# M.S. in Scientific Computing

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 provides broad yet rigorous training in areas of mathematics and computer science related to scientific computing. It aims to prepare people with the right talents and background for a technical career doing practical computing.

The program accommodates both full-time and part-time students, with most courses meeting in the evening. The masters program focuses on computational science, which includes modeling and numerical simulation as used in engineering design, development, and optimization. While data science is an increasingly important aspect of computational science, this program is distinct and different from the recently-created Masters of Science in Data Science within the NYU Center for Data Science. Students specifically interested in data science are encouraged to apply to that program instead.

### 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 high performance computing. 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. 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, which serves to integrate the classroom material.

### Admission Requirements

The program requires least three semesters of Calculus (including **multivariate calculus**), as well as**linear algebra**. Experience with **programming in a high-level language** (e.g., Java, C, C++, Fortran, Python) as well as **data structures**** and algorithms**, equivalent to a first-year sequence in computer science, is also required. It is highly desirable that applicants have undergraduate major or significant experience in mathematics, a quantitative science or engineering, or economics.

The deadline for application to the program is March 1st for the fall semester. 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 AffairsDepartment of Mathematics

Courant Institute of Mathematical Sciences

251 Mercer Street

New York, NY 10012-1185

admissions@math.nyu.edu

__Phone:__ (212) 998-3238

__Fax:__ (212) 995-4121

__Administrator__: Betty Tsang, btsang@cims.nyu.edu

### Degree Requirements

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

- 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 a master's capstone project.

Students with exceptional backgrounds may petition the program director for permission to substitute other appropriate courses for core courses. Advanced students may be permitted to do a masters thesis as an alternative to the master's capstone project.

### Core Courses

The following are the two required core courses in mathematics:

- MATH-GA 2010 Numerical Methods I (fall semester)
- MATH-GA 2020 Numerical Methods II (spring semester)

Students must also complete at least two of the following core courses in mathematics:

- MATH-GA 2701 Methods of Applied Mathematics (fall semester)
- MATH-GA 2490 Partial Differential Equations I (fall)
- MATH-GA 2702 Fluid Dynamics (fall semester)
- MATH-GA 2704 Applied Stochastic Analysis (spring semester)
- DS-GA 1002 Statistical and Mathematical Methods

Advanced students may also choose the two additional core courses from the following advanced topics courses in applied math and numerical analysis, typically offered bi-anually:

- MATH-GA Advanced Topics: Optimization
- MATH-GA Advanced Topics: Monte Carlo
- MATH-GA Advanced Topics: Computational Fluid Dynamics
- MATH-GA Advanced Topics: Finite Element Methods

The following are the two required core courses in computer science:

- CSCI-GA 1170 Fundamental Algorithms (fall, spring and summer terms)
- CSCI-GA 2110 Programming Languages (fall, spring, and summer terms)

Students must also complete at least two of the following core courses in computer science:

- CSCI-GA 3033 Open Source Tools (fall term)
- CSCI-GA 2270 Computer Graphics (spring term)
- CSCI-GA 2565 Machine Learning (fall term)
- CSCI-GA 2566 Foundations of Machine Learning
- DS-GA 1001 Introduction to Data Science (fall)
- DS-GA 1003 Machine Learning and Computational Statistics (spring)

Advanced students may also choose the two additional core courses from advanced topics courses in computer science of relevance to Scientific Computing, such as:

- CSCI-GA Graphics Processing Units (GPUs)
- CSCI-GA Advanced Topics: High-Performance Computing

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 a capstone project. 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 following is a list of courses approved to meet the capstone requirement:

- CSCI-GA Advanced Topics: High-Performance Computing
- DS-GA 1006 Capstone Project in Data Science
- CSCI-GA 2274 Advanced Computer Graphics
- CSCI-GA Multicore Processors: Architecture & Programming
- CSCI-GA 2440 Software Engineering

Advanced students can obtain permission from the director of the program to do an individual capstone project under the supervision of a faculty member. It is also possible for part-time students to do a research project under the supervision of senior research scientists at their place of employment, with the approval of the program director.

### 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. 2006, Princeton. 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.

**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, optimization and data 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.

**Miranda Holmes-Cerfon**. B.S. 2005 University of British Columbia, PhD 2010 NYU. Research interests: soft-matter physics, fluid dynamics, oceanography, stochastic methods.

**Antoine Cerfon**. B.S. 2003, M.S. 2005 Ecole des Mines de Paris, PhD 2010 MIT. Research interests: Computational plasma physics, multi-scale methods, fast algorithms.

**Dimitris GIannakis**. MSci 2001 Cambridge, PhD 2009 Chicago. Research interests: geometrical data analysis, statistical modeling, climate dynamics.

### 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 (including applications, transfer of credits, entrance exams, registration for courses, etc.) please contact

**Betty Tsang**

btsang@cims.nyu.edu

Phone: (212) 998-3257

For further *academic* information (e.g., substituting a course) please contact

**Aleksandar Donev**, Director of the Master's Program in Scientific Computing

donev@courant.nyu.edu

Revised Fall 2016