Director of undergraduate studies Daniel Spielman, 201 AKW, 436-1264, daniel.spielman@yale.edu; senior coordinator: Andrew Barron, 24 Hillhouse Ave., 432-0634, andrew.barron@yale.edu

FACULTY ASSOCIATED WITH THE PROGRAM OF APPLIED MATHEMATICS

Professors

Donald Andrews (Economics, Statistics), James Aspnes (Computer Science), Andrew Barron (Statistics), Donald Brown (Economics), Joseph Chang (Statistics), Ronald Coifman (Mathematics, Computer Science), Gustave Davis (School of Medicine), Eric Denardo (Operations Research), Julie Dorsey (Computer Science), Stanley Eisenstat (Computer Science), Michael Fischer (Computer Science), John Hartigan (Emeritus) (Statistics), Theodore Holford (Public Health, Statistics), Roger Howe (Mathematics), Peter Jones (Mathematics), Gil Kalai (Computer Science, Mathematics), Ravindran Kannan (Computer Science), Willard Miranker (Computer Science), A. Stephen Morse (Computer Science, Electrical Engineering), Steven Orszag (Mathematics), Peter Phillips (Economics, Statistics), David Pollard (Statistics), Nicholas Read (Applied Physics, Physics), Vladimir Rokhlin (Computer Science, Mathematics), Holly Rushmeier (Computer Science), Herbert Scarf (Economics), Martin Schultz (Computer Science), Mitchell Smooke (Mechanical Engineering, Applied Physics), Daniel Spielman (Computer Science), Katepalli Sreenivasan (Adjunct) (Mechanical Engineering), Steven Zucker (Computer Science, Biomedical Engineering)

Associate Professors

Josephine Hoh (School of Medicine), Hannes Leeb (Statistics), Sekhar Tatikonda (Electrical Engineering, Statistics), Hongyu Zhao (School of Medicine)

Assistant Professors

Lisha Chen (Statistics), Eugenio Culurciello (Electrical Engineering), John Emerson (Statistics), Mokshay Madiman (Statistics)

J. W. Gibbs Assistant Professors

Yoel Shkolnisky, Amit Singer, Mark Tygert

Mathematical models are widely used throughout science and engineering in fields as diverse as physics, bioinformatics, robotics, image processing, and economics. Despite the broad range of applications, there are a few essential techniques used in addressing most problems. The Applied Mathematics major provides a foundation in these mathematical techniques and trains the student to use them in a substantive field of application.

The interdisciplinary major permits a great deal of flexibility in design. It is intended to appeal to students who wish to study the more mathematical aspects of science or engineering as well as those whose primary interest is in mathematics and statistics and who wish to become acquainted with applications. Core courses are drawn from Computer Science, Mathematics, Statistics, and Engineering and Applied Science. Courses applying mathematics may be drawn from participating programs in Astronomy, the biological sciences (Biology, Molecular Biophysics and Biochemistry), Chemistry, Computer Science, Economics, the various programs in engineering (Biomedical, Chemical, Electrical, Environmental, and Mechanical Engineering, as well as Applied Physics), Geology and Geophysics, Mathematics, Operations Research, Physics, and Statistics. The Applied Mathematics degree program requires a three-course concentration in a field in which mathematics is used.

Students may pursue a major in Applied Mathematics as one of two majors and can thereby equip themselves with mathematical modeling skills while being fully engaged in a field of application. In this case, the concentration requirement of the Applied Mathematics program is flexible in order to recognize the contribution of the other major. A two-course overlap is permitted in satisfying the requirements of the two majors.

Prerequisite and introductory courses. Multivariable calculus and linear algebra are required and should be taken before or during the sophomore year. This requirement may be satisfied by MATH 120a or b and MATH 222a or b or 225a or b, or equivalents. Computer programming skills are also required and may be acquired by taking ENAS 130b or CPSC 112a or b.

Details of individual programs must be worked out in consultation with the director of undergraduate studies, whose signed permission is required.

Requirements of the major for the B.A. degree program. The program requires eleven term courses beyond the prerequisites, including the senior seminar, comprising a coherent program:

1. A course in differential equations (ENAS 194a or b or MATH 246a or b)

2. A course in probability (STAT 241a or 238a)

3. A course in data analysis (STAT 361a or 230b)

4. A course in discrete mathematics (AMTH 244a or CPSC 202a)

5. A selection of at least three of the following: (a) a course in optimization (AMTH 237a) or linear programming (AMTH 235a); (b) stochastic processes (STAT 251b); (c) statistics (STAT 242b); (d) a course in algorithms (CPSC 365b) or numerical computation (ENAS 440a or CPSC 440b); (e) graphs and networks (AMTH 462a); (f) game theory (ECON 156b); (g) a course in signals, dynamics, applications of differential or difference equations, or time series (AMTH 342a, ENAS 391a, EENG 310a, 397b, 436b, 450a, or ECON 163b) or in applied functional analysis (AMTH 260a); (h) a course in image or vision analysis (BENG 445a or CPSC 475a) or information theory (AMTH 364b)

6. At least three courses in a field of concentration involving the application of mathematics to that field, at least two of which are advanced courses. Programs in science, engineering, computer science, statistics, economics, and operations research are natural sources of concentration. Alternatively, when two majors are undertaken, if the second major is in a participating program, then, recognizing that there can be an overlap of two courses, the student may take for the remaining course an additional choice relevant to the Applied Mathematics major such as listed in point 5 above or for the B.S. degree below. Details of a student's program to satisfy the concentration requirement must be worked out in consultation with, and with the approval of, the director of undergraduate studies

7. The senior seminar (AMTH 490b)

The B.S. degree program. In addition to the courses indicated for the B.A. major, the B.S. degree, which totals fourteen term courses beyond the prerequisites, must also include:

1. Topics in analysis (MATH 300b)

2. An additional course selected from the list in item 5 above

3. Another course numbered 300 or higher from the list above, or a mathematics, applied mathematics, statistics, or quantitative computer science or engineering course numbered 300 or higher, subject to the approval of the director of undergraduate studies

Alternatively, students may petition to receive a B.S. in Applied Mathematics by fulfilling the B.A. requirements in Applied Mathematics and the B.S. requirements in another program.

REQUIREMENTS OF THE MAJOR

Prerequisites:  MATH 120a or b and MATH 222a or b or 225a or b, or equivalents; ENAS 130b or CPSC 112a or b

Number of courses:  B.A.—11 term courses beyond prereqs (incl senior sem); B.S.—14 term courses beyond prereqs (incl senior sem)

Specific courses required:  B.A.—ENAS 194a or b or MATH 246a or b; STAT 238a or 241a; STAT 361a or 230b; AMTH 244a or CPSC 202a; B.S.—same, plus MATH 300b

Distribution of courses:  B.A.—at least 3 courses in a field of concentration concerning the application of math to that field, at least 2 of them advanced; 3 addtl courses as specified; B.S.—same, with 2 addtl courses as specified

Senior requirement:  Senior sem (AMTH 490b)

Unless otherwise indicated, courses in Applied Mathematics do not count toward the natural science requirement for the Class of 2008.

Websites of Universities and Colleges that offer Applied Mathematics