nyu math phd admissions

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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Application Requirements

There are a number of things to accomplish—and deadlines to be aware of—when applying to graduate or professional school. Understanding sooner rather than later what to do and when to do it can help make the application process less daunting. Below you’ll find some general information and insights to help make your first steps toward applying to an NYU graduate program a bit easier.

First Things First

Common application requirements, additional application requirements, deadlines and decisions.

Virtual Office Hours: Monday – Friday, 9 a.m. to 5 p.m. Eastern In-Person Drop-in Hour s:  Monday, Wednesday - Friday 10 a.m. to 4 p.m. Email: [email protected] Phone: 212-992-GRAD (4723)

The first thing to understand when applying to an NYU graduate or professional program is that each graduate school, center, or institute—and their individual departments and programs in many cases—determines its own application requirements. While this page provides a general introduction to applying to NYU, the information here may or may not apply to your specific program. Therefore, it is extremely important for you to speak directly with the admissions counselors at your school and program of interest. When you determine the NYU program that’s right for you, don’t wait to reach out.

There are a handful of items that, in many cases, are common across graduate school applications. It’s worth repeating, however, that you should get in touch with your school and program directly to learn exactly what your application requires. Some more common application items include:

• Letter(s) of Recommendation: Some programs ask for one. Others may ask for up to four. There may also be specific expectations about who should write these letters, but in general they should come from individuals who know you well and are able to speak directly to your abilities, accomplishments, and potential.
• Statement of Purpose/Personal Statement/Personal Essay: This is your chance to tell admissions who you are, explain your goals (both academic and professional), and share the ways in which the program will benefit by bringing you in. It’s possible that the program may have a more specific prompt or ask you to address a specific question or series of questions.
• Transcripts and Degrees: Since you’re taking your academics to the next level, you need to prove that you’ve successfully completed the previous level(s). The graduate or professional program to which you’re applying will usually determine the transcripts and degree(s) you’re expected to provide. Applying to a master’s program commonly requires a bachelor’s degree and transcripts from all undergraduate institutions. Similarly, applying to a PhD or other doctoral program may require a master’s degree and transcripts from all graduate institutions.
• English Language Proficiency Exam: If you’re an international applicant, or you completed your previous degree outside the United States at an institution where English is not the language of instruction, you may be required to submit scores from an English Language Proficiency Exam (ELPE). There are a number of ELPEs out there. Make sure you’re taking the right one by contacting your program’s graduate admissions office.
• Application Fee: Application fees vary by school and program. Get in touch with your program’s graduate admissions office if you have questions.

Depending on the program you’re interested in, there may be some requirements in addition to—or in place of—the more common ones listed above. You’ll often encounter these additional requirements when applying to programs in the medical, legal, or artistic fields, but they’re not limited to those areas. While your program’s graduate admissions office will be able to tell you exactly what you need to submit with your application, you can learn about a few of them here:

• Entrance Exam(s): While graduate school entrance exams might be considered common by some, exactly which exam you might be required to take can vary across programs. The most common exam is the GRE (Graduate Record Examination), but the GMAT (Graduate Management Admission Test), LSAT (Law School Admission Test), and MCAT (Medical College Admissions Test) are also quite well known.  
• Creative Submission(s): Even though portfolio submissions and auditions are common when applying to an arts program, others may also ask you to provide writing samples, musical scores, or video submissions. These requirements give you the chance to display your abilities and show programs firsthand why they should admit you.
• Interviews: You may be asked to sit for an in-person interview with one or more individuals from your program. Like a job interview, these conversations give you the chance to introduce yourself to the people you’ll be working with and answer questions about your academic, professional, and personal goals. 
• Résumé or CV: You may be expected to submit a résumé or CV that showcases your academic and/or professional experiences, particularly those that are most relevant to your field of study. A résumé or CV is also an opportunity to share your research experience and academic publications, which may be required for certain research-based programs.

Application deadlines and admissions decision dates are quite varied across NYU’s graduate and professional schools, centers, and institutes. Application deadlines depend on a number of factors, including the program you’re applying to, when you’re planning to start, and whether you plan to be a full- or part-time student. Additionally, early decision applications have a different deadline than regular decision applications. Talk to your admissions counselor and make sure you understand your program’s application deadlines.

Like application deadlines, admissions decision dates vary across NYU. Admissions decisions also depend on the program and starting term as well as the schedules of individual schools, centers, or institutes. Some programs have set admissions decision dates, while others provide time frames or utilize rolling decisions. Your admissions counselor will be able to give you an idea of when you can expect to receive your admissions decision.

Online Application for the Graduate School of Arts and Science (GSAS) at New York University

To start a new application:   Click "Start New Application" at the bottom of this screen. To continue an application:   Click "(year) Application" on the left side of the screen below. Submitting your online application, including all required supporting materials, must be completed by no later than the application deadline of the program to which you are applying. This includes not only documents you are required to upload, but also materials that are sent by others such as official test scores and letters of recommendation.  Please refer to the Instructions section of your online application for our complete policies and procedures. You may submit only one application to the Graduate School of Arts and Science (GSAS) for consideration in a given term. If you submit more than one application to GSAS for a term, all applications submitted after the first one will be held and will not be considered for admission. Thus, please determine carefully the one GSAS program to which you will apply.  Applicants are permitted to submit admissions applications to two (or more) programs if they are within different schools at NYU . For example, you may apply to a program in GSAS and to a different program at the Steinhardt School. However, you may not apply to both Computer Science and Economics at the same time because both are within GSAS. If you choose to apply to programs that are in different schools, it will be necessary to complete and submit separate applications and pay each school a separate application fee. The following NYU graduate schools are separate from GSAS: Tandon (Engineering), Tisch (Arts), Sackler (Medicine), School of Law, Steinhardt (Culture, Education and Human Development), Stern (Business), Public Health, Wagner (Public Service), Silver (Social Work) and Gallatin (Individualized Study).

• 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

Graduate Study in Mathematics

While a career in mathematics can be very attractive, it takes time to acquire the necessary skills, particularly for basic research at the Ph.D. level.  Graduate study is essential for most fields. The undergraduate course sequence provides a foundation upon which more advanced mathematics will be built. In graduate study, one or two further years of coursework completes this basic training. Thereafter, more specialized courses, often at the frontiers of research, are taken.  Applied mathematics students will take courses in various application areas to acquire experience in modeling the real world, and to learn how mathematics can help with problems from the physical and biological sciences, and in finance.

The breadth and depth of work will depend on the degree level.  With an M.S. degree, the student is prepared for many jobs in government, business, and industry; with the Ph.D. degree the choices are wider.  Many Ph.D. mathematicians join the faculty of a university or four-year college, where they not only teach but also conduct research and publish their results in scholarly journals and books.  Others take post-doctoral positions at various laboratories around the world, where work of interest to them is being done.  Still others pursue careers in corporate research and management.  With either an M.S. or a Ph.D., starting salaries are significantly higher than those of graduates with bachelor's degrees.

At both the M.S. and Ph.D. levels, graduate study in mathematics develops a number of important skills for solving problems suggested either by mathematics or by real world questions.  Foremost is the ability to break complex issues into smaller, more manageable problems, until a model is reached which can be thoroughly studied and understood.  Applied mathematics develops the art of extracting quantitative models from problems of physics, biology, engineering and economics.   This ability comes from experience, such as that acquired gradually from examples studied in graduate courses.

• 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.