Approximately 100 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. These positions are currently filled by individuals of universally recognized distinction: Luis Caffarelli, Cameron Gordon, John Tate and Karen Uhlenbeck. The program of chairs has stimulated faculty recruitment at all levels.
In 1993 the University established an interdisciplinary program for
graduate education and research in Computational and Applied Mathematics
(CAM). Jerry Bona, one of the nation's most respected applied mathematicians,
was appointed to fill the first Chair in Computational and Applied Mathematics
and thereby to assume the leadership in developing the Department's contributions
to the CAM endeavor. At the same time, the College of Engineering hired
into Chair positions two premier numerical analysts, Ivo Babushka and Mary
Wheeler, to advance its build-up in the CAM area. New University initiatives
are now underway in Digital Science and Computational Biology. These are
expected to have a broad interface with Mathematics and the CAM program.
The University's Academic Computing and Instructional Technology Services provides extensive on-campus computing facilites. In addition, the High Performance Computing Facility (HPCF) at the Pickle Research Campus in north Austin maintains two multi-processor Cray J90 supercomputers and a Cray T3E Parallel System. Jointly HPCF and the Texas Institute for Computational and Applied Mathematics run a Visualization Lab for computer graphics centered on a Silicon Graphics Power Onyx system in Taylor Hall.
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. During 1996-97 there were seminars in mathematical physics, topology, Banach spaces, harmonic analysis, complex analysis, partial differential equations, computational and applied mathematics, number theory, dynamical systems, differential geometry, gauge theory, iterative methods, statistics, algebra, and algebraic geometry. It is expected that most of these will continue during the coming year.
The Mathematics Department includes mathematical statisticians with varied research interests. In addition to the relation of their work to the rest of mathematics, they also collaborate with statisticians and data analysts at The University of Texas. This is facilitated by a campus-wide Center for Statistical Sciences which includes more than 30 faculty and many student members from various UT departments. A common goal of both the Center and Department is to stimulate excellence in statistics by bringing visiting statisticians to campus, offering seminars, encouraging research projects, and most importantly by providing a forum for the promotion of interdisciplinary statistical research.
The steps in obtaining a Ph.D. degree in Mathematics are as follows:
1. passing three preliminary exams.
2. selection of an area of specialization and appointment of an advisory
committee.
3. passing a candidacy exam in the area of specialization.
4. certification by the advisory committee of the candidate's knowledge
of the chosen area and of the adequacy of the proposed program of coursework.
5. completion of any remaining Graduate School requirements and formal
admission to Ph.D. candidacy.
6. writing a dissertation.
7. passing a final oral exam on the dissertation research.
A 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 by passing three of the associated exams or by passing the exams in two of the areas and completing the prelim option discussed below in the third area. 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 the preliminary exam, the only restriction being that the student has completed the associated course sequence with a grade of "A" for each semester. The student can then substitute for passage of the prelim exam 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 or work will consist 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 50 minute lecture on some reasonably advanced topic in the area. The lecture will be announced in the department calendar, and attendance will be open to all mathematics faculty and graduate students. (The logical forum for such a lecture would be the 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 the student has passed two prelim exams by January of the second year and uses this alternate 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 candidacy exam.
A student who wants to do interdisciplinary research (e.g., mathematical biology) may replace one of the prelim exams by an exam that covers material primarily from the other discipline (e.g., biology). A syllabus for such an exam shall be developed with input from suitable faculty. The student shall submit that syllabus to the ASGSC (Administrative Subcommittee of the GSC) for approval. If the syllabus is approved by the ASGSC, then the Chair of the GSC shall appoint three people to serve on the exam committee, and the exam may be either written or oral as determined by that exam committee.
A student who has taken graduate level courses at another university may petition the ASGSC for prelim relief in one or more areas.
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 three exams 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 qualified), but the third year will be the terminal year for the student in the Ph.D. program. An exception to this rule is the student who enters the Ph.D. program upon completion of a Master's degree in this department; such a student must have credit for passing three prelim exams 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.
2. Advisory Committee
After passing the preliminary exams a student will select an area of specialization and obtain the agreement of a member of the GSC to supervise the student's doctoral dissertation. In consultation with the student and the prospective Ph.D. supervisor, the Graduate Advisor will appoint a three-person committee, chaired by the proposed supervisor, that will help 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 which is sufficiently broad and deep, and (c) to meet formal Graduate School requirements. In particular, the advisory committee will see that the student's choice of minor subject and foreign language are made so as to represent a meaningful and useful addition to the total program. This committee will also have responsibility for administering the candidacy exam.
3. Candidacy Exam
No later than one year after completion of the preliminary exam process or by the end of the fifth long semester in residence, whichever is later, the advisory committee will examine the student in his or her chosen area of specialization. The exam may be written or oral - at the committee's discretion. The style, coverage and time of the exam will be set by the advisory committee in consultation with the student. If the advisory committee deems that the student has failed the candidacy exam, 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. Certification
When a student has passed the candidacy exam and his or her advisory committee is satisfied with the student's proposed research area of specialization, subject preparation, program of coursework and choice of foreign language, it shall so certify to the GSC.
5. Formal Admission to Ph.D. Candidacy
Upon receipt of the required certification from the advisory committee, the Chair of the GSC will appoint a five-person Doctoral Committee - this committee is to be proposed by the student, is to be chaired by his or her doctoral supervisor and is subject to certain Graduate School requirements as to its composition - and will make a formal recommendation to the Graduate School that the student be admitted to Ph.D. candidacy. A Ph.D. student must fulfill all requirements for admission to Ph.D. candidacy (i.e., prelim exams, language requirement, candidacy exam) by the beginning of his or her fourth year in the doctoral program.
6. Dissertation
The dissertation is the most important part of the Ph.D. program. It involves original research in mathematics by the student, and the research topics covered in the dissertation are selected by the student in consultation with the student's supervising professor. The student is expected to complete the dissertation within three years of admission to Ph.D. candidacy. Information about the required format for the written dissertation can be obtained from the Graduate School office.
7. Final Oral Exam on Dissertation
After the dissertation is written, there is a final oral exam on the
dissertation. This exam must be scheduled through the Graduate School
office at least two weeks in advance of the exam date. The Doctoral
Committee for the student administers the exam. After the student
passes this exam, the student is eligible to receive the Ph.D. degree after
the student submits the dissertation and some paperwork to the Graduate
School office.
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.
1. Groups: Finite groups, including Sylow
theorems, p-groups, direct products and sums, semi-direct products,
permutation groups, simple groups, finite Abelian groups; infinite groups,
including normal and composition series, solvable and nilpotent groups,
Jordan-Holder theorem, free groups.
References: Goldhaber Ehrlich, Ch. I except 14;
Hungerford, Ch. I, II; Rotman, Ch. I-VI, VII (first three sections).
2. Rings and modules: Unique factorization
domains, principal ideal domains, modules over principal ideal domains
(including finitely generated Abelian groups), canonical forms of matrices
(including Jordan form and rational canonical form), free and projective
modules, tensor products, exact sequences, Wedderburn-Artin theorem, Noetherian
rings, Hilbert basis theorem.
References: Goldhaber Ehrlich,
Ch. II, III 1,2,4, IV, VII, VIII; Hungerford, Ch. III except
4,6, IV 1,2,3,5,6, VIII 1,4,6.
3. Fields: Algebraic and transcendental
extensions, separable extensions, Galois theory of finite extensions, finite
fields, cyclotomic fields, solvability by radicals.
References: Goldhaber Ehrlich,
Ch. V except 6; Hungerford, Ch. V, VI; Kaplansky, Part I.
References:
Goldhaber Ehrlich,
Algebra, reprint with corrections, Krieger, 1980.
Hungerford, Algebra,
reprint with corrections, Springer, 1989.
Isaacs, Algebra, a Graduate
Course, Wadsworth, 1994.
Kaplansky, Fields and
Rings, 2nd Edition, University of Chicago Press, 1972.
Rotman, An Introduction
to the Theory of Groups, 4th Edition, W.C. Brown, 1995.
Real Analysis
1. Measure theory: Lebesgue measure
on Rn and its elementary properties, regularity
of Lebesgue measure; measurable functions, Egorov's Theorem, Lusin's Theorem;
measure spaces and measurable functions in an abstract setting.
2. Integration: Lebesgue integration
in Rn and in an abstract setting; Fatou's Lemma,
the Monotone and Dominated Convergence Theorems; product measures and the
Fubini-Tonelli Theorems with applications such as convolution.
3. Differentiation: Properties
of monotone functions, absolutely continuous functions and functions of
bounded variation; the Fundamental Theorem of Lebesgue Integral Calculus;
singular functions, the Cantor function.
4. Lp-spaces:
Convergence almost everywhere, in norm and in measure; approximation in
Lp-norm; the Jensen, Holder and Minkowski inequalities;
Lp-spaces, Lp-
Lq duality.
Complex Analysis
1. Analytic functions: Definition and
elementary examples; power series and their properties; the Cauchy-Riemann
equations; Mobius transformations.
2. Complex integration: Paths and contour
integrals; homotopy; Cauchy's Theorem and Integral Formulae; power series
representation; the Maximum Principle, Schwarz's Lemma.
3. Singularities: Laurent series
and classification of isolated singularities; the Residue Theorem and its
applications; counting zeros and poles --- the Argument Principle; Rouche's
Theorem, the Open Mapping Theorem.
4. Convergence: Uniform convergence
on compact sets and its implications for analytic functions.
References:
Ahlfors, Complex Analysis,
3rd Edition, McGraw-Hill, 1979, Ch. 1-6.
Conway, Functions of
One Complex Variable, Springer, 1978, Ch. 1-7.
Palka, An Introduction
to Complex Function Theory, corrected 2nd printing, Springer, 1995,
Ch. 1-10.
Royden, Real Analysis,
3rd Edition, Prentice-Hall, 1988, Ch. 1-7, 9-11 (omit 11.4-11.6), 12.1-12.4.
Rudin, Real and Complex
Analysis, 3rd Edition, McGraw-Hill, 1987, Ch. 1-4, 6-8, 10, 11.1-11.4,
12, 13, 14.5-14.6.
Metric spaces: Elementary metric space
topology, with special emphasis on euclidean spaces; sequences in metric
spaces --- limits, accumulation points, subsequences, etc.; Cauchy sequences
and completeness; compactness in metric spaces; compact sets in R;
connectedness in metric spaces; countable and
uncountable sets.
Continuity: Limits and continuity of
mappings between metric spaces, with particular attention to real-valued
functions defined on subsets of R; preservation
of compactness and connectedness under continuous mapping; uniform
continuity.
Differentiation on the line: The definition and geometric significance of the derivative of a real-valued function of a real variable; the Mean Value Theorem and its consequences; Taylor's theorem; L'Hospital's rules.
Riemann integration on the line: The definition and elementary properties of the Riemann integral; existence theorems for Riemann integrals; the Fundamental Theorems of Calculus.
Sequences and series of functions: Uniform convergence, uniform convergence and continuity, uniform convergence and integration, uniform convergence and differentiation.
(An appropriate text might be Rudin's Principles of Mathematical
Analysis, and the course should cover roughly its first seven chapters.)
1. Manifolds: Identification (quotient) spaces and identification (quotient) maps; topological n-manifolds, including surfaces, Sn, RPn, CPn, and lens spaces.
2. Triangulated manifolds: Representation of triangulated, closed 2-manifolds as connected sums of tori or projective planes.
3. Fundamental group and covering spaces:
Fundamental group, functoriality, retract, deformation retract; Van
Kampen's Theorem, classification of surfaces by abelianizing Pi1;
covering spaces, path lifting, homotopy lifting, uniqueness of lifts, general
lifting theorem for maps, covering transformations, regular covers,
correspondence between subgroups of Pi1(x) and covering
spaces of X; computing Pi1 of
the circle, RPn, lens spaces via covering spaces.
4. Simplicial homology: Homology groups,
functoriality, topological invariance, Mayer-Vietoris sequence; applications,
including Euler characteristic, classification of closed triangulated surfaces
via homology and via Euler characteristic and orientability; degree of
a map between oriented manifolds, Lefschetz number, Brouwer Fixed Point
Theorem.
References:
Armstrong, Basic Topology,
Springer, 1983 (principal text).
Greenberg, Lectures on
Algebraic Topology, W.A. Benjamin, 1967.
Massey, Algebraic Topology,
an Introduction, 4th corrected printing, Springer, 1977.
Munkres, Elements of
Algebraic Topology, Addison-Wesley, 1984.
Differential Topology
1. Smooth mappings: Inverse Function Theorem, Local Submersion Theorem (Implicit Function Theorem).
2. Differentiable manifolds: Differentiable manifolds and submanifolds; examples, including surfaces, Sn, RPn, CPn and lens spaces; tangent bundles; Sard's Theorem and its applications; differentiable transversality; orientation.
3. Vector fields and differential forms:
Integrating vector fields; degree of a map, Brouwer Fixed Point Theorem,
No Retraction Theorem, Poincare-Hopf Theorem; differential forms, Stokes
Theorem.
References:
Guillemin Pollack,
Differential Topology, Prentice-Hall, 1974 (basic reference).
Hirsch, Differential
Topology, Springer, 1976.
Milnor, Topology from
the Differentiable Viewpoint, University of Virginia Press, 1965.
Spivak, Calculus on Manifolds,
Benjamin, 1965 (differentiation, Inverse Function Theorem, Stokes
Theorem).
For the examples indicated we refer to the books of Greenberg, Hirsch
and Munkres.
Definitions of topological space: Basis, sub-basis, metric space.
Countability properties: Dense sets, countable basis, local basis.
Separation properties: Hausdorff, regular, normal.
Covering properties: Compact, countably compact, Lindelof.
Continuity and homeomorphisms: Properties preserved by continuous functions, Urysohn's Lemma, Tietze Extension Theorem.
Connectedness: Definition, examples,
invariance under continuous functions.
Reference: Munkres, Topology: a First
Course, Prentice-Hall, 1975.
1. Banach spaces: Normed linear spaces and convexity; convergence, completeness, and Banach spaces; continuity, open sets, and closed sets; continuous linear transformations; Hahn-Banach Extension Theorem; linear functionals, dual and reflexive spaces, and weak convergence; the Baire Theorem and uniform boundedness; Open Mapping and Closed Graph Theorems; Closed Range Theorem; compact sets and Ascoli-Arzelà Theorem; compact operators and the Fredholm alternative.
2. Hilbert spaces: Basic geometry, orthogonality, bases, projections, and examples; Bessel’s inequality and the Parseval Theorem; the Riesz Representation Theorem; compact and Hilbert-Schmidt operators; spectral theory for compact, self-adjoint and normal operators; Sturm-Liouville Theory.
3. Distributions: Seminorms and locally convex spaces; test functions and distributions; calculus with distributions.
4. The Fourier Transform and Sobolev Spaces: The Schwartz space and tempered distributions; the Fourier transform; the Plancherel Theorem; convolutions; fundamental solutions of PDE’s; Sobolev spaces; Imbedding Theorems; the Trace Theorems for Hs.
5. Variational Boundary Value Problems (BVP): Weak solutions to elliptic BVP’s; variational forms; Lax-Milgram Theorem; Green’s functions.
6. Differential Calculus in Banach Spaces and Calculus of Variations: The Fréchet derivative; the Chain Rule and Mean Value Theorems; Banach’s Contraction Mapping Theorem and Newton’s Method; Inverse and Implicit Function Theorems, and applications to nonlinear functional equations; extremum problems, Lagrange multipliers, and problems with constraints; the Euler-Lagrange equation.
7. Asymptotic Analysis: Definitions and fundamental properties; examples of transcendental equations and initial-value problems.
References:
The first four references cover most of the syllabus for the exam. The other references also cover some topics in the syllabus.
1. C. Carath'eodory, Calculus of Variations and Partial Differential Equations of the First Order, 2nd English Edition, Chelsea, 1982.
2. F.W.J. Olver, Asymptotics and Special Functions, Academic Press, 1974.
3. M. Reed and B. Simon, Methods of Modern Physics, Vol. 1, Functional analysis.
4. R.E. Showalter, Hilbert Space Methods for Partial Differential Equations, available at World Wide Web address http://ejde.math.swt.edu//mono-toc.html .
5. A. Avez, Introduction to Functional Analysis, Banach Spaces, and Differential Calculus, Wiley, 1986.
7. L. Debnath and P. Mikusi'nski, Introduction to Hilbert Spaces with Applications, Academic Press, 1990.
8. I.M. Gelfand and S.V. Fomin, Calculus of Variations, Prentice-Hall, 1963.
9. E. Kreyszig, Introductory Functional Analysis with Applications, 1978.
10. J.T. Oden and L.F. Demkowicz, Applied Functional Analysis, CRC Press, 1996.
11. W. Rudin, Functional Analysis, McGraw-Hill, 1991.
12. W. Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill, 1987.
13. K. Yosida, Functional Analysis, Springer-Verlag, 1980.
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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.)
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 Graduate Advisor. Finances permitting, we hope to support ten to twelve students per summer with fellowships.
On the above Web page, you need to select the appropriate application. U.S. citizens and permanent residents should select "U.S. Graduate/Permanent Resident Application." If you are not a U.S. citizen or permanent resident, you should select "International Graduate Application." Since the Mathematics program, the Computational and Applied Mathematics program, and the Statistics program are separately administered programs, you need to decide which program is appropriate for you. For questions about the Mathematics program, contact the Mathematics Graduate Advisor: Frank Gerth <gradadv@math.utexas.edu>. For questions about the Computational and Applied Mathematics program, contact the Computational and Applied Mathematics Graduate Advisor: Clint Dawson <clint@ticam.utexas.edu>. For questions about the Statistics program, contact the Statistics Graduate Advisor: Peter John <pwmj@math.utexas.edu>. When selecting the "Proposed Graduate Major" or the "Proposed Graduate Program of Study" in the online application, you need to select either "Mathematics" or "Computational and Applied Mathematics" or "Statistics", whichever is the appropriate program for you.
If you select "Mathematics" as your "Proposed Graduate Major" or "Proposed Graduate Program of Study", then after filling out the online application, you need to send various information to the Graduate and International Admission Center and to the Graduate Advisor in the Department of Mathematics.
The following information should be sent to the Graduate and International Admissions Center, UT-Austin, P.O. Box 7608, Austin, TX 78713-7608, USA.
(a) GRE scores (general test : verbal and quantitative parts).
These must be sent directly by the testing service.
(b) TOEFL scores for international students. These must be sent
directly by the testing service.
(c) Official transcripts of undergraduate and previous graduate
work.
(d) Application fee of $50.00 for U.S. citizens and permanent
residents and $75.00 for international students. Your application
will not be processed until you pay this fee.
The following information should be sent to the Graduate Advisor, Department of Mathematics, University of Texas, Austin, TX 78712, USA. (If you are applying to the Computational and Applied Mathematics program or to the Statistics program, send the information listed below to the Graduate Advisor for that program.)
(a) Three letters of recommendation from faculty who are familiar
with your advanced mathematical training.
(b) Statement of Purpose describing your mathematical interests
and your reasons for doing graduate work at the University of Texas.
(c) Unofficial copies of your GRE scores (and TOEFL scores for
international students).
(d) Unofficial copies (photocopies) of your transcripts.
If you are accepted for admission to our graduate program, you will automatically be considered for financial assistance; no separate application for financial assistance is required. Although there are a small number of fellowships, most of our beginning graduate students are supported by Teaching Assistantships. International students must be able to speak fluent English in order to receive a Teaching Assistantship. We expect international students to score at least 630 on the TOEFL test (or at least 267 on the computer-based TOEFL test) and pass an oral English assessment exam administered after they arrive at the University of Texas in order for them to receive Teaching Assistantships. If you are an international student and you expect to receive fellowship or scholarship assistance from a government agency in your home country, you should mention that in your Statement of Purpose.
U.S. citizens and permanent residents who are not able to use the online application can request a paper application from the Graduate and International Admissions Center at the address listed above. International students who are not able to use the online application should request a paper application from the Graduate Advisor in the Math Department at the address listed above. (In your request for an application, please indicate that you are not able to use the online application, and hence you are requesting a paper application. International students requesting a paper application should indicate their TOEFL scores.)
Ivo M. Babuska, Ph.D., Technical University (Czechoslovakia), 1951, Mathematics, Ph.D., Czechoslovak Academy of Sciences (Czechoslovakia), 1955, Mathematics: Applied Mathematics, Numerical Computation and Partial Differential Equations Robert B. Trull Chair in Engineering.
William Beckner, Ph.D., Princeton, 1975, Mathematics: Analysis. Paul V. Montgomery Centennial Memorial Professor in Mathematics.
Sterling Berberian, Ph.D., Chicago, 1955, Mathematics: Operators in Hilbert Space, Operator Algebras, and Integration Theory. (Emeritus)
Klaus Bichteler, Ph.D., Hamburg (Germany), 1965, Physics: Probability.
Jerry L. Bona, Ph.D., Harvard University, 1972, Mathematics: Partial Differential Equations, Computational and Applied Mathematics Chair I.
Robert S. Boyer, Ph.D., Texas (Austin), 1971, Mathematics: Program Verification, Automatic Theorem Proving, and Artificial Intelligence. Professor in Computer Sciences (No. 4 & No. 5).
Patrick L. Brockett, Ph.D., California (Irvine), 1975, Mathematics: Probability and Mathematical Statistics. Gus Wortham Memorial Chair in Risk Management and Insurance.
Luis A. Caffarelli, Ph.D., University of Buenos Aires, 1972, Mathematics: Harmonic Analysis and Partial Differential Equation. Sid W. Richardson Foundation Regents Chair (No. 1).
L. Ray Carry, Ph.D., Stanford, 1968, Mathematics Education: Mathematics Learning and Curriculum Evaluation.
E. Ward Cheney, Ph.D., Kansas, 1957, Mathematics: Approximation Theory and Numerical Analysis.
Alan K. Cline, Ph.D., Michigan (Ann Arbor), 1970, Mathematics: Mathematical Software, Numerical Analysis, and Scientific Computing. David Bruton, Jr. Centennial Professor in Computer Sciences (No. 2).
James W. Daniel, Ph.D., Stanford, 1965, Mathematics: Actuarial Mathematics, Numerical Computation and Optimization. Paul V. Montgomery Centennial Memorial Professor in Actuarial Mathematics.
Rafael de la Llave, Ph.D., Princeton, 1983, Mathematics: Mathematical Physics and Dynamical Systems.
Edsger W. Dijkstra, Ph.D., Amsterdam, 1959, Physics: Program Correctness, Algorithms, Systems. Schlumberger Centennial Chair in Computer Sciences.
John D. Dollard, Ph.D., Princeton, 1963, Physics: Mathematical Physics and Scattering Theory. Associate Dean, Graduate Studies.
John R. Durbin, Ph.D., Kansas, 1964, Mathematics: Group Theory.
William T. Eaton, Ph.D., Utah, 1967, Mathematics: Geometric Topology.
Don E. Edmondson, Ph.D., California Institute of Technology, 1954, Mathematics: Lattice Theory. (Emeritus)
Daniel S. Freed, Ph.D., California (Berkeley), 1985, Mathematics: Differential Geometry.
Irene Martinez Gamba, Ph.D., University of Chicago, 1989, Mathematics: Applied Mathematics, Partial Differential Equations.
Clifford S. Gardner, Ph.D., New York University, 1953, Mathematics: Applied Mathematics and Dynamical Systems. (Emeritus)
Frank E. Gerth III, Ph.D., Princeton, 1972, Mathematics: Algebraic Number Theory. Department Graduate Advisor.
John E. Gilbert, Ph.D., Oxford (England), 1963, Mathematics: Harmonic Analysis and Functional Analysis.
Leonard Gillman, Ph.D., Columbia, 1953, Mathematics: Rings of Continuous Functions. (Emeritus)
Robert E. Gompf, Ph.D., California (Berkeley), 1984, Mathematics: Geometric Topology. Joe B. and Louise Cook Professor in Mathematics.
Cameron McA. Gordon, Ph.D, Cambridge (England), 1971, Mathematics: Geometric Topology. Sid W. Richardson Foundation Regents Chair (No. 2).
William T. Guy Jr., Ph.D., California Institute of Technology, 1951, Mathematics: Integral Transforms. Distinguished Teaching Professor.
Gary C. Hamrick, Ph.D., Virginia, 1971, Mathematics: Algebraic Topology. Department Undergraduate Coordinator.
Raymond C. Heitmann, Ph.D., Wisconsin, 1974, Mathematics: Algebra and Commutative Rings.
Peter W. M. John, Ph.D., Oklahoma, 1955, Mathematics: Statistical Design of Experiments and Quality Assurance.
Hans Koch, Ph.D., Geneva (Switzerland), 1978, Physics: Mathematical Physics and Statistical Mechanics.
George Lorentz, Ph.D., Tubingen (Germany), 1945, Mathematics: Analysis and Approximation Theory. (Emeritus)
John E. Luecke, Ph.D., Texas (Austin), 1985, Mathematics: Topology.
Stephen J. McAdam, Ph.D., Chicago, 1970, Mathematics: Commutative Algebra.
Edward W. Odell, Ph.D., Massachusetts Institute of Technology, 1975, Mathematics: Functional Analysis.
J. Tinsley Oden, Ph.D., Oklahoma State, 1962, Engineering Mechanics: Numerical Computation and Partial Differential Equations. Cockrell Family Regents Chair in Engineering #2.
Bruce P. Palka, Ph.D., Michigan (Ann Arbor), 1972, Mathematics Complex Analysis. Department Associate Chairman. Marian Harris Thornberry Centennial Professor in Mathematics. (on leave, 1998-99)
Charles Radin, Ph.D., Rochester, 1970, Physics: Mathematical Physics.
Haskell Rosenthal, Ph.D., Stanford, 1965, Mathematics: Functional Analysis. John T. Stuart III Centennial Professor.
David J. Saltman, Ph.D., Yale, 1976, Mathematics: Algebra and Division Algebras. Mildred Caldwell and Baine Perkins Kerr Centennial Professor.
William F. Schelter, Ph.D., McGill (Canada), 1972, Mathematics: Algebra. Pennzoil Company Regents Professor.
Ralph E. Showalter, Ph.D., Illinois (Urbana-Champaign), 1968, Mathematics: Partial Differential Equations. Jane and Roland Blumberg Centennial Professor in Mathematics.
Martha Smith, Ph.D., Chicago, 1970, Mathematics: Ring Theory.
Michael P. Starbird, Ph.D., Wisconsin, 1974, Mathematics: Topology.
John Tate, Ph.D., Princeton, 1950, Mathematics: Algebraic Number Theory. Sid W. Richardson Foundation Regents Chair (No. 4).
Philip Uri Treisman, Ph.D., California (Berkeley), 1985, Science and Mathematics Education: Undergraduate Mathematics Development. Director, Charles A. Dana Center for Mathematics and Science Education.
Karen K. Uhlenbeck, Ph.D., Brandeis, 1968, Mathematics: Non-linear Analysis, Differential Geometry, and Dynamical Systems. Sid W. Richardson Foundation Regents Chair (No. 3).
Jeffrey Vaaler, Ph.D., Illinois, 1974, Mathematics: Analytic Number Theory.
James W. Vick, Ph.D., Virginia, 1968, Mathematics: Algebraic Topology. Vice President for Student Affairs. Ashbel Smith Professor and Distinguished Teaching Professor.
Mary F. Wheeler, Ph.D., Rice University, 1971, Mathematics: Numerical Analysis and Partial Differential Equations Ernest and Virginia Cockrell Chair in Engineering.
Robert F. Williams, Ph.D., Virginia, 1954, Mathematics: Dynamical Systems and Global Analysis. (Emeritus)
Gary L. Wise, Ph.D., Princeton, 1974, Electrical Engineering: Applied Probability. Jewel McAlister Smith Professor.
David M. Young, Ph.D., Harvard, 1950, Mathematics: Numerical Analysis. Ashbel Smith Professor. Director, Center for Numerical Analysis. (Emeritus)
Ralph W. Cain, Ph.D., (Austin), 1964, Mathematics: Secondary Mathematics Education.
Katherine M. Davis, Ph.D., Cornell, 1974 Mathematics: Harmonic Analysis.
Charles N. Friedman, Ph.D., Princeton, 1971, Mathematics: Mathematical Physics, Functional Analysis, and Differential Equations.
Sean M. Keel, Ph.D., Chicago, 1989, Mathematics: Algebraic Geometry and Intersection Theory.
Alan W. Reid, Ph.D., University of Aberdeen (U.K.), 1988, Mathematics: Topology.
Lorenzo Sadun, Ph.D., California (Berkeley), 1987, Physics: Mathematical Physics, Differential Geometry, and Analysis.
Mikhail M. Vishik, Ph.D., Moscow (Russia), 1980, Mathematics: Number Theory, Fluid Dynamics.
Jose Felipe Voloch, Ph.D., Cambridge (U.K.), 1985, Mathematics: Number Theory, Algebraic Geometry.
Dale E. Walston, Ph.D., Texas (Austin), 1961, Mathematics: Differential Equations, Numerical Analysis, and Mathematics Education. (Emeritus)
Fernando Rodriguez-Villegas, Ph.D., Ohio State University, 1990, Mathematics: Number Theory.
Zoran Grujic Ph.D, Indiana University, 1998, Mathematics: Nonlinear parabolic PDE's.
Timur Oikhberg, Ph.D., Texas A&M University, 1998, Mathematics: Non-commutative analogs of Classical Banach Space Results.
Nicholas S. Ormes, Ph.D., University of Maryland at College Park, 1997, Mathematics: Topological Dynamics, Ergodic Theory, Matrix Theory.
Cristian D. Popescu, Ph.D., Ohio State University, 1996, Mathematics: Algebraic Number Theory and Arithmetic Algebraic Geometry.
Michael Rudnev, Ph.D., CalTech, 1997, Mathematics: Dynamical Systems (Hamiltonian Perturbation Theory, Geometric Methods). Brachman Bing Fellow.
Margaret Symington, Ph.D., Stanford, 1996, Mathematics: Symplectic Topology.
David Weiland, Ph.D., Washington University, 1997, Mathematics: Harmonic Analysis. R. H. Bing Fellow.
Jiahong Wu, Ph.D., University of Chicago, 1996, Mathematics: Nonlinear PDEs, Fluid Mechanics.
Yu Yuan, Ph.D., University of Minnesota, 1998, Mathematics: PDE and Differential Geometry. R. H. Bing Fellow.
Olivier Collin, Ph.D., University of Oxford (England), 1997, Mathematics: Gauge Theory and Low-dimensional Topology.
Jose Carrillo, Ph.D., University of Granada, 1996, Mathematics: Partial Differential Equations.
Qingbo Huang, Ph.D., Temple University, 1998, Mathematics: PDE and Real Harmonic Analysis.
Nurit Krausz, Ph.D., Technion (Israel), 1998, Mathematics: Quantum Dynamics on Non-compact Group Manifolds.
Victoria Rayskin, Ph.D., University of California at Berkeley, 1997, Mathematics: Dynamical Systems.
Adriana Sofer, Ph.D., Ohio State University, 1993, Mathematics: Number Theory.
Maorong Zou, Ph.D., University of Arizona, 1992,
Mathematics: Hamiltonian Mechanics, Symplectic Geometry.