Rankings 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 consistently ranked in the United States as #1 in applied mathematics. Other strong points are Analysis (#6 as of 2022) and geometry (#12 as of 2022). Within the field of
computer science, CIMS concentrates in
machine learning,
theory,
programming languages,
computer graphics and
parallel computing. In 2022, the computer science program was ranked #19 among computer science and information systems programs globally. In 2022, the
Academic Ranking of World Universities placed the Courant Institute as #9 worldwide in the subject ranking for mathematics. Louis Nirenberg also received the
Chern Medal in 2010, and
Subhash Khot won the
Nevanlinna Prize in 2014.
Amir Pnueli and
Yann LeCun won the 1996 and 2018
Turing Award respectively. In addition,
Jeff Cheeger was also awarded the
Shaw Prize in Mathematical Sciences in 2021.
Admissions The Courant Institute offers
Bachelor of Arts,
Bachelor of Science,
Master of Science and
PhD degree programs in both
mathematics and
computer science with program acceptance rates ranging from 3% to 29%. The overall acceptance rate for all CIMS graduate programs is 15%, 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. Consistent with its scientific breadth, the institute welcomes applicants whose primary background is in quantitative fields such as economics, engineering, physics, or biology, as well as mathematics. Undergraduate program admissions are not directly administrated by the institute but by the NYU undergraduate admissions office of College of Arts and Science.
Graduate program The Department of Mathematics at the Courant Institute offers PhDs in Mathematics, Atmosphere-Ocean Science, and Computational Biology; Masters of Science in Mathematical Finance, Mathematics, and Scientific Computing. The Graduate Department of Computer Science offers a PhD in computer science. In addition it offers Master of Science degrees in computer science, information systems (in conjunction with the
Stern School of Business), and in scientific computing. For the PhD program, every PhD computer science student must receive a grade of A or A− on the final examination for algorithms, systems, applications, and a PhD-level course chosen by the student that does not satisfy the first three requirements, such as cryptography and numerical methods. Students may take the final exam for any these courses without being enrolled in the course. The Computer Science Masters program offers instruction in the fundamental principles, design and applications of computer systems and computer technologies. Students who obtain an MS degree in computer science are qualified to do significant development work in the computer industry or important application areas. Those who receive a doctoral degree are in a position to hold faculty appointments and do research and development work at the forefront of this rapidly changing and expanding field. The emphasis for the MS in Information Systems program is on the use of computer systems in business. For the Master of Science in Scientific Computing, it is designed to provide broad training in areas related to scientific computing using modern computing technology and mathematical modeling arising in various applications. The core of the curriculum for all computer science graduate students consists of courses in algorithms, programming languages, compilers, artificial intelligence, database systems, and operating systems. Advanced courses are offered in many areas such as natural language processing, the theory of computation, computer vision, software engineering, compiler optimization techniques, computer graphics, distributed computing, multimedia, networks, cryptography and security, groupware and
computational finance. Adjunct faculty, drawn from outside academia, teach special topics courses in their areas of expertise. Unless outside fellowships or scholarships are available to the students, all admitted Courant PhD students are granted with the GSAS MacCracken award. The fellowship covers the tuition and provides 9 months of stipend along with other benefits such as health insurance and special housing opportunities. The MacCracken funding is renewable for a period of up to five years, assuming satisfactory progress toward the degree. Doctoral students take advanced courses in their areas of specialization, followed by a period of research and the preparation and defense of the doctoral thesis. Courant Students in PhD programs may earn a master's degree while in progress toward the PhD program. Areas where there are special funding opportunities for graduate students include: Mathematics, Mechanics, and Material Sciences, Number Theory, Probability, and Scientific Computing. All PhD candidates are required to take a written comprehensive examination, oral preliminary examination, and create a dissertation defense. Each supported doctoral student has access to his or her own dedicated Unix workstation. Many other research machines provide for abundant access to a variety of computer architectures, including a distributed computing laboratory.
Undergraduate program 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 an undergraduate math lounge on the 11th floor and an undergraduate computer science lounge on the 3rd 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. An undergraduate computer science course on Computer Vision, for example, requires students to be in small teams to use and apply recently developed algorithms by researchers around the world on their own. One example assignment requires a student to study a paper written by researchers from
Microsoft Research Cambridge in order to do an assignment on Segmentation and Graph Cut. To encourage innovation, students in advanced coursework are allowed to use any means to complete their assignment, such as a programming language of their choice and hacking a
Kinect through legal means. The Courant Institute's undergraduate program also 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. With permission of their advisers or faculty, undergraduate students may take graduate-level courses. Courant undergraduate students through the years and alumni contribute greatly to the vitality of the Mathematics and Computer Science departments. Some accomplishments by current and former undergraduate Courant students include an Apple Worldwide Developers Conference Scholarship Winner, development of Object Category Recognition Techniques to sort garbage for recycling for the NYC's trash program, placement in 7th out of 42 in the ACM International Collegiate Programming Contest (ICPC), and inventors of the
Diaspora (software) social network. The undergraduate division of the Department of Computer Science offers a Bachelor of Arts (BA) degree, and fours minors. These are the computer science minor, web programming and applications minor, joint minor in computer science/mathematics, and the computer science education minor available in collaboration with
NYU Steinhardt. The BA degree can also be pursued with honors. Students may combine the degree with other majors within the College of Arts and Science to create a personalized joint major. Two specific combined degrees are the joint major in computer science/economics and the joint major in computer science/mathematics. The Department of Computer Science also offers a BS/BE Dual Degree in computer science and engineering and an accelerated master's program available to qualifying undergraduates in conjunction with the
Tandon School of Engineering.
Academic research The Department of Mathematics at Courant occupies a leading position in analysis and applied mathematics, including
partial differential equations,
differential geometry,
dynamical systems,
probability and
stochastic processes,
scientific computation,
mathematical finance,
mathematical physics, and
fluid dynamics. A special feature of the 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, Courant Institute has maintained its own research journal,
Communications on Pure and Applied Mathematics. While the journal represents the full spectrum of the institute's mathematical research activity, most articles are 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 institute also publishes its own series of lecture notes. They are based on the research interests of the faculty and visitors of the institute, originated in advanced graduate courses and mini-courses offered at the institute. ==Resources==