Courant Institute of Mathematical Sciences

The Courant Institute of Mathematical Sciences (CIMS) is an independent division of New York University (NYU) under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics. The Director of the Courant Institute directly reports to New York University's Provost and President and works closely with deans and directors of other NYU colleges and divisions respectively. The Courant Institute is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972.

The Courant Institute of Mathematical Sciences is considered one of the most prestigious and leading mathematics schools and mathematical sciences research centers in the world. The Courant Institute of Mathematical Sciences is ranked #1 in applied mathematical research, #5 in citation impact worldwide, and #12 in citation worldwide. On the Faculty Scholarly Productivity Index, it is ranked #3 with an index of 1.84. It is also known for its extensive research in pure mathematical areas, such as partial differential equations, probability and geometry, as well as applied mathematical areas, such as computational biology and computational neuroscience. The Mathematics Department of the Courant Institute has 18 members of the National Academy of Sciences (more than any other mathematics department in the U.S.) and five members of the National Academy of Engineering. Four faculty members have been awarded the National Medal of Science, one was honored with the prestigious Kyoto Prize, and nine have received career awards from the National Science Foundation. Courant Institute professors Peter Lax, S. R. Srinivasa Varadhan, Mikhail Gromov won the 2005, 2007 and 2009 Abel Prize respectively for their research in partial differential equations, probability and geometry.

Academic programs
The Courant Institute specializes in applied mathematics, mathematical analysis and scientific computation. There is emphasis on partial differential equations and their applications. The mathematics department is constantly ranked in the United States as #1 in applied mathematics, #5 in analysis , and #10 in geometry. Within the field of computer science, CIMS concentrates in theory, programming languages, computer graphics and parallel computing. The computer science program is ranked 28th among computer science programs in the US.

The Courant Institute offers Bachelors of Arts, Bachelors of Science, Master of Science and Ph.D. degree programs in both mathematics and computer science with program acceptance rates ranging from 5% to 33%. The overall acceptance rate for all CIMS graduate programs is 16%, and program admissions reviews are holistic. A high undergraduate GPA and high GRE score are typically prerequisites to admission to its graduate programs but are not required. Majority of accepted candidates met these standards. However, character and personal qualities and evidence of strong quantitative skills are very important admission factors. For doctoral programs, research experience is required. Undergraduate program admissions is not administrated by CIMS but the NYU undergraduate admissions office of College of Arts and Science.

In conjunction with the Stern School of Business, CIMS has a Master of Science program in Mathematical Finance, which is regarded as one of the top ten quantitative finance programs in the US with an acceptance rate of 8% and job placement rate of nearly 100% at time of graduation.

There are currently about 230 full-time and 370 part-time graduate students and 1,500 undergraduates majoring in math and/or computer science. About 120 M.S. degrees and 25 Ph.D.'s (15 Mathematics, 10 Computer Science) are awarded per year.

Recent CIMS doctoral placements include the following:
 * Columbia University
 * Columbia Law School
 * University of Chicago
 * Harvard University
 * Carnegie Mellon University
 * UC Berkeley
 * University of Minnesota
 * Ohio State University
 * Max Planck Institute for Mathematics
 * Instituto Superior Técnico (Portugal)
 * University of Washington
 * Cal Tech
 * Rutgers University
 * Stony Brook University
 * St. John's University

The Courant Institute houses New York University's undergraduate programs in computer science and mathematics. In addition, CIMS provides opportunities and facilities for undergraduate students to do and discuss mathematical research, including a undergraduate math lounge on the 11th floor and a undergraduate computer science lounge on the 2nd floor of Warren Weaver Hall.

The mathematics and computer science undergraduate and graduate programs at the Courant Institute has a strong focus on building quantitative and problem-solving skills through teamwork. The Courant Institute's undergraduate program encourages students to engage in research with professors and graduate students. About 30% of undergraduate students participate in academic research through the competitive Research Experiences for Undergraduates program funded by the National Science Foundation or research funded primarily by the Dean's Undergraduate Research Fund. The Courant Institute has one of the highest percentage of undergraduate students doing research within New York University.

Although run independently by the Courant Institute, the undergraduate programs and graduate programs at the Courant Institute are formally associated with the NYU College of Arts and Science and NYU Graduate School of Arts and Science respectively.

Academic research
The Department of Mathematics at CIMS occupies a leading position in analysis and applied mathematics, including partial differential equations, differential geometry, dynamical systems, probability and stochastic processes, scientific computation, mathematical physics, and fluid dynamics. A special feature of the Courant Institute is its highly interdisciplinary character — with courses, seminars, and active research collaborations in areas such as financial mathematics, materials science, visual neural science, atmosphere/ocean science, cardiac fluid dynamics, plasma physics, and mathematical genomics. Another special feature is the central role of analysis, which provides a natural bridge between pure and applied mathematics. The Department of Computer Science has strengths in multimedia, programming languages and systems, distributed and parallel computing, and the analysis of algorithms.

Since 1948, CIMS has maintained its own research journal, Communications on Pure and Applied Mathematics, which currently has the highest impact factor internationally among mathematics journals. It publishes original research originating from or solicited by the Courant Institute, typically in the fields of applied mathematics, mathematical analysis, or mathematical physics. Its contents over the years amount to a modern history of the theory of partial differential equations. Most articles originate within the Institute or are specially invited. The journal represents the full spectrum of the Institute's mathematical research activity. CIMS publishes its own series of lecture notes. They are based on the research interests of the faculty and visitors of the Courant Institute. These lecture notes originated in advanced graduate courses and mini-courses offered at the Courant Institute.

Warren Weaver Hall
CIMS consists of the NYU Departments of Mathematics and Computer Science as well as a variety of research activities. It is housed in Warren Weaver Hall on Mercer Street in NYU's Greenwich Village campus. Unlike many NYU buildings, it does not have an NYU flag. The building contains lecture halls on the first and second floors, a small meeting/seminar room on every floor from the 3rd floor to the 13th floor, a large common lounge on the 13th floor used for studying and open discussions in topics of mathematics and computer science, and its own extensive Courant library on the 12th floor. It also houses a variety of well-equipped laboratories and offices in Warren Weaver Hall for students and faculty to do research and discuss topics in mathematical sciences.

Courant Institute Library
The Courant Institute Library contains one of the United States's most complete mathematics collections with more than 275 journals and 54,000 volumes. Faculty and students at CIMS have access to MathSciNet and Web of Science (also known as the Science Citation Index), and a vast database containing hundred thousands of electronic journals related to mathematics and computer science.

Computing resources
CIMS has a IBM eServer BladeCenter system capable of peak performance of 4.5 TeraFlops. According to the TOP500 List, a ranking of supercomputers published at www.top500.org, CIMS’s supercomputer is the fastest in New York City and the 117th fastest supercomputer in the world. The acquisition of this supercomputer was funded by IBM and federal funding and is used primarily for research by the faculty and graduate and undergraduate students of CIMS. Computers at CIMS run Windows XP Professional, Solaris, Mac OS X, and Red Hat Enterprise Linux operating systems. There are also many other specialized Linux-based operating systems for research purposes. Every faculty / student office room is fully equipped with scientific software and computer stations. Wi-Fi and X terminals are available in public CIMS locations and every faculty / student office.

All graduate students are provided with an CIMS account to access computers and other resources within the CIMS network upon request. Undergraduate students are only provided CIMS accounts with the approval of their advisor, sponsorship by a CIMS professor, or for research purposes. CIMS computing resources are not accessible to non-CIMS students without sponsorship by a CIMS professor or approval by either the Department of Mathematics or Department of Computer Science. Students with CIMS account have access to free full-featured software provided by the MSDN Academic Alliance and specialized computing resources used primarily for research.

Major research resources
CIMS houses an advanced multi-million-dollar Courant Applied Mathematics Laboratory that opened in 1998, co-founded by Stephen Childress and Michael Shelley, and sponsored by US Department of Energy and the National Science Foundation. It comprises an experimental facility in fluid mechanics and other applied areas and a visualization and simulation facility. The Center for Atmosphere-Ocean Science is also housed at CIMS and is an interdisciplinary research and graduate program within the Courant Institute of Mathematical Sciences.

cSplash
Every year, CIMS offers cSplash or Courant Splash, a festival mathematics and computer science program for high school students. It is a one-day festival of classes in the mathematical and computer sciences, designed and taught by graduate and undergraduate students, faculty, and others associated with the Courant Institute of Mathematical Sciences.

Extracurricular activities
There are many clubs within the Courant Institute open to undergraduate and graduate students alike. These clubs include the Courant Student Organization, The ACM at NYU, Women-in-Computing (WinC), The Mathematics Society, Masters Association for Computer Science and many more. Additionally, CIMS sponsors and holds seminars and colloquiums almost daily on weekdays on topics of interest, in which some of whom may be held outside of Warren Weaver Hall. Many speakers of these seminars and colloquiums are experienced researchers from corporations from a variety of industries and researchers from private and government research laboratories, top universities, and NYU. Every academic year, CIMS holds award ceremonies, showcases, and parties to celebrate their faculty and undergraduate and graduate students and keep the academic atmosphere fun and enjoyable at CIMS. One such example is the NYU Computer Science Department Showcase held every semester to showcase projects that have been completed in various computer science graduate and undergraduate courses.

History
In 1934, Richard Courant left Göttingen University in Germany to become a visiting professor at NYU. He was given the task of building up the Department of Mathematics at the NYU Graduate School of Arts and Science. He was later joined by Kurt O. Friedrichs and James J. Stoker. In 1946, the department was renamed "Institute for Mathematics and Mechanics". Also in 1946, NYU Professor Morris Kline focused on mathematical problems of electromagnetic wave propagation. This project gave rise to the Institute's Division of Wave Propagation and Applied Mathematics. In 1952, the U.S. Atomic Energy Commission installed one of the first (electronic) computers at New York University, which led to the creation of the Courant Mathematics and Computing Laboratory. The Division of Magnetofluid Dynamics was initiated by a project on plasma fusion by NYU Professor Harold Grad in 1954. The Institute was in the forefront of advanced hardware use, with an early IBM 7094 and the third produced CDC 6600. The Division of Computational Fluid Dynamics was created in 1978, arising from a project of NYU Professor Paul R. Garabedian.

Directors

 * Richard Courant (1935–1958)
 * James J. Stoker (1958–1966)
 * Kurt O. Friedrichs (1966–1967)
 * Jürgen Moser (1967–1970)
 * Louis Nirenberg (1970–1972)
 * Peter Lax (1972–1980)
 * S. R. Srinivasa Varadhan (1980–1984)
 * Cathleen Synge Morawetz (1984–1988)
 * Henry McKean (1988–1994)
 * David W. McLaughlin (1994–2002)
 * Charles M. Newman (2002–2006)
 * Leslie Greengard (2006–present)

Notable Courant faculty
This is a small selection of Courant's famous faculty over the years and a few of their distinctions:


 * Gérard Ben Arous, Davidson Prize
 * Marsha Berger, NASA Software of the Year, National Academy of Engineering, National Academy of Sciences
 * Sylvain Cappell, Guggenheim Fellowship
 * Sourav Chatterjee, Davidson Prize
 * Jeff Cheeger, Veblen Prize, Max Planck Research Prize
 * Steven Childress, Guggenheim Fellowship, American Physical Society Fellow
 * Demetrios Christodoulou, 1993 MacArthur Fellow
 * Richard J. Cole, Guggenheim Fellowship
 * Martin Davis, Steele Prize
 * Percy Deift, George Polya Prize, Guggenheim Fellowship, National Academy of Sciences, American Academy of Arts and Science
 * Kurt O. Friedrichs, 1976 National Medal of Science
 * Paul Garabedian, NAS Prize in Applied Mathematics, National Academy of Sciences, American Academy of Arts and Science
 * Leslie Greengard, Steele Prize, Packard Foundation Fellowship, NSF Presidential Young Investigator, National Academy of Engineering, National Academy of Sciences
 * Mikhail Gromov, 2009 Abel Prize, Wolf Prize, Steele Prize, Kyoto Prize, Balzan Prize,
 * Helmut Hofer, Ostrowski Prize, National Academy of Sciences
 * Fritz John, 1984 MacArthur Fellow
 * Joseph B. Keller, 1988 National Medal of Science, Wolf Prize
 * Michel Kervaire
 * Subhash Khot, 2010 Alan T. Waterman Award
 * Morris Kline
 * Peter Lax, Abel Prize winner, 1986 National Medal of Science, Steele Prize, Wolf Prize, Norbert Wiener Prize
 * Lin Fanghua, Bocher Prize, American Academy of Arts and Science
 * Andrew Majda, NAS Prize in Applied Mathematics, John von Neumann Prize (SIAM)
 * Henry McKean, National Academy of Science, American Academy of Arts and Science
 * David W. McLaughlin, National Academy of Science, American Academy of Arts and Science
 * Bud Mishra, Association for Computing Machinery Fellow
 * Cathleen Synge Morawetz, 1998 National Medal of Science, Steele Prize, Birkhoff Prize, Noether Lecturer, National Academy of Sciences, American Academy of Arts and Science
 * Jürgen Moser, Wolf Prize, James Craig Watson Medal
 * Assaf Naor, European Mathematical Society Prize, Packard Fellowship, Salem Prize
 * Charles Newman, National Academy of Science, American Academy of Arts and Science
 * Louis Nirenberg, 1995 Crafoord Prize, National Medal of Science, Steele Prize, Bocher Prize, American Academy of Arts and Science
 * Charles S. Peskin, 1983 MacArthur Fellow, Birkhoff Prize, National Medal of Science,
 * Amir Pnueli, National Academy of Engineering, Israel Prize, Turing Award, Association for Computing Machinery Fellow
 * Jack Schwartz, who developed the programming language SETL at NYU
 * Michael J. Shelley, American Physical Society Fellow, François Naftali Frenkiel Award (APS)
 * Jonathan Sondow
 * Joel Spencer
 * S. R. Srinivasa Varadhan, Abel Prize winner, Steele Prize, National Academy of Sciences, American Academy of Arts and Science, Fellow of the Royal Society
 * Akshay Venkatesh, Salem Prize, Packard Fellowship
 * Margaret H. Wright, National Academy of Science, National Academy of Engineering
 * Lai-Sang Young, National Academy of Science, Satter Prize, Guggenheim Fellowship, American Academy of Arts and Science
 * Victor Shoup, who with Ronald Cramer developed the Cramer–Shoup cryptosystem

Notable Courant alumni
This is a small selection of Courant's alumni:


 * Anjelina Belakovskaia (Masters in Finance 2001), U.S. Women's Chess Champion.
 * Anita Borg (PhD 1981), founding director of the Institute for Women and Technology (IWT)
 * Charles Epstein (PhD 1983), hyperbolic geometry
 * Corwin Hansch (PhD 1944), statistics
 * Barbara Keyfitz (PhD 1970), Director of the Fields Institute
 * David Korn (PhD 1969), creator of the Korn shell,
 * Sergiu Klainerman (PhD 1978), Professor at Princeton
 * Morris Kline (PhD 1936), NYU Professor (1938–1975),
 * Peter Lax (PhD 1949), recipient of the Abel Prize,
 * Chen Li-an, (PhD 1968) Taiwanese Minister of Defence
 * Louis Nirenberg (PhD 1949), Crafoord Prize, Bôcher Prize, National Medal of Science
 * Brian J. McCartin (PhD 1981), recipient of the 2010 Chauvenet Prize,
 * Cathleen Morawetz (PhD 1950), National Medal of Science, Birkhoff Prize, Lifetime Achievement Award from the AMS, professor emeritus at Courant Institute
 * Stanley Osher (PhD 1966), Level Set method, professor at University of California, Los Angeles
 * George C. Papanicolaou (PhD 1969), professor at Stanford University
 * Susan Mary Puglia (BA in Computer Science and Math), Vice President at IBM
 * Gary Robinson, software engineer noted for anti-spam algorithms
 * Shmuel Weinberger (PhD 1982), topology and geometry, Professor at University of Chicago
 * Jacob Wolfowitz (PhD 1942),