The Department of Mathematics

TThe Department of Mathematics provides a comprehensive education in mathematics which takes place in a stimulating environment of intensive research activity. The graduate program includes both pure and applied areas of mathematics. Ten to fifteen graduate courses are offered every quarter. Several seminars take place every afternoon. There is an active visitors’ program with mathematicians from around the world coming for periods from a few days to a few months. There are four major lecture series each year: the Adrian Albert Lectures in Algebra, the Antoni Zygmund and Alberto Calderón Lectures in Analysis, the Unni Namboodiri Lectures in Topology, and the Charles Amick Lectures in Applied Mathematics. The activities of the department take place in Eckhart and Ryerson Halls. These contiguous buildings are shared with the Departments of Statistics and Computer Science. The Department of Mathematics and the Department of Computer Science have several joint appointments, and they coordinate their activities. The Department of Mathematics also has joint appointments and joint activity with the Department of Physics.

Graduate Degrees in Mathematics

The graduate program of the Department of Mathematics is oriented towards students who intend to earn a Ph.D. in mathematics on the basis of work done in either pure or applied mathematics. The department also offers the degree of Master of Science in mathematics, which is acquired as the student proceeds on to the Ph.D. degree. Students are not admitted with the Master of Science degree as their final objective. In addition, the department offers a separate Master of Science in Financial Mathematics degree program which is taught in the evenings. See "The Degree of Master of Science in Financial Mathematics"below for more information.

The divisional requirements for these degrees can be found in the section on the Division of the Physical Sciences in these Announcements. The departmental requirements for students choosing the program in applied mathematics are described below under the heading, “Graduate Degrees in Applied Mathematics.” Otherwise, the requirements are as follows.

The Degree of Master of Science

The candidate must pass, to the instructor’s satisfaction, the nine basic first-year graduate courses in the areas of algebra (Mathematics 32500, 32600, 32700), analysis (Mathematics 31200, 31300, 31400), and topology (Mathematics 31700, 31800, 31900). With the approval of the department, the exceptionally well prepared student may place out of one or more of these courses, and substitute a more advanced course.

If any of these courses are not passed to the instructor’s satisfaction, the student will be required to take an oral exam in those subject areas before receiving the Master of Science degree.

The student must also pass a reading exam (in a form approved by the department) in French, German or Russian.

The Degree of Doctor of Philosophy

For admission to candidacy for the Doctor of Philosophy, an applicant must demonstrate the ability to meet both the divisional requirements and the departmental requirements for admission.

The applicant must satisfy the above mentioned requirements for the degree of Master of Science in mathematics.

The applicant must satisfactorily complete an oral “topic presentation.” This presentation covers material that is chosen by the student in consultation with members of the department and is studied independently. The topic presentation is normally made by the end of the student’s second year of graduate study.

The applicant must also successfully complete the department’s program of preparatory training in the effective teaching of mathematics in the English language at a level commensurate with the level of instruction at the University of Chicago.

After successful completion of the topic presentations, the student is expected to begin research towards the dissertation under the guidance of a member of the department. The remaining requirements are to: (1) complete a dissertation containing original, substantial, and publishable mathematical results; (2) present the contents of the dissertation in an open lecture; and (3) pass an oral examination based both on the dissertation and the field of mathematics in which it lies.

Graduate Degrees in Applied Mathematics

The Department of Mathematics, through the Computational and Applied Mathematics Program (CAMP), offers interdisciplinary programs in applied mathematics leading to S.M. 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 the 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 31200, 31300, 31400. 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 Department of Mathematics or from those of another department. Possible choices of sequences outside the Department of Mathematics are Astronomy & Astrophysics 30100, 30200, 30300; Chemistry 36100, 36200, 36300; Economics 30500, 30600, 30700; Geophysical Sciences 35100, 35200, 35300; Physics 31500, 32300, 32400.

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

The Degree of Master of Science in Financial Mathematics

The program on financial mathematics is designed to produce graduates with a good understanding of the theoretical background of pricing models for financial derivatives, but more importantly a real understanding of the underlying assumptions and an ability to critically ascertain the applicability and limitations of the various models. A significant part of the program will be taught by professionals from the financial industry and will be devoted to examining how models behave in practice under a variety of market conditions, to examine how realistic the underlying assumptions are and to understand what happens when these assumption are violated. Students will learn to use the models to set up hedges and to evaluate the effectiveness of these hedges by simulating various market conditions.

The program consists of four components: Mathematics, Probability Theory, Economics, and Financial Applications and Simulations.

The Mathematics component runs over three quarters, Probability Theory over two quarters and Economics over one quarter. The Financial Applications and Simulations is a three quarter component. Courses in each component meet for three hours per week except for the courses in the Financial Applications component which will meet for four hours for a total of ten hours of instruction per week. The Mathematics and Probability Theory will be taught by faculty members from the Departments of Mathematics and Statistics, respectively. The Economics course will be taught by a faculty member from the Department of Economics. The Financial Applications courses will be taught by professionals from financial institutions and will also include a computer lab.

The contents and curriculum for the program has been worked out jointly by faculty members at the University and by practitioners in the field to insure the relevance of the material. The teaching of the program relies heavily on the use of computer simulations to illustrate the material. This both makes it possible to cover more material and teaches students to implement the theory at every stage.

Various software packages are licensed to the program and will be provided free of charge for the course work. Course material and assignments will be available and submitted on-line.

The program has a nine quarter course requirement for obtaining the Master of Science degree.

The program is structured to allow part-time enrollment to complete the program over two or three years. The courses will be taught evenings at the main campus of the University located in Hyde Park.

The requirements for acceptance to the program are a solid undergraduate background in mathematics, ideally a major in mathematics or science/engineering, with some background also in probability theory. Some experience in C/C++ programming will also be useful. Persons with practical experience in the financial industry but with less of a mathematical background will be considered but may be required to acquire additional skills in mathematics.

This text was last revised on 9/02/2003.