The Master of Science in Scientific Computing

The Program

The departments of mathematics and computer science at NYU's Courant Institute of Mathematical Sciences offer a master's degree in scientific computing. The program, which began in the fall semester of 1995, provides broad yet rigorous training in areas related to scientific computing, including modern computing tools and methods, and the numerical and mathematical analysis arising in various applications.

The program accommodates both full-time and part-time students, with most courses scheduled to meet in the evening. The program is self-contained and terminal, providing a complete set of employment skills in a field where the need is greater than the supply. Within the master's program, two concentrations are available: (1) data science and (2) modeling and simulation. The concentration in modeling and simulation focuses on classical computational science, as used in engineering design, development, and optimization. The concentration in data science focuses on the analysis of data, including big data and the associated computational, mathematical, and statistical methodologies.

Scientific Computing: Overview

Scientific computing is an indispensable part of almost all scientific investigation and technological development at universities, government laboratories, and within the private sector. Typically a scientific computing team consists of several people trained in some branch of mathematics, science, statistics, or engineering. What is often lacking is expertise in modern computing tools such as visualization, modern programming paradigms, and Unix tools. The master's program in scientific computing aims to satisfy these needs, without omitting basic training in numerical analysis and computer science. Many graduates of this program work at technologically advanced institutions, especially in research and development, where their skills and experience complement those without interdisciplinary degrees. The program is also open to students who will go on to pursue doctoral studies in computer science, mathematics, or statistics.

The master's program in scientific computing focuses on the mathematics and computer science related to advanced computer modeling and simulation (for those concentrating on modeling and simulation) and to data analytics (for those concentrating on data science). The program is similar in structure to terminal master's programs in engineering, combining classroom training with practical experience. The coursework ranges from foundational mathematics and fundamental algorithms to such practical topics as data visualization and software tools. Electives encourage the exploration of specific application areas such as mathematical and statistical finance, applications of machine learning, fluid mechanics, finite element methods, and biomedical modeling. The program culminates in a master's project or thesis, which serves to integrate the classroom material.

Admission Requirements

Students accepted into the program should have taken at least three semesters of Calculus, as well as linear algebra (or its equivalent, e.g., econometrics, or through work experience). Experience with programming in a high-level language, not necessarily through coursework, is also required. Advanced Calculus, differential equations, and coursework in data structures are desirable. A strong background in linear algebra is of particular importance, with mastery of the following subjects:

Gaussian elimination, existence of solutions to systems of linear equations, matrix rank, determinant, and inverse.
Vector spaces, linear (in)dependence, bases, vector norms, inner products, and orthogonality.
Eigenvalues and eigenvectors, diagonalization and similarity transformations, and special matrices: normal, symmetric, Hermitian, orthogonal, and unitary matrices.

Students with promise who lack the requisite mathematical background should take the course MATH-GA 1002 Multivariable Calculus and/or an undergraduate course on linear algebra before applying for admission to the master's program. (Note that the course MATH-GA 1002 Multivariable Calculus does not carry credit toward completion of this master's degree.)

The deadlines for application to the program are June 1 for the fall semester and November 1 for the spring. The program admits students both on a full-time and on a part-time basis. The application process takes place online via the Graduate School of Arts and Sciences; please visit the Graduate School Admissions site.

For more information, please contact us at

Office of Admissions and Student Affairs

Department of Mathematics

Courant Institute of Mathematical Sciences

251 Mercer Street

New York, NY 10012-1185

Tel. (212) 998-3238

Fax (212) 995-4121

e-Mail: admissions@math.nyu.edu

e-Mail: arnon@cims.nyu.edu

web page: http://www.math.nyu.edu

Degree Requirements

Concentration in Modeling and Simulation

A candidate for a master's degree in scientific computing concentrating in modeling and simulation must accrue the following:

30 points of course credit (10 courses) comprised of

4 core courses (12 points) in mathematics
4 core courses (12 points) in computer science
2 elective courses (6 points)

6 points of credit from writing a master's thesis

33 points of course credit (11 courses) comprised of

4 core courses (12 points) in mathematics
4 core courses (12 points) in computer science
3 elective courses (9 points)

3 points of credit from the master's project capstone course.

As indicated above, the student chooses between (1) writing a master's thesis and (2) taking an extra elective course as well as the project capstone course.

Concentration in Data Science

A candidate for a master's degree in scientific computing concentrating in data science must accrue the following:

33 points of course credit (11 courses) comprised of

3 core courses (9 points) in mathematics
3 core courses (9 points) in computer science
5 elective courses (15 points)

3 points of credit from the master's project capstone course

33 points of course credit (11 courses) comprised of

2 core courses (6 points) in mathematics
3 core courses (9 points) in computer science
6 elective courses (18 points)

3 points of credit from the master's project capstone course.

As indicated above, the student chooses between (1) taking the core course MATH-GA 2043 Scientific Computing and (2) taking both core courses MATH-GA 2010 Numerical Methods I and MATH-GA 2020 Numerical Methods II.

Core Courses

Concentration in Modeling and Simulation

The following are the four core courses in mathematics for the concentration in modeling and simulation:

MATH-GA 2010 Numerical Methods I (fall semester)
MATH-GA 2020 Numerical Methods II (spring semester)
MATH-GA 2701 Methods of Applied Mathematics (fall semester)
MATH-GA 2702 Fluid Dynamics (fall semester)

The following are the four core courses in computer science for the concentration in modeling and simulation:

CSCI-GA 1170 Fundamental Algorithms (fall, spring and summer terms)
CSCI-GA 2110 Programming Languages (fall, spring, and summer terms)
CSCI-GA 3033 Open Source Tools (fall term)
CSCI-GA 2270 Computer Graphics (spring term)

Concentration in Data Science

The following are the core courses in mathematics for the concentration in data science:

MATH-GA 2962 Mathematical Statistics (spring semester)
MATH-GA 2043 Scientific Computing (fall and spring semesters)
MATH-GA 2010 Numerical Methods I (fall semester)
MATH-GA 2020 Numerical Methods II (spring semester)

The following are the three core courses in computer science for the concentration in data science:

CSCI-GA 1170 Fundamental Algorithms (fall, spring and summer terms)
CSCI-GA 2565 Machine Learning (fall term)
CSCI-GA 3033 Open Source Tools (fall term)

With approval of the director of the program, students with sufficient preparation may be able to waive certain core courses. Should any core course not be available for any reason, a re-arrangement of the curriculum can be discussed with the director of the program.

The departments of mathematics and computer science publish annual brochures describing all courses offered each year. Students should consult these lists of course offerings to determine the availability of desired courses.

The Capstone Project

The master's program culminates in either a capstone project or a master's thesis (see below). The capstone project course is usually taken during the final year of study. During the project, students go through the entire process of solving a real-world problem, from collecting and processing data to designing and fully implementing a solution. The problems and data sets come from settings identical to those encountered in industry, academia, or government.

The Computational Master's Thesis

An alternative to the capstone project is the master's thesis. Preparing the master's thesis normally occurs in the final year of study. The thesis requires the approval of the director of the master's program; a member of the faculty supervises the thesis. Writing a master's thesis requires registration for six points of coursework, designated MATH-GA 3771, 3772, 3773, or 3774 Independent Study.

The master's thesis need not be as original or substantial as a doctoral dissertation, but it should include several elements:

it should involve a substantial scientific computation
it should use modern techniques of software development
it should employ computer graphics, visualization, and/or computer-assisted publication facilities.

Some recent thesis titles include

“Investigation of Computational and Visualization Methods for the Incompressible Navier-Stokes Equations,” Langston, Matthew Harper

“Branching and Capping of a Femur End,” Lord, Dan

“Spiral Waves in a Reaction-Diffusion System,” Mao, Yiwen

“Axisymmetric Acoustic Scattering by Interpolation,” Meyer, Perrin

“Novel Sampling Algorithms for Biomolecular Simulations,” Minary, Peter

“Region Explorer: Software for Region of Interest Analysis of FMRI Data,” Pasley, Brian

“Solar System Simulation with 3-D Visualization,” Tumolo, Greg

Computing Facilities

The Courant Institute makes available for graduate training and coursework a network of workstations maintained by systems administrators. All graduate students have computer accounts for the duration of their studies. NYU also runs a high-performance computing center with both shared-memory and distributed-memory computers.

Faculty

Many members of the departments of mathematics and computer science have research interests bearing on scientific computing. The list includes

Marsha J. Berger. B.S. 1974, Binghamton; M.S. 1978, Ph.D. 1982, Stanford. Research interests: computational fluid dynamics, adaptive mesh refinement, parallel computing.

Yu Chen. B.S. 1982, Tsinghua; M.S. 1988, Ph.D. 1991, Yale. Research Interests: numerical scattering theory, ill-posed problems, scientific computing.

Aleksandar Donev. B.S. 2001, Michigan State; Ph.D. 1991, Yale. Research interests: multi-scale methods, fluctuating hydrodynamics, coarse-grained particle methods, jamming and packing.

Davi Geiger. B.S. 1980, Pontifica (Brazil); Ph.D. 1990, MIT. Research interests: computer vision, information theory, medical imaging, and neuroscience.

Jonathan B. Goodman. B.S. 1977, MIT; Ph.D. 1982, Stanford. Research interests: numerical analysis, fluid dynamics, computational physics, partial differential equations.

Leslie Greengard. B.A. 1979, Wesleyan; M.S. 1987, Yale School of Medicine; Ph.D. 1987, Yale. Research interests: scientific computing, fast algorithms, potential theory.

Yann LeCun. B.S. 1983, ESIEE (Paris); D.E.A. 1984, Ph.D. 1987, Pierre and Marie Curie University (Paris). Research interests: machine learning.

Andrew Majda. B.S. 1970, M.S. 1971, Ph.D. 1973, Stanford. Research interests: modern applied mathematics, atmosphere/ocean science, turbulence, statistical physics.

David W. McLaughlin. B.S. 1966, Creighton; M.S. 1969, Ph.D. 1971, Indiana. Research interests: applied mathematics, nonlinear wave equations, neural science.

Bhubaneswar Mishra. B.S. 1980, India Institute of Technology, Kharagpur; M.S. 1982, Ph.D. 1985, Carnegie-Mellon. Research interests: robotics, mathematical and theoretical computer science.

Michael L. Overton. B.S. 1974, British Columbia; M.S. 1977, Ph.D. 1979, Stanford. Research interests: numerical linear algebra, optimization, linear and semidefinite programming.

Kenneth Perlin. B.A. 1979, Harvard; M.S. 1984, Ph.D. 1986, NYU. Research interests: computer graphics, simulation, computer-human interfaces, multimedia.

Charles S. Peskin. B.A. 1968, Harvard; Ph.D. 1972, Yeshiva. Research interests: physiology, fluid dynamics, numerical methods.

Aaditya V. Rangan. B.A. 1999, Dartmouth; Ph.D. 2003, Berkeley. Research interests: large-scale scientific modeling of physical, biological, and neurobiological phenomena.

Tamar Schlick. B.S. 1982, Wayne State; M.S. 1984, Ph.D. 1987, NYU. Research interests: mathematical biology, numerical analysis, computational chemistry.

Michael J. Shelley. B.S. 1981, Colorado; M.S. 1984, Ph.D. 1985, Arizona. Research interests: scientific computation, fluid dynamics, neuroscience.

Eero Simoncelli. B.A. 1984, Harvard; M.S. 1988, Ph.D. 1993, MIT. Research interests: image processing, computational neuroscience, computer vision.

Esteban Tabak. Bach. 1988, Buenos Aires; Ph.D. 1992, MIT. Research interests: fluid dynamics, conservation laws.

Mark Tygert. B.A. 2001, Princeton; Ph.D. 2004, Yale. Research interests: statistics; computational science and engineering, particularly numerical analysis.

Olof B. Widlund. C.E. 1960, Tekn. L. 1964, Technology Institute, Stockholm; Ph.D. 1966, Uppsala. Research interests: numerical analysis, partial differential equations, parallel computing.

Margaret H. Wright. B.S. 1964, M.S. 1965, Ph.D. 1976, Stanford. Research interests: mathematical optimization, numerical methods, nonlinear programming.

Denis Zorin. B.S. 1991, Moscow Institute of Physics and Technology; M.S. 1993, Ohio State; Ph.D. 1997, Caltech. Research interests: computer graphics, geometric modeling, subdivision surfaces, multiresolution surface representations, perceptually based methods for computer graphics.

Academic Standards

To register for courses, students must maintain good academic standing, fulfilling the following requirements:

Students must maintain an average of B or better over their first twelve credits. Students who fail to achieve this cannot continue in the master's program.
Students cannot obtain a master's degree unless they have maintained an overall average of B or better. Students at risk of failing to meet this requirement receive a warning letter from the department.
Students cannot obtain more than four no-credit grades, withdrawals, or unresolved incomplete grades during their academic tenure, and no more than two such grades in the first six courses for which they have registered.

Up to two core courses taken elsewhere can earn transfer credit, subject to the normal NYU graduate school restrictions on transfer of credit and the approval of the program director. At least 30 credits must be taken at NYU.

For further administrative information please contact

            Tamar Arnon
            arnon@cims.nyu.edu
            Tel. 212 998-3257

For further academic information please contact

            Mark Tygert, Director of the Master's Program in Scientific Computing
            tygert@cims.nyu.edu

Revised Fall 2012