Graduate Program

General Information

Fields of Study

The Graduate Program in Applied Mathematics comprises mathematics and its applications to a range of areas, to the mathematical sciences (including computer science and statistics), and to the other sciences and engineering. Topics covered by the program include classical and modern applied harmonic analysis, linear and nonlinear partial differential equations, numerical analysis, scientific computing and applications, discrete algorithms, combinatorics and combinatorial optimization, graph algorithms, geometric algorithms, discrete mathematics and applications, statistical theory and applications, probability theory and applications, information theory, econometrics, financial mathematics, statistical computing, and applications of mathematical and computational techniques to fluid mechanics, combustion, and other scientific and engineering problems.

Requirements for the Ph.D. in Applied Mathematics

All students are required to: (1) complete 12 term courses (including reading courses) at the graduate level, at least two with Honors grades; (2) pass a qualifying examination on their general applied mathematical knowledge (in algebra, analysis, and probability and statistics) by the end of their second year; (3) submit a dissertation prospectus; (4) participate in the instruction of undergraduates; (5) be in residence for at least three years; and (6) 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 four core courses in each of the methods of applied analysis, numerical computation, algorithms, and probability; these should be taken during the first year. The qualifying examination is normally taken by the end of the third term and will test knowledge of the core courses as well as more specialized topics. 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)-(5) and obtaining an adviser.

In addition to the above, all first year students (including terminal MS students) must successfully complete one course on the responsible conduct of research (e.g. MATH 991 or CPSC 991) and AMTH 525 Seminar in Applied Mathematics.

Master’s Degrees

M. Phil. The Master of Philosophy is awarded en route to the Ph.D. The minimum general requirements for this degree are that a student shall have completed all requirements for the Ph.D. except the prospectus and dissertation. Students will not generally have satisfied the requirements for the Master of Philosophy until after two years of study, except where graduate work done before admission to Yale has reduced the student’s graduate course work at Yale. In no case will the degree be awarded for less than one year of residence in the Yale Graduate School.

M.S. The Master of Science in Applied Mathematics is offered only in the Master’s Degree Program in Applied Mathematics, decribed as follows:

Master’s Degree Program. Students may also be admitted to a terminal master’s degree program. This program is normally completed in one year, but a part-time program may be spread over as many as four years. To qualify for the M.S., the student must pass ten graduate-level courses. Courses taken as part of the M.S. program must be preapproved by the director of graduate studies to ensure that a suitable distribution of topics is covered. The Master’s Degree Program does not offer financial aid.

Honors Requirement for the Ph.D.

To meet the minimum Graduate School quality requirement for the Ph.D., students must achieve the grade of Honors in at least one full-year or two full-term graduate courses, taken after matriculation in the Graduate School and during the nine-month academic year. The Honors requirement must be met in courses other than those concerned exclusively with dissertation research and preparation.

A student who has not met the Honors requirement at the end of the fourth term of full-time study will not be permitted to register for the fifth term. In exceptional circumstances, the director of graduate studies may petition the degree committee, through the appropriate dean, that a student who has not met the Honors requirement be permitted to continue study. Such a petition should be made before the end of the fourth term of study in time to be considered by the degree committee at its meeting that term.

Financial Support for the Ph.D. student

Yale provides a stipend as well as full tuition and medical coverage for the first four years of the Ph.D. program in Applied Mathematics. The university offers the preceding support to each student for the first three terms of the four-year program. During the summers and beginning with the fourth term, the student is expected to have found an adviser with research funds to support the student’s stipend, tuition and medical coverage.

Teaching Requirement

Each student is expected to have taught as a teaching fellow in two undergraduate courses by the end of the fourth term.

Required Examinations / Admissions

All applicants are required to submit official results of the Graduate Record Examination (GRE) General Test, which is administered in the United States and abroad by the Educational Testing Service (ETS). This examination should be taken no later than the November testing date. The GRE Subject Test is encouraged.

Additionally, the Test of English as a Foreign Language (TOEFL) is required of all international applicants whose native language is not English. This requirement is waived only for international applicants who have successfully attended, for at least two years, a university where English is the primary language of instruction. The Educational Testing Service also administers the TOEFL.

Applicants whose native language is not English must present evidence of proficiency in English by satisfactorily completing the Test of English as a Foreign Language (TOEFL), which is administered by ETS. This examination should be taken no later than the November testing date. The TOEFL requirement is waived only for applicants who have successfully attended for at least two years a university where English is the language of instruction.

Students who do not demonstrate sufficient proficiency in English may be restested and/or asked to take courses in English for speakers of other languages. A high level of proficiency in English is required in order for students to serve as teaching fellows and fulfill the teaching requirement.

Official score reports must be submitted for all required examinations. Ask the Educational Testing Service to report your scores to the Yale Graduate School.

Program materials and additional information concerning degrees offered and admissions requirements are available upon request to the Office of Admissions, Graduate School of Arts and Sciences, Yale University, PO Box 208323, New Haven CT 06520-8323. Or contact them by email at <>.