Graduate Studies in Mathematics

The Doctoral Program

The graduate doctoral program of the Department of Mathematics is oriented towards students who intend to earn a PhD. degree in mathematics, either pure or applied. The Department also offers the degree of Master of Science in Mathematics to students in the doctoral program, although students are not admitted with this as their final objective. In addition, the department offers a separate Master of Science in Financial Mathematics degree (M.S.F.M.). See the Program on Financial Mathematics for more information.

Certain basic graduate courses are offered every year and provide a thorough background for present-day mathematics. Among these are the Analysis, Topology, and Algebra sequences of the first-year graduate program:


Each of the nine courses is taught by a different tenured faculty member. First year students concentrate on these courses and have no teaching duties. These courses are required of first year students, although a student may be excused from any of them by satisfying the instructor that he or she already understands the material. Every year a substantial number of advanced graduate courses are offered; these are usually quite different from year to year. For more more information, see the list of 2006-2007 courses and descriptions of first year courses.

There are, in addition, many continuing informal seminars in which student participation is encouraged, and frequent individual lectures or series of lectures by visiting mathematicians. The Friday afternoon colloquia deal with the background and aims of current mathematical research; these lectures are intended to be of general interest to both students and faculty. In addition, there are four named lecture series:


In addition to its seminars and lectures, the Department supports informal gatherings which foster a congenial and productive atmosphere for graduate students and faculty members to socialize and share ideas. The Afternoon Tea, held each day in the Commons Room in Eckhart Hall, is one such gathering. Also, graduate students in mathematics have organized a Friday afternoon "Pizza Seminar" which proves a forum for students to present lectures and conduct discussions on their current research or on topics in mathematics of particular interest to them. Traditionally, students in the Department participate in discussion groups organized to create a system of mutual support among students working on specific areas of mathematical research. These groups, extending through the summer months, help to make Chicago a friendly and exciting place for mathematical research.

Degree Requirements

Pure Mathematics

All first-year graduate students, except those in the Applied Mathematics Program, are required to demonstrate proficiency in each of the nine basic courses, either by passing the course or by passing a placement examination on the material of the course. Students who fail to pass one or more of the first-year courses will be required to do additional work in the particular subject(s) or take the course(s) again. Each student is also required to pass an exam in a scholarly language other than English (usually in French, German, or Russian).

As a prerequisite for candidacy for the Ph.D., and as evidence of the student's capacity for research, students are required to make an oral "topic presentation," along with a brief written report. These presentations cover material that is chosen by the student in consultation with members of the Department and is studied independently. The topic presentation is normally given by the end of the Winter Quarter of the student's second year of graduate study.

After successful completion of the topic presentation, the student is expected to begin research towards the dissertation under the guidance of a member of the faculty. The remaining requirements are (a) to complete a dissertation containing original, substantial, and publishable mathematical results; (b) to present the contents of the dissertation in an open lecture; and (c) to pass an oral examination based on the material of the dissertation and the field of mathematics in which it lies.

Applied Mathematics

The Department of Mathematics, through the Computational and Applied Mathematics Program (CAMP), offers interdisciplinary programs in applied mathematics leading to M.S. and Ph.D. degrees. These programs overlap with, but are different from, the program in pure mathematics and allow for variations depending on the direction of applications the student chooses. Students choosing the applied mathematics program will participate in courses and seminars not only with pure mathematics students, but also with students in the sciences who have chosen an applied-mathematics emphasis in their own departments.

Expanded activity in applied mathematics is occurring within the Department of Mathematics and in the Division of Physical Sciences. Moreover, the Department recognizes that students enter applied mathematics from diverse backgrounds, and that some otherwise well-qualified students may require more than one year to satisfy the requirements described below.

To obtain the degree of Master of Science in mathematics under the auspices of CAMP, the candidate must meet the departmental requirements stated above, with the modification that the nine graduate courses to be passed are not restricted to those listed above. These nine courses must, however, include the analysis sequence, Mathematics 312, 313, 314. They must also include a second, approved three-quarter sequence of Mathematics courses. This will normally be a sequence of applied-mathematics courses emphasizing differential equations, ordinary and partial, and their numerical treatment. They may, however, consist of the algebra or topology sequence.

A third approved sequence of courses may be chosen from the offerings of the Mathematics Department of from those of another department. Possible choices of sequences outside the Mathematics Department are:

The requirements for the Ph.D. in applied mathematics under the auspices of the CAMP are the same as the departmental requirements listed above.

The Teaching Program

Most graduates of the Department go on to careers in teaching, and a structured teaching apprenticeship is an integral part of our program. All second-year students serve as apprentice teachers in an undergraduate mathematics course under the direction of a member of the faculty. Duties include class attendance, assistance in constructing and grading examinations, and supervised lecturing. Upon recommendation of the faculty mentor, third-year students are approved by the College to assume the position of Lecturer in the College. Qualified graduate students may continue as Lecturers, with a stipend furnished by the College, until the end of the fifth year of graduate study. No student teaches more than one course per quarter.

Students whose native language is not English must improve their language skills in order to teach in English, in a manner commensurate with University standards.

The Building

The Department of Mathematics is housed in Eckhart and Ryerson Halls, two interconnected buildings centrally located on the University of Chicago campus. These buildings also house the Statistics and Computer Science Departments. Eckhart Hall has a full Mathematics Library, as well as a computer center for use by mathematics graduate students. All graduate students in mathematics are given office space either in Eckhart Hall or in the Mathematics graduate students' building just across the street.

Admission

Admission to the Department of Mathematics is highly selective. Full academic transcripts and three letters of recommendation must be sent with the application. Although the Graduate Record Examination is not required for admission, it is highly recommended that applicants take both the general and the mathematics subject tests early in the Autumn. The application deadline is January 5. Because the first-year program consists of three course sequences beginning in the Autumn, it is our policy not to admit students mid-year. Exceptions are made only for those students who have already undertaken advanced studies of mathematics. The Department particularly welcomes applications from women and minorities.

Students whose native language is not English must take the TOEFL test and achieve a sufficiently high score to meet University and Departmental standards.

Financial Aid

Students who matriculate and maintain satisfactory academic progress may expect up to five years of financial support, including full tuition scholarship, a generous living stipend, and summer support, the last contingent on current levels of NSF support. Funding comes from the University of Chicago, the National Science Foundation, and the National Need Fellowship Program of the Department of Education.

The VIGRE program offers U.S. citizens and permanent residents some support without teaching duties.

After Graduate School

Most students who graduate with doctoral degrees go on to academic positions. In 2003-4, students went on to jobs at Cornell University, the Max-Planck Institute, Notre Dame, Ohio State University, University of Arizona, University of California at Berkeley, University of California at Davis, University of Illinois at Urbana-Champaign, University of Michigan and Wellesley College. In 2004-5, students went on to jobs at the Institute for Advanced Study, Loyola, MIT, Ohio State, Stanford, St. Katherine's, Tufts, University of California at Davis, University of Massachusetts and University of Oklahoma. In 2005-6, students took jobs at Brown, Ecole Polytechnique, Hanover, Harvard, Haverford, Institute for Advanced Study, MIT, New York University, Oxford, Purdue, Stanford, University of California at Riverside and Yale. Students who did not take academic jobs typically went into the private sector at places such as Credit Suisse or McKinsey & Co., or went to work for the government at places like the Department of Defense, the National Security Agency or Sandia National Labs.

Admissions information: admissions@math.uchicago.edu

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