Graduate School of Arts and Sciences Bulletin of Yale University
 
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Mathematics

10 Hillhouse, 432.4172
M.S., M.Phil., Ph.D.

Chair
Gregory Margulis

Director of Graduate Studies
Gregg Zuckerman (423 DL, 432.4198, zuckerman-gregg@yale.edu)

Professors
Richard Beals, Donald Brown (Economics), Andrew Casson, Ronald Coifman, Walter Feit, Michael Frame, Igor Frenkel, Howard Garland, Roger Howe, Peter Jones, Ravidran Kannan (Computer Science), Serge Lang, Ronnie Lee, Douglas Lind (Visiting), Benoit Mandelbrot, Gregory Margulis, Vincent Moncrief (Physics), Gregory Moore (Physics), Steven Orszag, Ilya Piatetski-Shapiro, David Pollard (Statistics), Vladimir Rokhlin (Computer Science), Katepalli Sreenivasan (Mechanical Engineering), Efim Zelmanov, Gregg Zuckerman

Gibbs Instructors
David Fisher, Greg Friedman, Aleksei Kazarnovskii-Krol, Irina Kogan, Anna Mazzucato, Gabriel Rosenberg, Olivier Schiffmann, Agata Smoktunowicz, Jeb Willenbring, Catalin Zara

Fields of Study
Fields include real analysis, complex analysis, functional analysis, classical and modern harmonic analysis; linear and nonlinear partial differential equations; dynamical systems and ergodic theory; homological algebra; homotopy theory; the theory of fiber bundles; finite and infinite groups; Lie algebras, Lie groups and discrete subgroups; representation theory; automorphic forms, L-functions; algebraic number theory and algebraic geometry; mathematical physics, relativity; differential topology and algebraic K-theory; numerical analysis; combinatorics and discrete mathematics.

Special Requirements for the Ph.D. Degree
All students are required to: (1) complete eight term courses at the graduate level, at least two with Honors grades; (2) demonstrate a reading knowledge of two of the following languages: French, German, or Russian; (3) pass qualifying examinations on their general mathematical knowledge; (4) submit a dissertation prospectus; (5) participate in the instruction of undergraduates; (6) be in residence for at least three years; and (7) complete a dissertation that clearly advances understanding of the subject it considers. The normal time for completion of the Ph.D. program is four years. Requirement (1) normally includes basic courses in algebra, analysis, and topology; these should be taken during the first year. The first language examination must be completed by the beginning of the third year of study, the second no later than the end of that year. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term, at intervals of about one month. All qualifying examinations must be taken by the end of the third term. The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)-(6) and obtaining an adviser.

Honors Requirement
Students must meet the Graduate School's Honors requirement by the end of the fourth term of full-time study.

Master's Degrees
M.Phil. In addition to the Graduate School requirements, a student must undertake a reading program of at least two terms' duration in a specific significant area of mathematics under the supervision of a faculty adviser and demonstrate a command of the material studied during the reading period at a level sufficient for teaching and research.

M.S. (en route to the Ph.D.). A student must complete six term courses with at least one Honors grade, pass one language examination, perform adequately on the general qualifying examination, and be in residence at least one year.

Master's Degree Program. Students may also be admitted to a terminal master's degree program that has the same requirements as the M.S. en route to the Ph.D., except that a sophisticated computer language may be substituted for French, German, or Russian in fulfillment of the language requirement. Full-time students must complete the program in two years, part-time students in three years. No financial aid is available.

Program materials are available upon request to the Director of Graduate Studies, Mathematics Department, Yale University, PO Box 208283, New Haven CT 06520-8283.

Courses
MATH 500au, Modern Algebra. Agata Smoktunowicz. Mon/Wed/Fri 1.30-2.20

MATH 515bu, Intermediate Complex Analysis. Gregg Zuckerman. Tues/Thurs 11.30-12.45

MATH 520au, Measure Theory and Integration. Gabriel Rosenberg. Tues/Thurs 1-2.15

MATH 525bu, Introduction to Functional Analysis. Staff. Tues/Thurs 1-2.15

MATH 544a, Introduction to Algebraic Topology. Staff. Mon/Wed/Fri 10.30-11.20

Each term between ten and twelve advanced courses in different fields of study are offered by junior and senior faculty. In addition to the graduate courses, there are regular weekly seminars in algebra, analysis, topology, discrete mathematics, Lie groups, applied mathematics, and mathematical physics.

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