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The Courant Institute of Mathematical Sciences (CIMS) is a division of New York University (NYU) and serves as a center for research and advanced training in computer science and mathematics. The Institute is named after Richard Courant, a mathematics professor at NYU from 1936 to 1972 and is a part of NYU's faculty of arts & sciences.

The institute is highly regarded throughout the world as a leader in applied mathematics, mathematical analysis, and scientific computation. There is emphasis on partial differential equations and their applications. Within the field of computer science, CIMS is regarded as a leader in theory, programming languages, computer graphics, and parallel computing.

The Institute offers Master of Science and Ph.D. programs in both mathematics and computer science. There are currently about 230 full-time graduate students and another 370 part-time students. About 120 M.S. degrees and 25 Ph.D.'s are awarded per year.

CIMS comprises NYU's Departments of Mathematics and Computer Science as well as a variety of research activities. It is housed in Warren Weaver Hall in NYU's Greenwich Village campus.

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.

This is a small selection of Courant's famous faculty over the years and a few of their distinctions [1]:

• Marsha Berger, NASA Software of the Year, National Academy of Engineering, National Academy of Sciences
• Sylvain Cappell, Guggenheim Fellowship
• Jeff Cheeger, Veblen Prize, Max Planck Research Prize
• Martin Davis, Steele Prize
• Percy Deift, George Polya Prize
• Kurt O. Friedrichs, 1976 National Medal of Science
• Paul Garabedian, NAS Prize in Applied Mathematics
• Leslie Greengard, Steele Prize, Packard Foundation Fellowship, National Academy of Engineering
• Mikhael Gromov, Wolf Prize, Steele Prize, Kyoto Prize
• Helmut Hofer, Ostrowski Prize
• Fritz John, 1984 MacArthur Fellow
• Joseph B. Keller, 1988 National Medal of Science
• Michel Kervaire,
• Morris Kline,
• Peter Lax, Abel Prize winner, 1986 National Medal of Science, Steele Prize,Wolf Prize
• Fang-Hua Lin, Bocher Prize
• Andy Majda, NAS Prize in Applied Mathematics
• Henry McKean, National Academy of Science
• David W. McLaughlin, National Academy of Science
• Cathleen Synge Morawetz, 1998 National Medal of Science, Steele Prize, Birkhoff Prize, Noether Lecturer
• Jürgen Moser,
• Charles Newman, National Academy of Science
• Louis Nirenberg , 1995 National Medal of Science, Steele Prize, Bocher Prize
• Charles S. Peskin, 1983 MacArthur Fellow, Birkhoff Prize
• Amir Pnueli, National Academy of Engineering
• Jack Schwartz, who developed the programming language SETL at NYU
• Alan Sokal (known for the Sokal Affair),
• Jonathan Sondow,
• Joel Spencer,
• S. R. Srinivasa Varadhan, Abel Prize winner
• Margaret H. Wright, National Academy of Science, National Academy of Engineering
• Lai-Sang Young, National Academy of Science, Satter Prize, Guggenheim Fellowship

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
• George C. Papanicolaou (PhD 1969)
• Jacob Wolfowitz (PhD 1942),

• S. R. S. Varadhan
• List of New York University People

• Courant Institute of Mathematical Sciences
• Department of Mathematics, New York University
• Undergraduate Mathematics Club, New York University
• New York University Computer Science
• New York University Mathematics in Finance