Department of Mathematics (GRAD)
The Department of Mathematics offers graduate training leading to the degrees of master of arts, master of science, and doctor of philosophy. A master's degree may be included or bypassed in the doctoral program. All of a student's graduate work may be done within the department or, when appropriate, may be done under the direction of an approved advisor in an allied discipline. The Department of Mathematics is housed in Phillips Hall and Chapman Hall. The Department of Mathematics offers a number of teaching assistantships and teaching fellowships each year. Applicants for financial aid are also considered for several University fellowships awarded by The Graduate School in the University-wide competition. Applications for admission and financial assistance may be obtained from The Graduate School. Applications filed by the posted deadline will receive full consideration.
Courses
Numbered 400-999:
The general regulations of The Graduate School govern the work for graduate degrees in mathematics. Specific requirements are explained below. In general, a graduate student in mathematics may receive credit only for mathematics courses numbered 600 and above.
These descriptions summarize the requirements for the master's and Ph.D. degrees. More detailed statements may be obtained from the department. The director of graduate studies must approve all aspects of a student's program. The purpose of the graduate programs is to develop mathematical skills appropriate for competition in academia or industry.
The course schedule for first-year students will depend upon each student's undergraduate training. The normal course load for a graduate student is three courses (nine credit hours) per semester. Graduate students must maintain full-time status in order to qualify for tuition and health insurance benefits. First-year students typically choose courses from five yearlong sequences in algebra (MATH 676, MATH 677), analysis (MATH 653, MATH 656), geometry-topology (MATH 681, MATH 680), scientific computation (MATH 661, MATH 662), and methods of applied mathematics (MATH 668, MATH 669).
The Ph.D. comprehensive exams are based on the content of the first-year sequences. These exams are offered in January and August of each year, just before the semester begins. A Ph.D. student can pass either the Pure Math option or the Applied Math option for the comprehensive examination. To pass the Pure Math option a student must pass any three of the five comprehensive exams. To pass the Applied Math option, a student is required to pass Methods of Applied Math and Scientific Computation.
During the second year a typical Ph.D. student will take the Ph.D. comprehensive exams and select courses from a list of 20 more advanced "second tier" courses. A typical master's student will complete that degree during the second year. The department considers two years to be the normal time needed to complete a master's degree.
A candidate for a master's degree must satisfy each of the following requirements:
- Earn at least two semesters of residency credit and complete all requirements within five years
- Demonstrate computer programming ability by passing an approved undergraduate or graduate course in programming
- Perform satisfactorily in 30 hours of graduate work in a program approved by the director of graduate studies. At least 15 of these hours must be in Department of Mathematics courses numbered 600 or above
- Complete a master's project or thesis for a master of science degree or a master's thesis for a master of arts degree
- Pass an oral examination upon completion of the master's project or master's thesis. The exam will cover coursework as well as the project or thesis
- A master's candidate must pass one of the written comprehensive exams given to doctoral students.
A candidate for a Ph.D. degree must satisfy each of the following requirements:
- Earn at least four semesters of residency credit and complete all requirements within eight years
- Satisfy the same computer programming requirement as a master's student
- Complete either the Pure Math option or the Applied Math option for comprehensive examinations by the beginning of the sixth semester
- Pass at least six courses from the following two lists: a) the second tier courses or b) first-year comprehensive courses that are not basic courses for any of the comprehensive exams passed by the student. Of these six courses at least three must be numbered over 700 and drawn from the second tier list.
- Pass the Teaching Assistant Teaching Seminar and perform a minimum of two semesters of instructional service
- Pass a preliminary oral exam on the chosen Ph.D. specialty area
- Write a Ph.D. thesis and defend it successfully during a final oral exam chaired by the thesis advisor
Minor in Mathematics
Graduate students in other departments who plan to offer mathematics as a (complete or partial) minor field for the Ph.D. should consult the director of graduate studies in mathematics for approval of their programs and for assignment of an advisor in the Department of Mathematics. This should be done at the earliest possible time in order to prevent disappointment for the student.
Following the faculty member's name is a section number that students should use when registering for independent studies, reading, research, and thesis and dissertation courses with that particular professor.
Professors
David Adalsteinsson (1), Applied Mathematics and Scientific Computation
Idris Assani (45), Dynamical Systems, Ergodic Theory of Operators
Prakash Belkale (57), Algebraic Geometry
Roberto A. Camassa (16), Mathematical Modeling, Nonlinear Waves, Propagation, Dynamical Systems
Yaiza Canzani (18), Geometric Analysis, Semiclassical Analysis, Perturbation Theory
Ivan V. Cherednik (48), Representation Theory, Mathematical Physics, Algebraic Combinatorics
Hans Christianson (8), Semiclassical Analysis and Partial Differential Equations
M. Gregory Forest (7), Nonlinear Waves, Solitons, Fiber Flows of Complex Liquids
Boyce Griffith (10), Numerical Analysis, Mathematical Biology
Jingfang Huang (51), Integral Equation Methods and Fast Algorithms
Shrawan Kumar (46), Representation Theory, Geometry of Flag Varieties
Yifei Lou (20), Image Processing, Sparse Signal Recovery, Numerical Analysis and
Optimization Algorithms
Jeremy Marzuola (9), Partial Differential Equations
Richard McLaughlin (50), Fluid Dynamics and Turbulent Transport
Jason Metcalfe (61), Partial Differential Equations
Sorin Mitran (58), Computational Methods for Partial Differential Equations, Continuum-Kinetic Methods, Fluid Dynamics, Biological Fluid Dynamics and Mechanics
Katherine Newhall (12), Applied Mathematics, Stochastic Differential Equations
Richard Rimanyi (59), Topology, Geometry, Singularities
Lev Rozansky (52), Three-Dimensional Topology
Justin Sawon (64), Differential Geometry
Alexander N. Varchenko (47), Geometry, Mathematical Physics
Mark Williams (36), Partial Differential Equations
Associate Professors
Olivia Dumitrescu (27), Algebraic Geometry, Enumerative Problems on Moduli Spaces
Jiuzu Hong (13), Representation Theory
David Rose (17), Categorification, Low-Dimensional Topology, Representation Theory
Pedro Saenz (21), Soft Matter Physics, Fluid Dynamics, Physical Mathematics
Andrey Smirnov (19), Representation Theory, Mathematical Physics
Assistant Professors
Arunima Bhattacharya (24), Geometric Analysis, Nonlinear Partial Differential Equations
Thomas Chandler (28), Applied Mathematics, Continuum Mechanics, Thin Elastic Materials, Complex Fluids, Fluid–Structure Interactions
Shahar Kovalsky (25), Optimization, Computational Geometry, Machine Learning, Medical Imaging
Caroline Moosmueller (23), Geometric Data Analysis, Computational Optimal Transport, Numerical Analysis and Approximation Theory
Casey Rodriguez (26), Partial Differential Equations, Continuum Mechanics
Philip Tosteson (63), Topology, Combinatorics, Representation Theory
Daping Weng (15), Cluster Theory, Representation Theory, Algebraic Geometry, Symplectic Geometry, and Mathematical Physics
Professors Emeriti
Joseph A. Cima
Patrick Eberlein
Ladnor Gessinger
Sue E. Goodman
Jane M. Hawkins
Christopher K.R.T. Jones
Ancel C. Mewborn
Karl Petersen
Joseph Plante
Robert A. Proctor
James Stasheff
Michael E. Taylor
Jonathan M. Wahl
Warren R. Wogen
Department of Mathematics
