nyu courant applied math phd

Mathematics (PhD)

Program description, dual-degree.

The Department of Mathematics is part of the Courant Institute of Mathematical Sciences , an independent division of New York University . Based in Warren Weaver Hall, at the heart of New York University’s Washington Square campus, it is one of the top-ranked Mathematics departments worldwide (#4 in the US and #9 in the world as per the Shanghai rankings ; #6 in the US and #8 in the world as per the QS rankings ).

For more on the Courant Institute and its pioneering history in the field of applied mathematics (our department is consistently ranked #1 in applied mathematics as per USNews), see the history page .

The study of mathematics can lead to a variety of exciting professional careers. Basic research, engineering, finance, business, and government service are among the opportunities open to those with mathematical training.  Moreover, with the increasing importance of basic science and information technology, prospects for careers in the mathematical sciences are very good. Mathematical analysis and computational modeling are important for solving some of the most pressing problems of our time - new energy resources, climate change, risk management, epidemiology, to name a few. We must strive to maintain our technological edge; mathematical skills will be crucial to this effort.

Some more specific business positions include portfolio analysis, design studies, statistical analysis, computer simulation, software design and testing, and other areas of operations research. There are extensive opportunities for mathematics in finance, the actuarial fields, and economic forecasting.

Many laboratories, both government and private, maintain independent research staffs that include mathematicians. Their work often deals with the development of new technology, including research in basic physics and software development, as well as applied mathematics. Numerical simulation, such as weather and climate forecasting, depends heavily on the use of supercomputers.

Practical considerations aside, there is the pleasure of learning, applying, and creating mathematics. Real world issues pose problems that can be studied by formulating and analyzing mathematical models. In some cases applications may lead to new mathematics, and a new branch of the science is born. In other cases abstract theory finds unexpected practical purpose. Working on research problems is exciting; solving difficult problems successfully is, for many, satisfaction enough.

All applicants to the Graduate School of Arts and Science (GSAS) are required to submit the  general application requirements , which include:

• Academic Transcripts
• Test Scores  (if required)
• Applicant Statements
• Résumé or Curriculum Vitae
• Letters of Recommendation , and
• A non-refundable  application fee .

See Mathematics for admission requirements and instructions specific to this program.

The Mathematics Department offers a dual-degree with the NYU School of Law: Mathematics PhD/Law JD.

Program Requirements

Written comprehensive examination, oral preliminary examination, dissertation defense, departmental approval.

The program requires the completion of 72 credits. It is possible, with departmental permission, to take courses relevant to students’ course of study in other departments at NYU or at other universities. A minimum of 32 credits must be completed at the Department of Mathematics.

Additional Program Requirements

The examination tests the basic knowledge required for any serious mathematical study; it is comprised of three individual examinations in Advanced Calculus, Complex Variables, and Linear Algebra, and is given on three consecutive days, twice a year, in early September (or, sometimes, late August) and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. Students may take the written examination twice; a third and final time requires the permission of the Director of Graduate Studies.

This examination is usually taken after two years of full-time study. Its purpose is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. Students may take the oral examination twice; a third and final time requires the permission of the Director of Graduate Studies. All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points. It is recommended that students attempt the examinations well before this deadline.

The oral defense is the final examination on the student’s dissertation. The defense is conducted by a panel of five faculty members (including the student’s advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student’s topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

All Graduate School of Arts & Science doctoral candidates must be approved for graduation by their department for the degree to be awarded.

Sample Plan of Study

Following completion of the required coursework for the PhD, students are expected to maintain active status at New York University by enrolling in a research/writing course or a Maintain Matriculation ( MAINT-GA 4747 ) course.  All non-course requirements must be fulfilled prior to degree conferral, although the specific timing of completion may vary from student-to-student.

Learning Outcomes

Upon successful completion of the program, graduates will have:

• Mastery of the fundamental methods of basic areas in mathematics broadly related to their future research.
• Deep working knowledge of the theories, concepts and open questions in the selected area of research.
• Mastery in written communication sufficient for writing research articles acceptable for publication in peer-reviewed journals.
• Proficiency in oral communication sufficient to give lectures and presentation at scientific conferences and symposiums.
• Lecturing skills which enables them to teach courses in the future in broad areas in mathematics.
• Mastery of the modern tools and classical methods in the selected area of research.
• The ability to formulate sound research programs and bring a research project to fruition in the form of a peer-reviewed publication.

NYU Policies

Graduate school of arts and science policies.

University-wide policies can be found on the New York University Policy pages .

Academic Policies for the Graduate School of Arts and Science can be found on the Academic Policies page . 

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• Prerequisites
• Graduate Study
• Careers in Mathematics
• Ph.D. in Mathematics
• Ph.D. in Atmosphere Ocean Science
• M.S. at Graduate School of Arts & Science
• M.S. at Tandon School of Engineering
• Current Students

Recommended Background

The most essential courses for an undergraduate student wishing to enter graduate studies in mathematics are the calculus sequence (often three one-term courses and a course in advanced calculus) and a course in linear algebra. For students interested in applied mathematics, the next most important courses would be introductory classes in ordinary and partial differential equations, followed by probability and statistics; it is also desirable for a student to master at least one computer language. For students interested in pure mathematics, a course in mathematical analysis would come next, followed by algebra or more advanced courses in analysis, depending on the student's focus.

Students can benefit from taking core courses from another department, such as physics, chemistry, biology or computer science. The Courant Institute welcomes applicants with undergraduate degrees in areas other than mathematics, such as physics, biology, computer science or engineering.

• Ph.D. in Mathematics
• Ph.D. in Atmosphere Ocean Science

M.S. in Mathematics

• M.S. in Scientific Computing
• M.S. in Mathematics in Finance
• Non-Degree Study
• M.S. at Tandon School of Engineering
• Current Students

The Master's degree in mathematics encompasses the basic graduate curriculum in mathematics, and also offers the opportunity of some more specialized training in an area of interest.  A typical Master's course of study will involve basic courses in real analysis, complex analysis and linear algebra, followed by other fundamental courses such as probability, scientific computing, and differential equations. Depending on their mathematical interests, students will then be able to take more advanced graduate courses in pure and applied mathematics.  Information about admission on a non-degree basis is  here .

See frequently-asked questions regarding the impact of the Covid-19 pandemic on MS programs.

Degree Requirements

A candidate for the Master's degree in mathematics must fulfill a number of departmental requirements .

The Written Comprehensive Examinations

Master’s students who choose the Written Comprehensive Examinations option must pass with an overall grade of B. The three-part Written Comprehensive Examination is administered by the department twice a year in early September and early January. Most Master's students tend to take the exam toward the end of their graduate studies.

Students are permitted to take the written examinations twice with no special permission.  A third and final attempt may be granted by the Department on a case-by-case basis.

The examinations, in advanced calculus, complex variables and linear algebra, may include some of the following material:

Advanced Calculus:  Real numbers. Functions of one variable: continuity, mean-value, differentiability, maxima and minima, integrals, fundamental theorem of calculus, inequalities, estimation of sums and integrals, elementary functions and their power series. Funtions of several variables: partial derivatives, chain rule, MacLaurin expansion, critical points, Lagrange multipliers, inverse and implicit function theorems, jacobian, divergence and curl, theorems of Green and Stokes.

Complex Variables:  Complex numbers, analytical functions, Cauchy-Riemann equations, Cauchy's integral and applications, power series, maximum principle, Liouville's theorem, elementary functions and their conformal maps, bilinear transformation, classification of singularities, residue theorem and contour integration, Laurent series, Rouche's theorem, number of zeros and poles. 

Linear Algebra:  Vector spaces, linear dependence, basis, dimension, linear transformation, inner product, systems of linear equations, matrices, determinants, ranks, eigenvalues, diagonalization of matrices, quadratics forms, symmetric and orthogonal transformations.

Cooperative preparation is encouraged, as it is for all examinations. Students may also find the following books helpful:

Buck,  Advanced Calculus ; Courant and John,  Introduction to Calculus and Analysis ; Strang,  Linear Algebra ; Churchill,  Complex Variables and Applications .

Master's Thesis

Students who have earned a GPA of 3.7 or higher and taken at least 18 credits in the program have the option to write a Master's thesis under the supervision of a Mathematics faculty member. In certain cases involving interdisciplinary research, a second advisor outside the Department of Mathematics may be approved by the Director of Graduate Studies. All students must submit the Thesis Proposal and Advisor Approval form, outlining the research plan for the thesis which has been approved by the thesis advisor, to the Program Administrator at least four months prior to the graduation date. The completed Master's thesis must be approved by two readers -- the thesis advisor and a second reader. At least one of the readers must be a full-time Courant Mathematics faculty member. You can find more detailed information in the Thesis Guidelines FAQ.

Academic Standards

To continue registering for courses in the Department of Mathematics, a student must be in a good academic standing, fulfilling the following requirements:

• Students must maintain an average of B or better (3.0) in their first 12 credits. Students failing to achieve this will not be permitted to continue in the program. Students cannot obtain an M.S. degree unless they have maintained an overall average of at least B
• Students will be allowed no 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.
• Credit will be given for up to two core courses taken elsewhere, subject to the normal GSAS restrictions on transfer of credit and the approval of the Program Coordinator. At least 24 course points must be taken at New York University.

For any questions 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 Phone (212) 998-3238 Fax (212) 995-4121 [email protected]

READY TO APPLY?

Please read all the information on this page before preparing your application.

Applications for all Mathematics in Finance programs at NYU Courant are handled by the  NYU Graduate School of Arts and Science (GSAS). The program receives applications from GSAS for review only when they are complete.

For non-degree programs, only domestic applicants and international applicants with an H1B Visa are permitted to apply online. Please visit the GSAS non-degree and visiting student instruction page  to learn more.

Admissions to the full-time program are competitive. We have many more qualified applicants than positions in the program.

READY TO GET TO WORK?

What to know before you apply.

The Mathematics in Finance program requires a high level of mathematical ability and focused preparation, so it’s important to completely and accurately represent your background, aptitudes, and interests on your application. Detailed application guidelines are provided below. Please follow them closely to help avoid confusion and prevent misunderstandings.

AFTER YOU APPLY

You can track the status of a submitted application on the GSAS application status page or via the application checklist. You can also review answers to frequently asked questions at the bottom of this page. Admissions decisions are announced on a rolling basis, so you may receive the decision on your application before or after another applicant. Any questions concerning your application can be directed to [email protected] .

Full-Time, Part-Time, And Advanced Certificate Application Requirements

• Fully completed application (online application required)

Statement of Purpose

• Three (3) Letters of Recommendation (submitted online)
• One (1) official academic transcript from each post-secondary institution attended (uploaded as part of the online application)
• Official GRE scores (Note: GMAT scores are not accepted)
• TOEFL or IELTS scores for international students (not required if previous degree(s) were earned at an institution where English is the primary language of instruction)
• Video submission (instructions provided below)
• CV / resume 

Note: After an application is submitted, we will not accept updated grades, resumes, or research or work experience.

Non-Degree Application Requirements

• If you are a US citizen or permanent resident, or an international student with an H1B Visa, you should apply for non-degree study by using the online application. If you are not a US citizen or permanent resident, or are an international student who does not hold an H1B Visa, please visit the GSAS non-degree instructions page for further guidance.
• One (1) official academic transcript from each post secondary institution you attended 
• CV / resume

MBA/MS in Mathematics in Finance Dual Degree Application Requirements

Application to the MS in Mathematics in Finance dual-degree program is limited to first-year, full-time MS in Mathematics in Finance students. Students who meet this criteria and wish to apply must complete the NYU Dual Degree Application by the MS application deadline.

To learn more about application requirements specific to the MS dual-degree program, please visit the NYU Stern dual degree application page .

APPLICATION DEADLINES

All application materials, including test results, must be received by GSAS by the dates provided below. It can take four weeks to receive official GRE results, so plan accordingly. The GSAS code for TOEFL and GRE scores is 2596 . We may be able to begin reviewing applications that include unofficial scores or transcripts, but we won’t be able to complete the review until we’ve received official scores and transcripts.

• Full-Time: February 8 Full-time students are accepted for fall admission only and are encouraged to submit their applications before the deadline date.
• Part-Time: August 1 for Fall, December 1 for Spring
• Non-Degree: August 1 for Fall, December 1 for Spring
• MS in Mathematics in Finance/MBA Deadlines:  February 15 for Fall

NOTIFICATION OF ADMISSION

Official notification of admission will be made by the Graduate Enrollment Service at GSAS. Please do not email the program to inquire about admission unless you have a response deadline from another program to which you applied. Due to the large number of applications we receive, it may take several weeks from the time of our decisions before all admitted students have received their official notification letter.

TUITION INFORMATION

Learn more about tuition and fees by using NYU’s tuition calculator .

APPLICATION GUIDANCE

Pay close attention to these suggestions to ensure your application is as strong as possible.

Application

Make sure you’ve answered all questions and the application is complete.

Please address the following three topics, individually, using at most 150 words for each: You may offer additional information you want us to consider in a Personal Statement, which is a separate and optional part of the application. Please note that content generated by tools like ChatGPT is less effective than personally crafted material because it lacks the specificity of the writer’s unique facts and ideas.

• What is your motivation for pursuing a career in the financial industry, and how does it fit with your quantitative interests and background?
• Describe a mathematical or scientific fact, or a theory, that you find particularly interesting or important.
• Describe one of the following: (a) a research project you participated in, (b) an interesting class you have taken, or (c) an internship/job you have done.

Letters of Recommendation

The most impactful letters of recommendation come from individuals who have personally witnessed your mathematical talent in challenging situations. Generally, these individuals are instructors of advanced courses that are specifically mathematical or heavily quantitative, such as science, engineering, or economics courses.

Your talent for, and preparation in, mathematics is perhaps the most important consideration for admission to the program. This talent and preparation could be represented by straightforward mathematics courses, or by highly quantitative courses in engineering, economics, or the sciences. Full-time applicants are encouraged to submit at least one letter that describes their academic mathematical abilities, and at least one letter that describes their computer science and/or academic programming experience. If you have significant work experience, a letter from your manager that describes your technical accomplishments would be appreciated. Only submit more than three (3) letters of recommendation if the additional letters provide significant new information. Two things to keep in mind:

• Letters of recommendation are not character references. As such, please refrain from asking for letters from individuals who do not have first-person insight into your mathematical and technical abilities.
• Don’t write a letter of recommendation for yourself. You may provide your recommenders with a resume, transcript, or a few details about yourself, but don’t write your own letters of recommendation.

Official Test Scores

We require official scores from the general GRE test, but we also encourage applicants to submit official scores from Subject GRE tests in mathematics, physics, or other highly quantitative disciplines. We may waive the GRE requirement for applicants who hold a highly quantitative Ph.D. Please email GSAS admissions  to request PhD waiver instructions.

The institution code for NYU GSAS is 2596 . You will need this for both the GRE and TOEFL tests.

The department code is 99 . You will only need this for the TOEFL test.

Video Submission

Full-time applicants are required to submit a  short video statement  along with their application. Our preliminary screening of applicants utilizes both your written statement of purpose and your video submission. Your video will be evaluated for its content, not its technical quality. Please see below for video guidelines.

• Your video should be no longer than five (5) minutes.
• Describe a challenging experience or project, and explain its relevance to your prospective career in quantitative finance.
• If your career goals involve a particular area of quantitative finance, share what type of quantitative finance that is and why it suits you.

CV / Resume

Please submit a professional quality resume. For your work experience, please provide the company and division where you worked, your dates of employment, the location of the company, and a brief overview of your responsibilities. Please include major non-academic and non-technical activities as well, such as military service, performing arts, or community service along with dates and locations. Lastly, please provide your educational background, including institutions, dates of attendance, and details of your degree(s), concentration(s), awards, GPA, thesis title, etc.

Department and Field of Study Codes

For non-degree study, please enter the following department and field of study codes on the paper application:  Non-Degree Study: MATF MAF

UPCOMING EVENTS

Filter posts:, alumni highlights information session internal events new course other program announcements public events uncategorized, math finance m.s. info session- september 9, math finance m.s. info session- october 7, math finance m.s. info session- november 4, math finance m.s. info session- december 2, have a question.

Start by reviewing the answers to these frequently asked questions. If you still have a question, send us an email: [email protected] .

Do you require applicants to have work experience for admission into the program?

It depends on which program you’re applying to. Full-time applicants are not required to have work experience, though it can be helpful in finding a job after graduation. Part-time and Non-Degree applicants are required to have work experience in order to apply.

Am I allowed to apply to multiple Mathematics in Finance programs at NYU Courant?

No. You are only permitted to apply to one NYU Courant program at a time. However, you are permitted to apply to multiple programs if they are at different NYU schools. Learn more about this GSAS policy .

Do you require a minimum GPA or GRE score?

No. We do not have a required minimum GPA or GRE score, but please remember that the program is competitive. Most accepted students achieve quantitative GRE scores above the 90th percentile.

Can I waive out of the TOEFL?

The TOEFL is not required if you have an undergraduate or more advanced degree from an English-speaking university.

Am I able to apply for financial assistance through the Mathematics in Finance program?

No. We do not accept applications for financial assistance. However, some students may be eligible for financial support through GSAS . Additionally, Mathematics in Finance students are occasionally hired as graders, but these positions cannot be arranged in advance and do not offer tuition remission.

Can I reapply if I applied previously but was not accepted?

Yes. Applicants who are not accepted can reapply up to two (2) additional times.

How much is the application fee?

The non-refundable application fee is $150.

Start your application now.

Published June 22, 2022

NYU Courant: Where Undergrads Crunch Numbers

Staff Writer

If you love problem-solving and analysis, an NYU bachelor’s degree in Computer Science or Mathematics may be a perfect fit. These programs pair technical classes, such as Data Structures and Discrete Mathematics, with core liberal arts courses, like Expressive Culture and International Writing. This combination produces well-rounded professionals who can analyze and solve challenges, then communicate those solutions to others. And you’ll do all this at the top applied mathematics institute for graduate studies in the United States: the NYU Courant Institute of Mathematical Sciences .

Study with Award-Winning Faculty

Established nearly 100 years ago as the nation’s first center for applied mathematics, Courant continues to rank No. 1 for its graduate programs thanks to its faculty research and teaching. What’s more, its undergraduate programs rank in the top 30. Here, faculty have received outstanding awards like the Abel Prize (often called the Nobel Prize of mathematics), the Kyoto Prize, and the National Medal of Science. And while you apply to the College of Arts and Science to receive your bachelor’s degree in Computer Science or Mathematics, most of your major courses are taught by NYU Courant’s award-winning professors.

In addition to being leading-edge researchers, Courant faculty are devoted and accessible teachers. They have won numerous university awards for their teaching. For example, innovative faculty have won the College of Arts and Science’s Golden Dozen Award for outstanding contributions to learning in the classroom. Working directly with such esteemed professors offers undergraduates unparalleled opportunities for research and experiential learning. As you grow your skills and perform your own research, you will have direct access to some of the world’s most brilliant minds in computer science and math. At NYU Courant, you’ll form a foundation of knowledge that will help you innovate the future.

Research and Resources Galore

Practical research experience and profound intellectual exploration allow Computer Science and Mathematics majors to build competencies that are otherwise difficult to hone. Whether you collaborate with students from other universities to create a map showing the spread of COVID-19 or work with the Guggenheim to restore an internet-based artwork, you will build important skills that expand your understanding of the field.

While conducting research, you can also take advantage of specific Courant resources. These include the Courant Library . This 60,000-plus-volume collection focuses on research-level materials in mathematics, computer science, and related fields, including fluid mechanics, image processing, and robotics. Furthermore, because computing is at the heart of Courant, you have access to a vast network of Solaris and Linux servers and workstations in addition to more standard Macs and PCs running Windows. From single-processor systems for class assignments to Linux clusters and shared-memory multiprocessors for high-level research, NYU Courant offers every computing resource you could need—and then some.

NYU’s Global Network Is Yours to Explore

In addition to all the resources available through Courant, studying computer science or mathematics at NYU offers the unique opportunity to study abroad while staying on track with your major requirements. Mathematics majors can take advanced math courses at NYU Abu Dhabi , NYU Berlin , NYU Paris , NYU London , and NYU Shanghai . And NYU Abu Dhabi, NYU Paris, and NYU Shanghai offer computer science courses. International experience and research can help set you apart as you apply for your first job or graduate school.

Whether you want to study mathematics or computer science at NYU, your degree will open up doors to the future. Both majors provide a strong foundation for many careers, from jobs in technology and finance to more unexpected paths, like law, medicine, or entrepreneurship. By gaining the vital analytical and critical thinking skills these majors are famous for, you build essential knowledge that will serve you well, no matter where life takes you.

Joint Programs

For the most ambitious students, NYU offers several joint-degree programs in both Computer Science and Mathematics. In addition to a BA in Computer Science and Mathematics at NYU Courant, joint programs and dual degrees include:

• Computer Science… and Economics (BA/BA) and Data Science (BA/BA) and Computer Engineering (BS/BS) and Electrical Engineering (BS/BS)
• Mathematics… and Civil Engineering (BS/BS) and Computer Engineering (BS/BS) and Data Science (BA/BA) and Economics (BA/BA) and Electrical Engineering (BS/BS) and Mechanical Engineering (BS/BS) and Teaching Mathematics (BA/MAT)

Math at NYU: So Many Ways to Study

It’s foundational. It’s expansive. And it can even improve lives. The world of mathematics is inspiring—explore the many ways to study math at NYU.

This or That: Computer Science vs. Computer Science

What's better than one computer science major? TWO computer science majors! Find out the differences here.

I Want to Do Research at NYU! But Where Do I Even Begin?

There are plenty of research opportunities at NYU. Curious how to get involved? Read on!

Applied Math Seminar (AMS)

Seminar Organizer(s): Mike O'Neil

Past Events

• Friday, December 10, 2021 TBA Corentin Herbert - Ecole Normale Superieure de Lyon 2:30PM, Warren Weaver Hall
• Friday, December 3, 2021 LIFE IN A TIGHT SPOT: HOW BACTERIA SWIM, DISPERSE, AND GROW IN CROWDED SPACES Sujit Datta - Princeton University 2:30PM, Warren Weaver Hall
• Friday, November 19, 2021 TBA Robert Dudley - Berkeley 2:30PM, Warren Weaver Hall
• Friday, November 12, 2021 TBA Aref Hashemi Amrei - Courant, NYU 2:30PM, Warren Weaver Hall
• Friday, November 5, 2021 TBA Niall Mangan - Northwestern University 2:30PM, Warren Weaver Hall
• Friday, October 29, 2021 TBA Jane Wang - Cornell University 2:30PM, Warren Weaver Hall
• Friday, October 29, 2021 Summer Undergraduate Research Experience SURE and AM-SURE Presentations 9AM, Warren Weaver Hall
• Friday, October 15, 2021 Untangling in time: designing time varying applied fields to reveal interior structure Graeme Milton - University of Utah 2:30PM, Warren Weaver Hall
• Friday, October 1, 2021 Surface gravity waves enhance the settling and dispersion of finite-size particles Michelle DiBenedetto - University of Washington 7:20PM, Warren Weaver Hall
• Friday, September 24, 2021 Singular measures and information capacity of turbulent cascades Gregory Falkovich - Weizmann Institute 2:30PM, Warren Weaver Hall
• Friday, September 17, 2021 Could convection in porous media explain the geysers of Enceladus? Samuel Boury - CIMS 2:30PM, Warren Weaver Hall

Admissions and Financial Support

• Degree Requirements

Who Should Apply

The AOSM PhD program lies within the Mathematics Department  and is a closely-related sibling program to the PhD in Mathematics . We seek to admit and train scholars who possess great intellectual potential to shape the future of the atmospheric and oceanic sciences, building bridges between applied mathematics and climate research.  

Candidates should have: (1) a strong background in mathematics, physics, and/or engineering; (2) experience in research (or the equivalent, e.g., through work or outreach); and (3), most importantly, a sincere interest (but not necessarily experience) in the dynamics that underlie Earth’s climate. 

Intellectual potential, a passion to understand the climate system, and the tenacity to overcome obstacles are the key attributes of successful PhD students in our program.  These qualities can be demonstrated in many ways.  Our students come from all across the United States and world, bringing diverse interests (from pure math to applied physics), educational, and life experiences.  

We strongly encourage applications from women, racial and ethnic minorities, and other individuals who are under-represented in our field, across color, creed, race, ethnic and national origin, physical ability, gender, and sexual identity. 

Please refer to the  AOSM Degree Requirements page for further information on coursework, examinations and other aspects of the program.

How to Apply

For complete information on applying to graduate programs at NYU, see the GSAS Application Resources Center . To apply to the AOSM PhD program, find our admissions guidelines and the online application portal at the  GSAS page for graduate programs in Mathematics .    Applications are due by January 4.

Financial Support

All AOSM PhD students are supported for up to five years by MacCracken Fellowships , which cover tuition, registration fees and the NYU individual comprehensive health insurance plan. MacCracken funding also provides a competitive nine-month stipend to cover the expenses of living in New York City.  During the summer, AOSM PhD students generally receive faculty grant funding to continue research. Students are also encouraged to apply for external fellowships; a list may be found at the Department of Mathematics Financial Aid Policies page.

For questions about the details of the AOSM PhD program and admissions requirements, please email our current Director of Graduate Studies at  [email protected] .

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Elena Kosygina

Visiting Professor of Mathematics, NYU Shanghai Email [email protected]

Elena Kosygina is a Visiting Professor of Mathematics at NYU Shanghai and a Professor of Mathematics at Baruch College and the CUNY Graduate Center. After completing her PhD at the Courant Institute of Mathematical Sciences, NYU, she was a (non-tenure-track) R. Boas Assistant Professor at Northwestern University, and then moved to CUNY to a tenure-track position and received tenure. She was a member of the Institute of Advanced Studies (Spring 2009) and a Simons Fellow in Mathematics (2014-2015). Prof. Kosygina’s research is in probability, stochastic processes, and partial differential equations. In particular, she is interested in scaling limits of self-interacting random walks and in homogenization of Hamilton-Jacobi equations in random media.

Select Publications

• Kosygina, E., Mountford, T., Peterson, J., Convergence and non-convergence of scaled self-interacting random walks to Brownian motion perturbed at extrema; Annals of Probability, 51 (2023), no. 5, 1684-1728
• Kosygina, E., Mountford, T., Peterson, J., Convergence of random walks on Markovian cookie stacks to Brownian motion perturbed at extrema; Probability Theory and Related Fields, 182 (2022), no. 1-2, 189-275.
• Kosygina, E., Zerner, M. P. W., A zero-one law for recurrence and transience of frog processes; Probability Theory and Related Fields, 168 (2017), no. 1-2, 317–346.
• Kosygina, E., Zerner, M. P. W., Excited random walks: results, methods, open problems. Bulletin of the Institute of Mathematics. Academia Sinica (New Series) 8 (2013), no. 1, 105-157.
• Kosygina, E., Rezakhanlou, F., Varadhan, S.R.S., Stochastic homogenization of Hamilton-Jacobi-Bellman Equations. Communications on Pure and Applied Mathematics, 59 (2006), no. 10, 1489-1521. 
• PhD, Mathematics Courant Institute of Mathematical Sciences, NYU
• Candidate of Sciences, Physics and Mathematics Moscow State University 

Research Interests

• Random walks and diffusions in random media, self-interacting random walks
• Homogenization of Hamilton-Jacobi equations in stationary ergodic media

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Gizem Kayar, PhD.

Computer Science Professor Computer Graphics & Phsyically Based Simulation Systems

Day: May 6, 2024

Please visit our itch.io page to play the game:  https://gizemkcnyu.itch.io/nyu-cg-app

Do not forget to share your ideas with us:  https://forms.gle/LEiDU9b8ZZPnnFfB6

DURF-URC 2024

I am so proud of my students: Yinlong and Tim, who presented their impressive work at NYU URC Poster Session on May 3rd and both won the first places among their groups, and Daniel and Philipp who presented their amazing work in the panel session. 

With my panel presenter advisees Daniel and Philipp, we are working on a sketch based model generation method which will be published soon.

Daniel, Philipp, Yinlong amd Tim: You will graduate soon and will study in some of the most prestigious universities as grad students. I am so happy and privileged to have been able to work with you guys. Thank you all.

Quick Links +

Applied ph.d. program requirements (fall 2024).

This plan requires a total of 60 units. Students will enroll for 12 units per quarter including research, academic, and seminar units. Before advancing to Candidacy for a doctoral degree, a student must have satisfied all requirements set by the graduate program, maintained a minimum GPA of 3.0 in all course work undertaken (except those courses graded S or U), passed the PhD Preliminary Examination, and passed the Qualifying Examination. A dissertation and an exit seminar are required.

Course Requirements

• Area A (12 units in one of the series) : (i) Analysis Series MAT 201AB/MAT 201C/MAT 205/MAT206 (Analysis) or (ii) Methods of Applied Mathematics MAT 207ABC.  
• Area B (8 units in one of the series): (i) Data Science series: Numerical Optimization (MAT 258A), Discrete and Mixed-Integer Optimization (MAT258B), Mathematics of Data Science (MAT 270); or (ii) Numerical Methods series: Numerical Methods: Fundamentals (MAT 226A), Numerical Methods: Large-Scale Matrix Computations (MAT 226B), Numerical Methods: Ordinary Differential Equations (MAT226C), Numerical Solutions of Differential Equations A, B and C (MAT 228ABC); or (iii) Probability series: Probability Theory A and B (MAT235AB), Mathematical Statistics III (STA231C); or (iv) Theoretical Computer Science series: Theoretical Computer Science (ECS220), Design and Analysis of Algorithms (ECS222).  
• Graduate Advanced Mathematics: 12 units of 200-level Mathematics courses whose course numbers are 279 or less. These include courses from areas A or B not selected as core courses. One mathematics-oriented graduate course outside of Mathematics, could be substituted but only with prior approval by GGAM Chair.  
• Field of Specialization (FOS): Minimum of 15 units in a field of specialization, such as, any courses in Area A or B not taken to satisfy the core requirements, optimization, and control, differential equations, probability and statistics, discrete mathematics, mathematical physics, mathematical biology, harmonic analysis and signal processing, etc. Out of this minimum of 15 units, at least one course of 3 or more units must be outside of Mathematics. Courses outside of the mathematics department have to be approved by the Chair of the graduate group. For a list of preapproved courses, see the GGAM webpage and consult with the potential thesis advisor. An updated list of courses can be found in https://appliedmath.ucdavis.edu/graduate/sample-depth-courses  
• Advanced Mathematics: Maximum of 12 units, in three 100 level (i.e.upper division) math courses.  
• GGAM miniconference: Attendance at the annual GGAM mini-conference, which takes place during winter quarter graduate welcome and consists of faculty talks and a student poster session showcasing the research being done at GGAM, is required in the first or second year, for which 1 unit of 290 will be given in order to document compliance.  
• MAT 290 seminars  
• MAT 390 and Teaching: Each student who accepts a TAship in the Department of Mathematics is required to complete MAT390, which is taught every Fall quarter. Most students take this in their first year, even if they are supported by a fellowship. MAT 390 does not count toward degree units (but does count for the 12-unit minimum required for registration each quarter). All PhD students are required to be teaching assistants for at least one quarter. Exceptions require approval of the GGAMEXEC. Students beyond their first year are encouraged to apply for positions as Associate-Instructors to develop and improve their lecturing skills.  
• Research Units: Students can register for research units but these units cannot substitute course requirements unless previously reviewed and approved by the chair of the graduate group.

Ph.D. Preliminary Examination

The Ph.D. Preliminary Examination is a written examination covering materials from the student’s chosen tracks Area A (MAT 201AB or MAT 207ABC) and Area B: Data Science: (MAT 168, MAT170); Numerical Methods (MAT128ABC); Probability (MAT 135AB); and Theoretical Computer Science (ECS220, ECS222). The exam is offered in June and September every year. PhD students are required to pass this examination before the end of their second year.  They may take the examination multiple times; what matters is when they pass, not how many attempts.

Qualifying Examination

Students must complete the course requirements before taking their Qualifying Examination (QE). The QE will consist of a written research proposal, a syllabus of materials relevant to the research proposal covered in the chosen tracks in Areas A and B, and oral examination. Approximately six weeks before the date of the proposed QE, the research proposal, along with the QE Application, is submitted to GGAMEXEC for approval. Once approved and required signatures obtained, the QE Application will be forwarded to the Office of Graduate Studies for final approval. The QE should be taken by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program. Passing the QE makes the student eligible for advancement to candidacy.

Dissertation

The doctoral dissertation is an essential part of the Ph.D. program. A topic will be selected by the student, under the guidance of the Dissertation Advisor. Students are encouraged to begin their research activity as early as possible. The dissertation must contain an original contribution of publishable quality to the knowledge of applied mathematics. Acceptance of the dissertation by the dissertation committee must follow Graduate Studies guidelines (Plan B). The program does not have any program-specific requirements, such as length or presentation format. Instructions on preparation of the dissertation and a schedule of dates for filing the thesis in final form are available from Graduate Studies; the dates are also printed in the UC Davis General Catalog.

Exit Seminar

Ph.D. students are required to give a 60-minute seminar presentation, open to the public, on their dissertation subject.

Optional Final Oral Examination (at the discretion of the Dissertation Committee)

After the exit seminar, the student’s dissertation committee may meet privately with the student to discuss the contents of the dissertation and ask additional questions. Satisfaction of this requirement must be verified by the Dissertation Committee Chair.