Academics

Applied Mathematics


Applied Mathematics Graduate Program


The academic program in applied mathematics, for students registered in the Department of Applied Physics and Applied Mathematics, emphasizes applied mathematics research in nonlinear dynamics, fluid mechanics, and scientific computation with a current emphasis on geophysical, biophysical, and plasma physics applications.

Applied mathematics deals with the use of mathematical concepts and techniques in various fields of science and engineering. Historically, mathematics was first applied with great success in astronomy and mechanics. Then it developed into a main tool of physics, other physical sciences, and engineering. It is now important in the biological, geological, and social sciences. With the coming of age of the computer, applied mathematics has transcended its traditional style and now assumes an even greater importance and a new vitality.

Compared with the pure mathematician, the applied mathematician is more interested in problems coming from other fields. Compared with the engineer and the physical scientist, he or she is more concerned with the formulation of problems and the nature of solutions. Compared with the computer scientist, he or she is more concerned with the accuracy of approximations and the interpretation of results. Needless to say, even in this age of specialization, the work of mathematicians, scientists, and engineers frequently overlaps. Applied mathematics, by its very nature, has occupied a central position in this interplay and has remained a field of fascination and excitement for active minds.

back to top

M.S. Program in Applied Physics / Concentration in Applied Mathematics


Admission

A strong background in undergraduate mathematics is required of all applicants.


M.S. Program Requirements

This 30-point program leads to a professional M.S. degree. Students must complete five core courses and five electives. The core courses provide a student with a foundation in the fundamentals of applied mathematics and contribute 15 points of graduate credit toward the degree. Students must complete five of the following seven courses:

  • APMA E6301: Analytic methods for partial differential equations
  • APMA E6302: Numerical analysis for partial differential equations

A student must select five elective courses from those listed below (or any of those not used to satisfy the core requirements from the list above) for a total of 15 points of graduate credit. Additional courses not listed below can be applied toward the elective requirements, subject to the approval of the faculty adviser. Computer science elective courses include:

  • C0MS W4236: Introduction to computational complexity

Industrial engineering/operations research elective courses include:

  • IEOR E4004: Introduction to operations research: deterministic models
  • IEOR E4106: Introduction to operations research: stochastic models
  • SIE0 W4150: Introduction to probability and statistics
  • IEOR E4403: Advanced engineering and corporate economics
  • IEOR E4700: Introduction to financial engineering

Other elective courses include:

  • MSAE E4215: Mechanical behavior of structural materials


back to top

Ph.D. Program in Applied Mathematics


Admission

The requirements listed below are special to the University Committee on Applied Mathematics and must be read in conjunction with the general requirements of the Graduate School of Arts and Sciences.

The applicant must be admitted in the usual way by one of the participating departments. (Students applying through the Engineering School are admitted under the aegis of the Department of Applied Physics and Applied Mathematics. In this case the M.S. degree, required for Ph.D. studies, is taken in applied physics but is specifically tailored towards the student’s interest in applied mathematics.) A strong background in undergraduate mathematics is required of all applicants.
Interested students should consult a member of the University Committee on Applied Mathematics at an early stage of their graduate career, or contact the chairman of the committee, Professor David Keyes.


Ph.D. Program Requirements


The Departments of Applied Physics and Applied Mathematics, Astronomy, Chemistry, Geological Sciences, Mathematics, and Physics cooperate in offering a doctoral program in applied mathematics. It is an interdepartmental Ph.D. option through the Graduate School of Arts and Sciences. The program focuses on the mathematics originating from and applied to the various fields of physical sciences and engineering, and it offers the students from the cooperating departments a sharper mathematical focus. The student must meet the minimum formal Ph.D. requirements set by the Department in which he/she is registered. Additional academic requirements will be set by the committee upon the recommendation of the student's advisor.

The M.S. degree requires the successful completion of 30 points of approved course work in basic and applied mathematics. Requirements for the M.Phil. degree include successful completion of a 30 point program beyond the M.S., a written qualifying examination, an oral exam and a thesis proposal evaluation. In addition to fulfilling the M.Phil. requirements, Ph.D. candidates must submit an approved dissertation, and complete the University residence requirements.

Specific course requirements are determined in consultation with the program advisor. Courses suggested for preparation at the level of the general, and subspecialty parts of the written qualifying examination are listed in the qualifying examination memorandum. Students interested in Atmospheric Science should consult with Professors Polvani or Sobel for additional course suggestions not listed below.


Core Courses



Related Courses of Specialization



Applied Mathematics Faculty

David E. Keyes (Chair)
Guillaume Bal
Daniel Bienstock, IEOR and APAM
Mark A. Cane, EE and APAM
C. K. Chu, Emeritus
Pierre Gentine
Lorenzo Polvani
Christopher Scholz, EE and APAM
Adam H. Sobel
Marc Spiegelman
Michael I. Weinstein
Chris H. Wiggins


Below is a list of other faculty members that can also act as research advisors to AM graduate students.

Larry Abott, Neuroscience
Brian Cairns, NASA/GISS and Adjunct Assoc. Professor, APAM
Vittorio Canuto, NASA/GISS and Adjunct Professor, APAM
Barbara Carlson, NASA/GISS and Adjunct Professor, APAM
Rama Cont, IEOR
Panagiota Daskalopoulos, Mathematics
Anthony Del Genio, NASA/GISS and Adjunct Assoc. Professor, APAM
Julien Dubedat, Mathematics
Donald Goldfarb, IEOR
Eitan Grinspun, Computer Science
Timothy Hall, NASA/GISS and Adjunct Professor, APAM
Ron Miller, NASA/GISS and Adjunct Professor, APAM
Ben O'Shaughnessy, Chemical Engineering
Ovidiu Savin, Mathematics
Bruce Shaw, LDEO
Edward Spiegel, Astronomy

    back to top