, numerical analysis, and topology, among others.

M. A. Program in Mathematics (Actuarial Focus)

In the spring of 1999, the Mathematics Department approved a special focus on Actuarial Studies within the general requirements of the standard M.A. in Mathematics. Students successful in this program receive an M.A. in Mathematics while taking classes that are actuarial or actuarially related. More information is available in the Actuarial Studies Website.

M. S. Program in Statistics

The M. S. program in Statistics requires a minimum of thirty-three semester hours and includes a report. An identifiable minor of six or nine hours is required. Some of the statistics courses that are included in the program are taught by faculty members in other departments and are crosslisted. Students are required to take a yearlong core sequence in Mathematical Statistics, M384C,D and courses in Regression Analysis, M384G and Analysis of Variance, M384E. 
Masters in Statistics Web Page

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Course Offerings

Each year the Department offers from 25 to 30 graduate courses covering a wide range of topics. In addition, there is a regular schedule of seminars. Two-semester course sequences aimed specifically at first-year graduate students are taught each year in algebra, analysis, methods of applied mathematics, numerical analysis and computation, statistics, and topology. Other standard offerings include courses in differential geometry, number theory, functional analysis, harmonic analysis, approximation theory, ordinary and partial differential equations, numerical solution of differential equations, multivariate statistical analysis, experimental design, algebraic topology, and geometric topology. Courses dealing with special topics are scheduled in response to faculty interest or student demand.

  Recent courses offered:

Algebraic number theory Algebraic geometry Applied statistics Approximation theory Banach spaces Calculus of variations Commutative ring theory Computational Modeling Dynamical systems Ergodic theory Group representations Group theory Harmonic Analysis Hilbert space methods in P.D.E. Iterative Methods for Linear Algebra Knot theory Lie groups and algebras Low dimensional topology

Nonlinear elliptic P.D.E. Markov processes Mathematical Modeling Mathematical physics Minimal surfaces Multiscale Problems Numerical Treatment of Differential Equations Numerical Analysis for PDEs Numerical Methods for Conservation Laws Quantum mechanics Quasiconformal mappings Statistical mechanics Stochastic processes Riemann surfaces Rings and modules Theory of algebraic groups Topological quantum field theory Wavelets

Note:  Individual conference courses are also encouraged. 
Other departments on campus offer courses with various mathematical contents such as operations research, optimization theory, optimal control theory, engineering mechanics, statistics, et cetera.

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Financial Support

It is the intent of Mathematics Department to provide six years (twelve semesters) of financial support to all Ph.D. students who are making satisfactory progress towards their degrees. Barring financial crises, we fully expect to be able to furnish such support. We may be able to provide financial aid to some Master students if sufficient funds are available.

Financial support takes three forms: (1) Teaching Assistantships and Assistant Instructorships; (2) Graduate Research Assistantships; (3) Fellowships. (Note: International students must speak fluent English and pass an oral English assessment exam administered by the University before they can be supported as Teaching Assistants or Assistant Instructors.)

Teaching Assistantships and Assistant Instructorships

The most common form of financial aid is a Teaching Assistantship (or for more advanced students, an Assistant Instructorship). Typically, a beginning Teaching Assistant assists in one calculus course. The Professor lectures three days a week; on the other two days the TA meets three discussion sections consisting of approximately 40 students each. The TA also has some responsibility for holding office hours. Assistant Instructors ordinarily teach one or two sections of pre-calculus level mathematics, in which they are the instructors of record.

Graduate Research Assistantships

When a student advances to candidacy in the Ph.D. program and begins doing individual work with a supervising Professor, there is a possibility that the student might receive a Graduate Research Assistantship (GRA) from that supervisor. Faculty members who apply for grants often request that the funding include extra money to support graduate students. If the faculty member obtains the grant, then he or she may use that extra money to give some student a GRA. This allows the student to pursue research without having to do any teaching. Selection of students for GRAs is left to the individual grant holders. In recent years, the department has had about ten GRA recipients per year.

Fellowships

The Mathematics Department has some money available that can be used to award fellowships to deserving students. These include the Edward Louis and Alice Laidman Dodd Fellowship, the Arthur LeFevre, Sr., Scholarship in Mathematics, the Regents Endowed Graduate Fellowships in Mathematics, the David Bruton, Jr. Graduate Fellowships in Mathematics, the Professor and Mrs. Hubert S. Wall Endowed Presidential Fellowship, the Charles Rubert Scholarship, and the John L. and Anne Crawford Endowed Presidential Scholarship. The fellowships and scholarships can be used either to augment TA salaries or to support students fully, allowing them to pursue research free from teaching duties. Each year, the Administrative Subcommittee of Graduate Studies Committee (ASGSC) selects worthy students to receive departmental fellowships. In recent years, from two to four students have been awarded full fellowships by the Department of Mathematics.

The University also has a number of fellowships, which are awarded on a competitive basis. The Graduate Advisor selects students to be nominated for these fellowships on the basis of their academic performance. Annually, between two and four students in the department receive University fellowships.

Finally, the Department of Mathematics tries to give some students summer fellowship support. Recipients are chosen by the ASGSC. Finances permitting, we hope to support ten to twelve students per summer with fellowships.

Cost of Study

Required tuition and fees during the 2008-2009 academic year for a full-time graduate student (taking nine semester hours) are approximately $3,300 per semester for Texas residents and recipients of any of the above assistantships, fellowships, or scholarships. The corresponding figure is approximately $6,600 for non-resident U.S. citizens and foreign students not holding one of the above awards.

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City of Austin

Information about the city of Austin can be found at: http://www.utexas.edu/austin/