The Department of Mathematics offers two master's degrees, one in Mathematics and the other in Statistics, and two doctoral degrees, one in Mathematics and one in Statistics. Areas of study for Mathematics include: algebra, algebraic geometry, real and complex analysis, differential geometry, and topology. The areas of study for Statistics are: mathematical statistics, survival analysis, modeling, statistical computing for massive data, Bayesian regulation, bioinformatics, longitudinal and functional data analysis, statistical computation, asymptotic theory, objective Bayes, bootstrap, postselection inference, and application of statistics to medicine. Because it is difficult to make up coherent programs for students entering in the middle of the year, students are ordinarily admitted only in the fall.
Graduate students have an opportunity when they first arrive to share common concerns and to become acquainted. One of the most attractive features of our program is the friendly and supportive atmosphere among the graduate students. Advanced courses in the Washington University math department can build on the common background shared by all students. As a result, these courses are richer and nearer to the level of PhD work than typical advanced courses.
Students typically complete the PhD program in five years. A student who comes here with advanced preparation may finish in less time. On the other hand, some students find that it is advisable for them to take preparatory work before attempting the qualifying courses. In special cases, the time schedule may be lengthened accordingly. Students should plan to develop a close relationship with their thesis advisers so that they may have a realistic idea of their progress.
Graduate study in mathematics is not for everyone. Entering students usually find that the time and effort required to succeed goes well beyond anything they encountered as undergraduates. Success requires both ample mathematical ability and the determination to grapple with a subject for many days or weeks until the light of understanding shines through. The experience can be daunting. Those who continue in their studies are largely those for whom the pleasure in attaining that understanding more than compensates for the required effort. For such persons, the life of a mathematician can be richly rewarding.
Email: kumar@wustl.edu or stenner@wustl.edu
Phone:  3149356760 

Website:  http://wumath.wustl.edu/graduate 
Chair
John E. McCarthy
Spencer T. Olin Professor of Mathematics
PhD, University of California, Berkeley
Analysis; operator theory; one and several complex variables
Directors
Mohan Kumar
Director of Graduate Studies; Professor of Mathematics
PhD, Bombay University
Algebraic geometry; commutative algebra
Ron Freiwald
Director of Undergraduate Studies; Professor of Mathematics
PhD, University of Rochester
General topology
Endowed Professor
John E. McCarthy
Spencer T. Olin Professor of Mathematics
PhD, University of California, Berkeley
Analysis; operator theory; one and several complex variables
Professors
QuoShin Chi
PhD, Stanford University
Differential geometry
Renato Feres
PhD, California Institute of Technology
Differential geometry; dynamical systems
Jefferson M. Gill
Professor, Political Science; Courtesy appointment, Mathematics
PhD, American University
Steven G. Krantz
PhD, Princeton University
Several complex variables; geometric analysis
Rachel Roberts
PhD, Cornell University
Lowdimensional topology
John Shareshian
PhD, Rutgers University
Algebraic and topological combinatorics
Edward Spitznagel
PhD, University of Chicago
Statistics; statistical computation; application of statistics to medicine
Xiang Tang
PhD, University of California, Berkeley
Symplectic geometry; noncommutative geometry; mathematical physics
Mladen Victor Wickerhauser
PhD, Yale University
Harmonic analysis; wavelets; numerical algorithms for data compression
David Wright
PhD, Columbia University
Affine algebraic geometry; polynomial automorphisms
Associate Professors
Roya Beheshti Zavareh
PhD, Massachusetts Institute of Technology
Algebraic geometry
Brian E. Blank
PhD, Cornell University
Representations of Lie groups; harmonic analysis
Jimin Ding
PhD, University of California, Davis
Statistics
José FigueroaLópez
PhD, Georgia Institute of Technology
Statistics; probability and stochastic processes; mathematical finance
Matthew Kerr
PhD, Princeton University
Algebraic geometry; Hodge theory
Gregory Knese
PhD, Washington University
Complex function theory, operators; harmonic analysis
Nan Lin
PhD, University of Illinois at UrbanaChampaign
Statistics
Jack Shapiro
PhD, City University of New York
Algebraic Ktheory
Brett Wick
PhD, Brown University
Analysis of several complex variables; harmonic analysis and operatory theory
Assistant Professors
Todd Kuffner
Assistant Professor of Mathematics
PhD, Imperial College London
Statistics; likelihood and asymptotics, econometrics
Ari Stern
Assistant Professor of Mathematics
PhD, California Institute of Technology
Geometric numerical analysis, computational mathematics
Michael Wendl
Assistant Professor of Genetics, The Genome Institute; courtesy appointment Mathematics Department
PhD, Washington University
Combinatorics, PDEs, probability, and statistical genetics
Professors Emeriti
William M. Boothby
PhD, University of Michigan
Differential geometry
Lawrence Conlon
PhD, Harvard University
Differential topology
Gary R. Jensen
PhD, University of California, Berkeley
Differential geometry
Robert McDowell
PhD, Purdue University
General topology
Richard Rochberg
PhD, Harvard University
Complex analysis, interpolation theory
Stanley Sawyer
PhD, California Institute of Technology
Probability and statistics; population biology, mathematical genetics
Guido L. Weiss
PhD, University of Chicago
Interpolation of operators; harmonic analysis, Lie groups
Edward N. Wilson
PhD, Washington University
Harmonic analysis, differential geometry
William Chauvenet Postdoctoral Lecturers
Michael Hartz
PhD, University of Waterloo
Yakov BerchenkoKogan
PhD, Massachusetts Institute of Technology
James Pascoe
NSF Postdoctoral Fellow
PhD, University of California, San Diego
Several complex variables
Coordinator Lower Division Teaching
Blake Thornton
Coordinator of Lower Division Teaching, Mathematics Department
PhD, University of Utah
Program Coordinator
Lisa M. Kuehne
Program Coordinator, University College & Center for Advanced Learning
AM Mathematics, Washington University
Undergraduate Mathematics Education
AM in Mathematics
General requirements: 36 units of course work and an optional thesis. 3 units may be for thesis research. The minimum residence requirement is one full academic year of graduate study. A grade point average of B or better must be maintained in graduate course work.
Optional thesis requirements: To be eligible for the thesis option, a student must maintain a cumulative grade point average of 3.5 or higher in the first 18 units of course work satisfying the program requirements.
Course requirements: There are four basic graduate sequences in pure mathematics:
Code  Title  units 

Math 5021 & Math 5022  Complex Analysis I and Complex Analysis II  6 
Math 5031 & Math 5032  Algebra I and Algebra II  6 
Math 5041 & Math 5042  Geometry I and Geometry II  6 
Math 5051 & Math 5052  Measure Theory and Functional Analysis I and Measure Theory and Functional Analysis II  6 
A candidate for the AM in Mathematics must include two of these sequences (12 units) in the required 36 units. The student, in consultation with his or her adviser, selects the remaining 24 units according to the student's interests and needs.
The AM examination: Candidates for the AM degree must pass at least two of the four PhD qualifying exams. Under exceptional circumstances, the graduate committee may allow the student to substitute the PhD qualifying exams mentioned above with a comprehensive examination on the contents of Math 4111 Introduction to Analysis–Math 4121 Introduction to Lebesgue Integration, Math 4171 Topology I–Math 4181 Topology II, and Math 429 Linear Algebra–Math 430 Modern Algebra.
AM in Statistics
General requirements: 36 units of course work and a thesis. 6 units may be for thesis research. The minimum residence requirement is one full academic year of graduate study. A grade point average of B or better must be maintained in graduate course work.
Course requirements: The student must take (or have taken) the following six required courses in mathematics or their equivalents:
Code  Title  units 

Math 493 & Math 494  Probability and Mathematical Statistics  6 
or Math 5061 & Math 5062  Theory of Statistics I and Theory of Statistics II  
Math 439  Linear Statistical Models  3 
Math 4392  Advanced Linear Statistical Models  3 
Math 459  Bayesian Statistics  3 
Math 475  Statistical Computation  3 
or a suitable substitute elective approved by the department 
In the case that an equivalent course has been taken and also proficiency in the course material has been demonstrated, other 400level and above electives may be substituted in consultation with the adviser. Additional 400level or higher electives will be chosen by the student in consultation with his or her adviser to make up the 36 units.
PhD in Mathematics
General requirements: Completion of the PhD requires four full years of graduate study, with at least 48 units spent in residence at Washington University. The student must spend at least one academic year as a fulltime student; this requirement cannot be met wholly by summer sessions or parttime study. The student may, with departmental permission, transfer part of the graduate units from other universities. A grade point average of B or better is required in graduate course work. Graduate students in mathematics may ordinarily expect up to five years of support. Continuation of support each year is dependent upon normal progress toward the degree and satisfactory performance of duties.
Specific course requirements: The course work must include four basic graduate sequences:
Code  Title  units 

Math 5021 & Math 5022  Complex Analysis I and Complex Analysis II  6 
Math 5031 & Math 5032  Algebra I and Algebra II  6 
Math 5041 & Math 5042  Geometry I and Geometry II  6 
Math 5051 & Math 5052  Measure Theory and Functional Analysis I and Measure Theory and Functional Analysis II  6 
Language requirement: For the PhD, the department requires two of these languages: English, French, German, or Russian. If the student's native language is English, then he or she must demonstrate competence in one of the other three languages by either:

submitting an undergraduate transcript showing one year of one of these languages passed with a grade of C or better;

taking a onesemester course in one of these languages while a graduate student at Washington University, and passing with a grade of B or better; or

passing one of the annual written exams given by the department in mathematical French or German or Russian, as decided by the thesis adviser.
Qualifying examinations: The qualifying exam is in two parts; one is a series of four written tests covering a range of topics, and one is an oral exam on two selected topics. The written tests cover the material in the four basic course sequences. Each spring, at the end of each sequence, all students enrolled in the course take a twohour final exam; this exam usually covers the second half of the sequence. Doctoral candidates take an additional onehour exam which covers the entire sequence. To pass the qualifying exam in one of the four areas, the student must pass the threehour combined exam.
The dissertation and final oral exam: The student's dissertation is the single most important requirement for the PhD degree. It must be an original contribution to mathematical knowledge and the student's opportunity to conduct significant independent research. Once the department has accepted the dissertation (on the advice of the thesis adviser), the student is required to pass a final oral examination. Part of this procedure is a question/answer period in which the student is expected to "defend" the thesis. For information about preparing the thesis and its abstract, and about the deadlines involved, please consult the following items from the Graduate School: the Forms page, and the Policies and Guides page (which includes the Doctoral Dissertation Guide). For a sample thesis TeX file and style file, visit the Department of Mathematics website.
PhD in Statistics
Degree Requirements Summary
Required graduate units, consisting of:
 24 required course work units total in fundamental topics and exam fields
 12 elective course work units
 6 course work units for staffing a walkin statistical consulting center to be setup by the department
 4 qualifying exams: 2 in statistics, 2 in mathematics
 Graduate School Teaching Requirement for PhD Students
 Major and minor oral presentation
 Dissertation research, thesis preparation, and defense (30 course work units)
General requirements: The PhD in Statistics general requirements mirror the PhD in Mathematics. For a more detailed explanation, please visit the PhD in Statistics webpage.
Specific course requirements: The course work must include two basic graduate statistics sequences:
Code  Title  units 

Math 5061 & Math 5062  Theory of Statistics I and Theory of Statistics II  6 
Math 439 & 4392  Linear Statistical Models and Advanced Linear Statistical Models  6 
and any two of the following pure math sequences:
Code  Title  units 

Math 5021 & Math 5022  Complex Analysis I and Complex Analysis II  6 
Math 5031 & Math 5032  Algebra I and Algebra II  6 
Math 5041 & Math 5042  Geometry I and Geometry II  6 
Math 5051 & Math 5052  Measure Theory and Functional Analysis I and Measure Theory and Functional Analysis II  6 
Prerequisites, if needed, are Math 429 Linear Algebra (0 units toward the degree) and Math 233 Calculus III (0 units toward the degree).
Language requirement: A student whose native language is not English must demonstrate proficiency in English. The student also is expected to become fluent in spoken English. In particular, any student who expects to gain teaching experience while pursuing a degree will need to do this as soon as possible. All students are expected to fulfill the language requirement during their first two years of graduate study.
Qualifying examinations: The qualifying exam is in two parts. One is a series of four written tests covering a range of topics, and one is an oral exam on two selected topics. The written tests cover the material in the four basic course sequences. Each spring, at the end of each sequence, all students enrolled in the course take a twohour final exam; this exam usually covers the second half of the sequence. Doctoral candidates take an additional onehour exam which covers the entire sequence. To pass the qualifying exam in one of the four areas, the student must pass the threehour combined exam.
The dissertation and final oral exam: The student's dissertation is the single most important requirement for the PhD degree. It must be an original contribution to mathematical knowledge and the student's opportunity to conduct significant independent research. The student is required to pass a final oral examination, and part of this procedure is a question/answer period in which the student is expected to "defend" the dissertation. For information about preparing the thesis and its abstract, and about the deadlines involved, please consult the Graduate School's academic information section of this Bulletin.