# The Master of Science in Scientific Computing

Notice to Fall 2014 Scientific Computing MS applicants:Notice to Fall 2014 Scientific Computing MS applicants:

*The department has started to review applications for Fall 2014. Please note that this process can take several weeks. If you have any questions and concerns regarding your application, please contact the Math Department via email at admissions@math.nyu.edu.*

[Posted April 1, 2014]

### 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 program is self-contained and terminal, providing a complete set of 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.We are in the process of discontinuing the concentration in Data Science. Instead of applying to this program, prospective candidates are encouraged to consider the recently-created Masters of Science in Data Science within the NYU Center for Data Science.

**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, 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 deadlines for application to the program are April 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) 995-4121e-Mail: admissions@math.nyu.edu

e-Mail: arnon@cims.nyu.edu

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

### Degree Requirements

Students should meet with program director Aleksandar Donev to discuss course selection before registering for classes, as offerings change and there may be several courses equivalents offered in the different departments (mathematics, computer science, and data science). Those students enrolled in the data science track should consult Professor Esteban Tabak for help in deciding on classes to take.#### 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.

#### 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.

*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)
and either
*MATH-GA 2043 Scientific Computing*(fall and spring semesters)
or both
*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.

“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. 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.

**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,
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.

Tamar Arnon

arnon@cims.nyu.edu

Tel. 212 998-3257

For further academic information please contact

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

donev@cims.nyu.edu

Revised summer 2013