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Applied Mathematics

ADDITIONAL INFORMATION

Applied Mathematics courses

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   Andrew Barron (Statistics), Donald Brown (Economics, Mathematics), Joseph Chang (Statistics), Ronald Coifman (Mathematics), Gustave Davis (School of Medicine), Eric Denardo (Operations Research), Stanley Eisenstat (Computer Science), Michael Fischer (Computer Science), Igor Frenkel (Mathematics), Roger Howe (Mathematics), Peter Jones (Mathematics), A. Stephen Morse (Electrical Engineering), David Pollard (Statistics), Nicholas Read (Physics, Applied Physics), Vladimir Rokhlin (Computer Science, Mathematics), Herbert Scarf (Economics), Peter Schultheiss (Emeritus) (Electrical Engineering), Martin Schultz (Computer Science), Mitchell Smooke (Mechanical Engineering, Applied Physics), Daniel Spielman (Computer Science), Van Vu (Mathematics), Günter Wagner (Ecology & Evolutionary Biology), John Wettlaufer (Geology & Geophysics, Physics), Huibin Zhou (Statistics), Steven Zucker (Computer Science, Biomedical Engineering)

Associate Professors   John Emerson (Statistics), Josephine Hoh (Epidemiology & Public Health), Sekhar Tatikonda (Electrical Engineering, Statistics)

Assistant Professors   Lisha Chen (Statistics), Thierry Emonet (Molecular, Cellular, & Developmental Biology, Physics), Mokshay Madiman (Statistics)

J. W. Gibbs Assistant Professors   Yael Algom-Kfir, Dan Kushnir, Adam Marcus, Neta Rabin, Andrew Wells

Lecturer   Matthew Hirn

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 Applied Physics, Astronomy, the biological sciences (Ecology and Evolutionary Biology, Molecular Biophysics and Biochemistry, and Molecular, Cellular, and Developmental Biology), Chemistry, Computer Science, Economics, the various programs in engineering (Biomedical, Chemical, Electrical, Environmental, and Mechanical Engineering), Geology and Geophysics, Mathematics, Operations Research, Physics, Political Science, 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 120 and MATH 222 or 225, or equivalents. It may also be satisfied by MATH 230, 231. Computer programming skills are also required and may be acquired by taking ENAS 130 or CPSC 112.

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 project, comprising a coherent program:

  1. A course in differential equations (ENAS 194 or MATH 246)
  2. A course in probability (STAT 241 or 238)
  3. A course in data analysis (STAT 361 or 230)
  4. A course in discrete mathematics (AMTH 244 or CPSC 202)
  5. Courses in at least three of the following areas: (a) optimization: AMTH 235, 237; (b) probability and statistics: STAT 242, 251, 312, 364, ECON 136, ENAS 496; (c) partial differential equations and analysis: MATH 247, 250, 260, 300, 301, 310; (d) algorithms and numerical methods: CPSC 365, 440, ENAS 440, 441; (e) graph theory: AMTH 462; (f) mathematical economics: ECON 350, 351; (g) electrical engineering: EENG 397, 436, 442, STAT 364; (h) data mining and machine learning: STAT 365, CPSC 445; (i) biological modeling and computation: AMTH 465, CPSC 475, BENG 445, ENAS 391; (j) physical sciences and engineering: MENG 280, 285, 361, 383, 463, 469, CENG 301, 315, ASTR 320, 420, G&G 322, 323, 421, PHYS 343, 401, 402, 410, 420, 430, 440, 442, 460, APHY 439, 448
  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 approved by, the director of undergraduate studies
  7. Senior seminar (AMTH 490) or special project completed during senior year (AMTH 491)

A maximum of one course credit taken Credit/D/Fail may be counted toward the requirements of the major.

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

  1. Topics in analysis (MATH 300) or introduction to analysis (MATH 301); the course selected may not be counted toward the area requirement for the major (see item 5 above)
  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 course numbered 300 or higher in mathematics, applied mathematics, statistics, or quantitative computer science or engineering, 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 120 and MATH 222 or 225, or equivalents; ENAS 130 or CPSC 112

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

Specific courses required   B.A.—ENAS 194 or MATH 246; STAT 241 or 238; STAT 361 or 230; AMTH 244 or CPSC 202; B.S.—same, plus MATH 300 or 301

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

Substitution permitted   MATH 230, 231 for mathematics prerequisites

Senior requirement   Senior sem (AMTH 490) or special project (AMTH 491)