# 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 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 15th 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 Affairs*

*Department of Mathematics*

*Courant Institute of Mathematical Sciences*

*251 Mercer Street*

*New York, NY 10012-1185*

__Tel.__(212) 998-3238

__Fax__(212) 995-4121e-Mail: admissions@math.nyu.edu

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

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

### 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)

*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*

- 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)

*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)

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

### 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:

- DS-GA-1006 Capstone Project in Data Science
- CSCI-GA Advanced Computer Graphics
- CSCI-GA Multicore Processors: Architecture & Programming
- CSCI-GA 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.

For further

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

Betty Tsang

btsang@cims.nyu.edu

Tel. 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