Natural Sciences and Mathematics

Mathematical sciences.

Doctor of Philosophy in Mathematics

The program offers extensive coursework and intensive research experience in theory, methodology, and applications of mathematics (see  degree requirements ). 

  • Faculty members with broad and diverse research interests are available to supervise doctoral dissertations .
  • Financial support in the form of assistantships, full tuition support, and scholarships and awards are provided. Additional scholarships are available for US citizens and permanent residents.
  • Our students, both domestic and international, have a strong record of starting in full-time jobs right after graduation .
  • Students have opportunities to participate in active seminar series in  Algebra and Combinatorics ;   Computational Science ;  Geometry, Topology and Dynamical Systems ; and  Nonlinear Analysis and Dynamical Systems ; and the departmental  Colloquium  series.
  • To enhance career prospects, students can pursue  Graduate Certificate in Data Science , and possibly use the certificate courses to fulfill the elective requirements.
  • NSM Career Success Center  is available to support professional development and experiential learning of students.  
  • GRE test score is not required for admission.

More than 85% of our 45 Mathematics PhD graduates since 2020, both domestic and international, secured full-time employment within a few months of receiving their degrees. 

Placement of 2022 & 2023 Mathematics PhD Graduates

See a more complete list  

Assistantships

Graduate Teaching Assistantships are offered to qualified PhD students on a competitive basis. These assistantships include a monthly stipend (currently set at $2,400) along with a full tuition waiver (covering 9 credit hours per term in the Fall and Spring semesters). The assistantship additionally covers the cost of health insurance purchased through the university and most fees. Graduate Research Assistantships for advanced PhD students are also available on some faculty members’ research grants. Typically, assistantship support is provided for five years and encompasses the Summer semester as well.

All admitted students are considered for assistantships; no separate application is necessary. 

Scholarships, Fellowships & Awards

PhD students are additionally supported through the following awards:

  • NSM McDermott PhD Admission Fellowship  (for highly qualified new students, offered at the time of admission)
  • Dean’s Fellowship  and  EEF Scholarship  (for highly qualified new students who are U.S. citizens and permanent residents, offered at the time of admission)
  • Julia Williams Van Ness Merit Scholarship  and  Mei Lein Fellowship
  • Outstanding Teaching Assistant of the Year Award
  • Dean of Graduate Education Dissertation Research Award
  • Best Dissertation Award ,  David Daniel Thesis Award , and  Outstanding Graduate Student Award

Conference Travel Support

NSM Conference Travel Award  and  Betty and Gifford Johnson Travel Award  are available to provide financial support to PhD students to present their research at professional conferences.

  • How To Apply
  • Frequently Asked Questions
  • Scholarships & Awards
  • Office of Admissions and Enrollment

Graduate Resources

  • Mathematics Research
  • Statistics & Actuarial Science Research
  • Graduate Advisors
  • Mathematics Courses
  • Statistics Courses
  • Actuarial Science Courses
  • Qualifying Exam Archive
  • Office of Graduate Education

Ready to start your application?

Before you apply, visit our  How to Apply  page to get familiar with the admission requirements and application process.

[email protected]

math phd time

Ph.D. Program Overview

Description.

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of  interests of the faculty . The department has outstanding groups in the areas of algebra, algebraic geometry,  analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of  applied mathematics ,  computer science ,  operations research , and  statistics .

Core Courses

A normal course load for a beginning graduate student is three courses per term. 

There are no qualifying exams, but the program requires that all students pass four courses to be selected from the six core courses. First-year students are allowed to place out of some (possibly, all) of the core courses. In order to place out of a course, students should contact the faculty member who is teaching the course during the current academic year, and that faculty member will make a decision. The minimum passing grade for the core courses is B-; no grade is assigned for placing out of a core course.

At least two core courses should be taken (or placed out) by the end of the first year. At least four core courses should be taken (or placed out) by the end of the second year (cumulative). These time requirements can be waived for students with health problems or other significant non-academic problems. They can be also waived for students who take time-consuming courses in another area (for example, CS) and who have strong support from a faculty; requests from such students should be made before the beginning of the spring semester. 

The core courses  are distributed among three main areas: analysis, algebra and topology/geometry. A student must pass at least one course from each group. All entering graduate students are encouraged to eventually take all six core courses with the option of an S/U grade for two of them. 

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

Students who are not ready to take some of the core courses may take MATH 4130-4140, Introduction to Analysis, and/or MATH 4330-4340, Introduction to Algebra, which are the honors versions of our core undergraduate courses.

"What is...?" Seminar

The "What Is...?" Seminar is a series of talks given by faculty in the graduate field of Mathematics. Speakers are selected by an organizing committee of graduate students. The goal of the seminar is to aid students in finding advisors.

Schedule for the "What Is...?" seminar

Special Committee

The Cornell Graduate School requires that every student selects a special committee (in particular, a thesis adviser, who is the chair or the committee) by the end of the third semester.

The emphasis in the Graduate School at Cornell is on individualized instruction and training for independent investigation. There are very few formal requirements and each student develops a program in conjunction with his or her special committee, which consists of three faculty members, some of which may be chosen from outside the field of mathematics. 

Entering students are not assigned special committees. Such students may contact any of the members on the Advising Committee if they have questions or need advice.

Current Advising Committee

Analysis / Probability / Dynamical Systems / Logic: Lionel Levine Geometry / Topology / Combinatorics: Kathryn Mann Probability / Statistics:  Philippe Sosoe Applied Mathematics Liaison: Richard Rand

Admission to Candidacy

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.

The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and his/her special committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the core graduate courses. 

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the special committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes five to six years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the special committee. By the time of the oral admission to candidacy examination, the candidate should have selected as chairperson of the committee the faculty member who will supervise the research. When the thesis is completed, the student presents his/her results at the thesis defense or B Exam. All doctoral students take a Final Examination (the B Exam, which is the oral defense of the dissertation) upon completion of all requirements for the degree, no earlier than one month before completion of the minimum registration requirement.

Masters Degree in the Minor Field

Ph.D. students in the field of mathematics may earn a Special Master's of Science in Computer Science. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for this degree, the student must have a member representing the minor field on the special committee and pass the A-exam in the major field. The rules and the specific requirements for each master's program are explained on the referenced page.

Cornell will award at most one master's degree to any student. In particular, a student awarded a master's degree in a minor field will not be eligible for a master's degree in the major field.

Graduate Student Funding

Funding commitments made at the time of admission to the Ph.D. program are typically for a period of five years. Support in the sixth year is available by application, as needed. Support in the seventh year is only available by request from an advisor, and dependent on the availability of teaching lines. Following a policy from the Cornell Graduate School, students who require more than seven years to complete their degree shall not be funded as teaching assistants after the 14th semester.

Special Requests

Students who have special requests should first discuss them with their Ph.D. advisor (or with a field member with whom they work, if they don't have an advisor yet). If the advisor (or field faculty) supports the request, then it should be sent to the Director of Graduate Studies.  

math phd time

  • Doing a PhD in Mathematics
  • Doing a PhD

What Does a PhD in Maths Involve?

Maths is a vast subject, both in breadth and in depth. As such, there’s a significant number of different areas you can research as a math student. These areas usually fall into one of three categories: pure mathematics, applied mathematics or statistics. Some examples of topics you can research are:

  • Number theory
  • Numerical analysis
  • String theory
  • Random matrix theory
  • Graph theory
  • Quantum mechanics
  • Statistical forecasting
  • Matroid theory
  • Control theory

Besides this, because maths focuses on addressing interdisciplinary real-world problems, you may work and collaborate with other STEM researchers. For example, your research topic may relate to:

  • Biomechanics and transport processes
  • Evidence-based medicine
  • Fluid dynamics
  • Financial mathematics
  • Machine learning
  • Theoretical and Computational Optimisation

What you do day-to-day will largely depend on your specific research topic. However, you’ll likely:

  • Continually read literature – This will be to help develop your knowledge and identify current gaps in the overall body of knowledge surrounding your research topic.
  • Undertake research specific to your topic – This can include defining ideas, proving theorems and identifying relationships between models.
  • Collect and analyse data – This could comprise developing computational models, running simulations and interpreting forecasts etc.
  • Liaise with others – This could take many forms. For example, you may work shoulder-to-shoulder with individuals from different disciplines supporting your research, e.g. Computer scientists for machine learning-based projects. Alternatively, you may need frequent input from those who supplied the data for your research, e.g. Financial institutions or biological research colleagues.
  • Attend a wide range of lectures, seminars and events.

Browse PhD Opportunities in Mathematics

Application of artificial intelligence to multiphysics problems in materials design, study of the human-vehicle interactions by a high-end dynamic driving simulator, physical layer algorithm design in 6g non-terrestrial communications, machine learning for autonomous robot exploration, detecting subtle but clinically significant cognitive change in an ageing population, how long does it take to get a phd in maths.

The average programme duration for a mathematics PhD in the UK is 3 to 4 years for a full-time studying. Although not all universities offer part-time maths PhD programmes, those that do have a typical programme duration of 5 to 7 years.

Again, although the exact arrangement will depend on the university, most maths doctorates will require you to first register for an MPhil . At the end of your first year, your supervisor will assess your progress to decide whether you should be registered for a PhD.

Additional Learning Modules

Best Universities for Maths PhD UK

Some Mathematics departments will require you to enrol on to taught modules as part of your programme. These are to help improve your knowledge and understanding of broader subjects within your field, for example, Fourier Analysis, Differential Geometry and Riemann Surfaces. Even if taught modules aren’t compulsory in several universities, your supervisor will still encourage you to attend them for your development.

Most UK universities will also have access to specialised mathematical training courses. The most common of these include Pure Mathematics courses hosted by Mathematics Access Grid Conferencing ( MAGIC ) and London Taught Course Centre ( LTCC ) and Statistics courses hosted by Academy for PhD Training in Statistics ( APTS ).

What Are the Typical Entry Requirements for A PhD in Maths?

In the UK, the typical entry requirements for a Maths PhD is an upper second-class (2:1) Master’s degree (or international equivalent) in Mathematics or Statistics [1] .

However, there is some variation on this. From writing, the lowest entry requirement is an upper second-class (2:1) Bachelor’s degree in any math-related subject. The highest entry requirement is a first-class (1st) honours Master’s degree in a Mathematics or Statistics degree only.

It’s worth noting if you’re applying to a position which comes with funding provided directly by the Department, the entry requirements will usually be on the higher side because of their competitiveness.

In terms of English Language requirements, most mathematics departments require at least an overall IELTS (International English Language Testing System) score of 6.5, with no less than 6.0 in each individual subtest.

Tips to Consider when Making Your Application

When applying to any mathematics PhD, you’ll be expected to have a good understanding of both your subject field and the specific research topic you are applying to. To help show this, it’s advisable that you demonstrate recent engagement in your research topic. This could be by describing the significance of a research paper you recently read and outlining which parts interested you the most, and why. Additionally, you can discuss a recent mathematics event you attended and suggest ways in how what you learnt might apply to your research topic.

As with most STEM PhDs, most maths PhD professors prefer you to discuss your application with them directly before putting in a formal application. The benefits of this is two folds. First, you’ll get more information on what their department has to offer. Second, the supervisor can better discover your interest in the project and gauge whether you’d be a suitable candidate. Therefore, we encourage you to contact potential supervisors for positions you’re interested in before making any formal applications.

How Much Does a Maths PhD Typically Cost?

The typical tuition fee for a PhD in Maths in the UK is £4,407 per year for UK/EU students and £20,230 per year for international students. This, alongside the range in tuition fees you can expect, is summarised below:

Note: The above tuition fees are based on 12 UK Universities [1]  for 2020/21 Mathematic PhD positions. The typical fee has been taken as the median value.

In addition to the above, it’s not unheard of for research students to be charged a bench fee. In case you’re unfamiliar with a bench fee, it’s an annual fee additional to your tuition, which covers the cost of specialist equipment or resources associated with your research. This can include the upkeep of supercomputers you may use, training in specialist analysis software, or travelling to conferences. The exact fee will depend on your specific research topic; however, it should be minimal for most mathematic projects.

What Specific Funding Opportunities Are There for A PhD in Mathematics?

Alongside the usual funding opportunities available to all PhD Research students such as doctoral loans, departmental scholarships, there are a few other sources of funding available to math PhD students. Examples of these include:

You can find more information on these funding sources here: DiscoverPhDs funding guide .

What Specific Skills Do You Gain from Doing a PhD in Mathematics?

A doctorate in Mathematics not only demonstrates your commitment to continuous learning, but it also provides you with highly marketable skills. Besides subject-specific skills, you’ll also gain many transferable skills which will prove useful in almost all industries. A sample of these skills is listed below.

  • Logical ability to consider and analyse complex issues,
  • Commitment and persistence towards reaching research goals,
  • Outstanding verbal and written skills,
  • Strong attention to detail,
  • The ability to liaise with others from unique disciple backgrounds and work as part of a team
  • Holistic deduction and reasoning skills,
  • Forming and explaining mathematical and logical solutions to a wide range of real-world problems,
  • Exceptional numeracy skills.

What Jobs Can You Get with A Maths PhD?

Jobs for Maths PhDs - PhD in Mathematics Salary

One of the greatest benefits maths PostDocs will have is the ability to pursue a wide range of career paths. This is because all sciences are built on core principles which, to varying extents, are supported by the core principles of mathematics. As a result, it’s not uncommon to ask students what path they intend to follow after completing their degree and receive entirely different answers. Although not extensive by any means, the most common career paths Math PostDocs take are listed below:

  • Academia – Many individuals teach undergraduate students at the university they studied at or ones they gained ties to during their research. This path is usually the preferred among students who want to continue focusing on mathematical theories and concepts as part of their career.
  • Postdoctoral Researcher – Others continue researching with their University or with an independent organisation. This can be a popular path because of the opportunities it provides in collaborative working, supervising others, undertaking research and attending conferences etc.
  • Finance – Because of their deepened analytical skills, it’s no surprise that many PostDocs choose a career in finance. This involves working for some of the most significant players in the financial district in prime locations including London, Frankfurt and Hong Kong. Specific job titles can include Actuarial, Investment Analyst or Risk Modeller.
  • Computer Programming – Some students whose research involves computational mathematics launch their career as a computer programmer. Due to their background, they’ll typically work on specialised projects which require high levels of understanding on the problem at hand. For example, they may work with physicists and biomedical engineers to develop a software package that supports their more complex research.
  • Data Analyst – Those who enjoy number crunching and developing complex models often go into data analytics. This can involve various niches such as forecasting or optimisation, across various fields such as marketing and weather.

What Are Some of The Typical Employers Who Hire Maths PostDocs?

As mentioned above, there’s a high demand for skilled mathematicians and statisticians across a broad range of sectors. Some typical employers are:

  • Education – All UK and international universities
  • Governments – STFC and Department for Transport
  • Healthcare & Pharmaceuticals – NHS, GSK, Pfizer
  • Finance & Banking – e.g. Barclays Capital, PwC and J. P. Morgan
  • Computing – IBM, Microsoft and Facebook
  • Engineering – Boeing, Shell and Dyson

The above is only a small selection of employers. In reality, mathematic PostDocs can work in almost any industry, assuming the role is numerical-based or data-driven.

Math PhD Employer Logos

How Much Can You Earn with A PhD in Maths?

As a mathematics PhD PostDoc, your earning potential will mostly depend on your chosen career path. Due to the wide range of options, it’s impossible to provide an arbitrary value for the typical salary you can expect.

However, if you pursue one of the below paths or enter their respective industry, you can roughly expect to earn [3] :

Academic Lecturer

  • Approximately £30,000 – £35,000 starting salary
  • Approximately £40,000 with a few years experience
  • Approximately £45,000 – £55,000 with 10 years experience
  • Approximately £60,000 and over with significant experience and a leadership role. Certain academic positions can earn over £80,000 depending on the management duties.

Actuary or Finance

  • Approximately £35,000 starting salary
  • Approximately £45,000 – £55,000 with a few years experience
  • Approximately £70,000 and over with 10 years experience
  • Approximately £180,000 and above with significant experience and a leadership role.

Aerospace or Mechanical Engineering

  • Approximately £28,000 starting salary
  • Approximately £35,000 – £40,000 with a few years experience
  • Approximately £60,000 and over with 10 years experience

Data Analyst

  • Approximately £45,000 – £50,000 with a few years experience
  • Approximately £90,000 and above with significant experience and a leadership role.

Again, we stress that the above are indicative values only. Actual salaries will depend on the specific organisation and position and responsibilities of the individual.

Facts and Statistics About Maths PhD Holders

The below chart provides useful insight into the destination of Math PostDocs after completing their PhD. The most popular career paths from other of highest to lowest is education, information and communication, finance and scientific research, manufacturing and government.

Percentage of Math PostDocs entering an industry upon graduating

Note: The above chart is based on ‘UK Higher Education Leavers’ data [2] between 2012/13 and 2016/17 and contains a data size of 200 PostDocs. The data was obtained from the Higher Education Statistics Agency ( HESA ).

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

Alan_Turing

Alan Turing was a British Mathematician, WW2 code-breaker and arguably the father of computer science. Alongside his lengthy list of achievements, Turning achieved a PhD in Mathematics at Princeton University, New Jersey. His thesis titled ‘Systems of Logic Based on Ordinals’ focused on the concepts of ordinal logic and relative computing; you can read it online here . To this day, Turning pioneering works continues to play a fundamental role in shaping the development of artificial intelligence (AI).

Ruth Lawrence

math phd time

Ruth Lawrence is a famous British–Israeli Mathematician well known within the academic community. Lawrence earned her PhD in Mathematics from Oxford University at the young age of 17! Her work focused on algebraic topology and knot theory; you can read her interesting collection of research papers here . Among her many contributions to Maths, her most notable include the representation of the braid groups, more formally known as Lawrence–Krammer representations.

Emmy Noether

math phd time

Emmy Noether was a German mathematician who received her PhD from the University of Erlangen, Germany. Her research has significantly contributed to both abstract algebra and theoretical physics. Additionally, she proved a groundbreaking theorem important to Albert Einstein’s general theory of relativity. In doing so, her theorem, Noether’s theorem , is regarded as one of the most influential developments in physics.

Other Useful Resources

Institute of Mathematics and its Applications (IMA) – IMA is the UK’s professional body for mathematicians. It contains a wide range of useful information, from the benefits of further education in Maths to details on grants and upcoming events.

Maths Careers – Math Careers is a site associated with IMA that provides a wide range of advice to mathematicians of all ages. It has a section dedicated to undergraduates and graduates and contains a handful of information about progressing into research.

Resources for Graduate Students – Produced by Dr Mak Tomford, this webpage contains an extensive collection of detailed advice for Mathematic PhD students. Although the site uses US terminology in places, don’t let that put you off as this resource will prove incredibly helpful in both applying to and undertaking your PhD.

Student Interviews – Still wondering whether a PhD is for you? If so, our collection of PhD interviews would be a great place to get an insider perspective. We’ve interviewed a wide range of PhD students across the UK to find out what doing a PhD is like, how it’s helped them and what advice they have for other prospective students who may be thinking of applying to one. You can read our insightful collection of interviews here .

[1] Universities used to determine the typical (median) and range of entry requirements and tuition fees for 2020/21 Mathematics PhD positions.

  • http://www.lse.ac.uk/study-at-lse/Graduate/Degree-programmes-2020/MPhilPhD-Mathematics
  • https://www.ox.ac.uk/admissions/graduate/courses/dphil-mathematics?wssl=1
  • https://www.graduate.study.cam.ac.uk/courses/directory/mapmpdpms
  • https://www.ucl.ac.uk/prospective-students/graduate/research-degrees/mathematics-mphil-phd
  • http://www.bristol.ac.uk/study/postgraduate/2020/sci/phd-mathematics/
  • https://www.surrey.ac.uk/postgraduate/mathematics-phd
  • https://www.maths.ed.ac.uk/school-of-mathematics/studying-here/pgr/phd-application
  • https://www.lancaster.ac.uk/study/postgraduate/postgraduate-courses/mathematics-phd/
  • https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd
  • https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05325/phd-pure-mathematics/
  • https://warwick.ac.uk/study/postgraduate/research/courses-2020/mathematicsphd/
  • https://www.exeter.ac.uk/pg-research/degrees/mathematics/

[2] Higher Education Leavers Statistics: UK, 2016/17 – Outcomes by subject studied – https://www.hesa.ac.uk/news/28-06-2018/sfr250-higher-education-leaver-statistics-subjects

[3] Typical salaries have been extracted from a combination of the below resources. It should be noted that although every effort has been made to keep the reported salaries as relevant to Math PostDocs as possible (i.e. filtering for positions which specify a PhD qualification as one of their requirements/preferences), small inaccuracies may exist due to data availability.

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Ph.D. in Mathematics

General info.

  • Faculty working with students: 37
  • Students: 52
  • Students receiving Financial Aid: 100%
  • Part time study available: No
  • Application terms: Fall
  • Application deadline: December 13

Mark Haskins Director of Graduate Studies Department of Mathematics Duke University Box 90320 Durham, NC 27708-0320

Phone: (919) 660-2800

Email:  [email protected]

Website:  http://www.math.duke.edu/graduate/

Program Description

The graduate program in Mathematics at Duke offers research training in a wide variety of topics in mathematics.  Major areas of research specialization include algebra, number theory, algebraic geometry, analysis, differential geometry and physics, topology, dynamical systems, partial differential equations, scientific computing, and stochastic processes.  There are strong groups in mathematical biology, and in the analysis of high-dimensional data using ideas from topology and harmonic analysis.  These and other research efforts often include collaborations with researchers in the medical school and other departments.  These opportunities for interdisciplinary research and the breadth of research areas in the department make the Duke math department an ideal place to prepare for a job inside or outside of academia.

  • Mathematics: PhD Admissions and Enrollment Statistics
  • Mathematics: PhD Completion Rate Statistics
  • Mathematics: PhD Time to Degree Statistics
  • Mathematics: PhD Career Outcomes Statistics

Application Information

Application Terms Available:  Fall

Application Deadline:  December 13

Graduate School Application Requirements See the Application Instructions page for important details about each Graduate School requirement.

  • Transcripts: Unofficial transcripts required with application submission; official transcripts required upon admission
  • Letters of Recommendation: 3 Required
  • Statement of Purpose: Required (see department guidance below)
  • Résumé: Required
  • GRE General (Optional)
  • GRE Subject: Mathematics (Optional)
  • English Language Exam: TOEFL, IELTS, or Duolingo English Test required* for applicants whose first language is not English *test waiver may apply for some applicants
  • GPA: Undergraduate GPA calculated on 4.0 scale required

Department-Specific Application Requirements (submitted through online application)

Statement of Purpose Guidelines Summarize your mathematical work/background and current interests.  (If your principal academic focus has been outside mathematics, tell us about that work and what brings you to mathematics now.)  Explain why you chose to apply to Duke Math (what makes the department a good fit for you?).  It is generally beneficial to keep the statement under two pages.

Writing Sample None required

We strongly encourage you to review additional department-specific application guidance from the program to which you are applying: Departmental Application Guidance

List of Graduate School Programs and Degrees

Mathematics, PhD

Zanvyl krieger school of arts and sciences.

The goal of our PhD program is to train graduate students to become research mathematicians. Each year, an average of five students complete their theses and  go on to exciting careers  in mathematics both inside and outside of academia.

Faculty research interests  in the Johns Hopkins University Department of Mathematics are concentrated in several areas of pure mathematics, including analysis and geometric analysis, algebraic geometry and number theory, differential geometry, algebraic topology, category theory, and mathematical physics. The department also has an active group in data science, in collaboration with the  Applied Math Department .

The Department values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from all interested parties.

A brief overview of our graduate program is below. For more detailed information, please see the links at the right.

Program Overview

All students admitted to the PhD program receive full tuition fellowships and teaching assistantships. Teaching assistant salaries for the 2022-2023 academic year are $33,000, and exceptional applicants are also considered for supplementary fellowships. Students making satisfactory progress can expect to be supported for six years.

PhD candidates take two or three courses per semester over the first several years of the program. These are a mix of required and intermediate-level graduate courses, independent studies, and special topics classes offered by our faculty.

By the beginning of their second year, students are asked to demonstrate competency in algebra and in analysis by passing written qualifying exams in these two broad areas. Students are then expected to choose an advisor, who will supervise their dissertation and also administer an oral qualifying exam to be taken in the second or third year. More specifics about all these requirements are described on the  requirements page .

All graduate students are invited to attend  weekly research seminars in a variety of topic areas  as well as regular department teas and a weekly wine and cheese gathering attended by many junior and senior members of the department. A graduate student lunch seminar series provides an opportunity for our students to practice their presentation skills to a general audience.

PhD students will gain teaching experience as a teaching assistant for undergraduate courses. Most of our students lead two TA sections per week, under the supervision of both the faculty member teaching the course and the director of undergraduate studies. Students wanting more classroom experience (or extra pay) can teach their own sections of summer courses. First-year students are given a reduced TA workload in the spring semester, in preparation for the qualifying exams.

In addition to their stipend, each student is awarded an annual travel allowance to enable them to attend conferences for which limited funding is available or visit researchers at other institutions.

Financial Aid

Students admitted to the Ph.D. program receive teaching assistantships and full tuition fellowships. Exceptional applicants become candidates for one of the university's George E. Owen Fellowships.

William Kelso Morrill Award

The William Kelso Morrill Award for excellence in the teaching of mathematics is awarded every spring to the graduate student who best exemplifies the traits of Kelso Morrill: a love of mathematics, a love of teaching, and a concern for students.

Excellence in Teaching Awards

Three awards are given each year to a junior faculty member and graduate student teaching assistants who have demonstrated exceptional ability and commitment to undergraduate education.

Admission Requirements

Admission to the PhD program is based on primarily on academic records, letters of recommendation, and a personal statement. The Department of Mathematics values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from all interested parties.

Via the online application , applicants should submit:

  • A Statement of Purpose
  • An optional Personal Statement
  • Transcripts from all institutions attended
  • Three letters of recommendation
  • Official GRE scores for both the general and the subject test
  • Official TOEFL scores (if English is not your first language)

The required Statement of Purpose discusses your academic interests, objectives, and preparation. The optional Personal Statement describes your personal background, and helps us create a more holistic understanding of you as an applicant. If you wish you may also discuss your personal background in the Statement of Purpose (e.g. if you have already written a single essay addressing both topics), instead of submitting separate statements.

Application fee waivers are available based on financial need and/or participation in certain programs .

Many frequently asked questions about the graduate admission process are answered here .

No application materials should be mailed to the department. All application materials are processed by the Graduate Admissions Office .

Undergraduate Background

The following is an example of what the math department would consider a good background for a student coming out of a four-year undergraduate program at a college or university in the U.S. (assuming a semester system):

  • Calculus in one variable (two semesters, or AP credits)
  • Multivariable Calculus (one semester)
  • Linear Algebra (one semester)
  • Complex analysis (one semester)
  • Real analysis (two semesters)
  • Abstract algebra (two semesters)
  • Point-set topology (one semester)

Many admitted students have taken upper-level undergraduate mathematics courses or graduate courses. Nevertheless, the department does admit very promising students whose preparation falls a little short of the above model. In such cases, we strongly recommend that the student start to close the gap over the summer, before arriving for the start of the fall semester.

Financial Support   

Students admitted to the PhD program receive full tuition fellowships and teaching assistantships. Teaching assistant salaries for the 2022–2023 academic year are $33,000. Students making satisfactory progress can expect to be supported for six years. Exceptional applicants are considered for supplementary fellowships of $6,000 each year for three years.

Students from underrepresented groups may be eligible for other university-wide supplemental fellowships. Summer teaching is available for students seeking extra income.

Additional Information for International Students

Student Visa Information:  The Office of International Services at Homewood  will assist admitted international students in obtaining a student visa.

English Proficiency: Johns Hopkins University requires students to have adequate English proficiency for their course of study. Students must be able to read, speak, and write English fluently upon their arrival at the university. Applicants whose native language is not English must submit proof of their proficiency in English before they can be offered admission and before a visa certificate can be issued. Proficiency can be demonstrated by submitting results from either the Test of English as a Foreign Language (TOEFL) or the IELTS . Johns Hopkins prefers a minimum score of 100 on the TOEFL or a Band Score of 7 on the IELTS. Results should be sent to Johns Hopkins directly by TOEFL or IELTS. Applicants taking the IELTS must additionally upload a copy of their score through the application system. However, do not send the student copy or a photocopy of the TOEFL.

Program Requirements

Course requirements.

Mathematics PhD candidates must show satisfactory work in Algebra (110.601-602), Real Variables (110.605), Complex Variables (110.607), and one additional non-seminar mathematics graduate course in their first year. The first-year algebra and analysis requirement can be satisfied by passing the corresponding written qualifying exam in September of the first year; these students must complete at least two courses each semester. In addition, PhD candidates must take Algebraic Topology (110.615) and Riemannian Geometry (110.645) by their second year. Students having sufficient background can substitute an advanced topology course for 110.615, or an advanced geometry course for 110.645 with the permission of the instructor.

Candidates must show satisfactory work in at least two mathematics graduate courses each semester of their second year, and if they have not passed their oral qualifying exam, in the first semester of their third year.

Qualifying Exams

Candidates must pass written qualifying exams by the beginning of their second year in Analysis (Real & Complex) and in Algebra. Exams are scheduled for September and May of each academic year, and the dates are announced well in advance.

Candidates must pass an oral qualifying examination in the student’s chosen area of research by April 10 of the third year. The topics of the exam are chosen in consultation with the faculty member who has agreed (provisionally) to be the student’s thesis advisor, who will also be involved in administering the exam.

PhD Dissertation

Candidates must produce a written dissertation based upon independent and original research. After completion of the thesis research, the student will defend the dissertation by means of the  Graduate Board Oral exam . The exam must be held at least three weeks before the Graduate Board deadline the candidate wishes to meet.

Our PhD program does not have a foreign language requirement.

Stanford University

PhD Program

During their first year in the program, students typically engage in coursework and seminars which prepare them for the  Qualifying Examinations .  Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis. Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics.

Current Course Requirements: To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297.

Within the 27 units, students must satisfactorily complete a course sequence. This can be fulfilled in one of the following ways:

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry

  • Math 216A, B, & C: Introduction to Algebraic Geometry
  • Math 230A, B, & C: Theory of Probability
  • 3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

Course Requirements for students starting in Autumn 2023 and later: 

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297. (The course sequence requirement is discontinued for students starting in Autumn 2023 and later.)

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will take their Area Examination, which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.

© Stanford University . Stanford , California 94305 .

Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The application deadline for fall 2024 admission has passed. Applications for fall 2025 admission will open in September 2024.

For information on admissions and financial support, please visit the Harvard Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

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Georgia Institute of Technology College of Sciences

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PhD in Mathematics

Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at  Doctoral Programs . The requirements for all these programs consist of three components:  coursework ,  examinations , and  dissertation  in accordance to the guidelines described in the  GT Catalogue .

Completion of required coursework, examinations, and dissertation normally takes about five years. During the first one or two years, students concentrate on coursework to acquire the background necessary for the comprehensive examinations. By the end of their third year in the program, all students are expected to have chosen a thesis topic, and begin work on the research and writing of the dissertation.

The program of study must contain at least 30 hours of graduate-level coursework (6000-level or above) in mathematics and an additional 9 hours of coursework towards a minor. The minor requirement consists of graduate or advanced undergraduate coursework taken entirely outside the School of Mathematics, or in an area of mathematics sufficiently far from the students area of specialization.

Prior to admission to candidacy for the doctoral degree, each student must satisfy the School's comprehensive examinations (comps) requirement. The first phase is a written examination which students must complete by the end of their second year in the graduate program. The second phase is an oral examination in the student's proposed area of specialization, which must be completed by the end of the third year.

Research and the writing of the dissertation represent the final phase of the student's doctoral study, and must be completed within seven years of the passing of comps. A final oral examination on the dissertation (theses defense) must be passed prior to the granting of the degree.

The Coursework

The program of study must satisfy the following  hours ,  minor , and  breadth  requirements. Students who entered before Fall 2015 should see  the old requirements , though they may opt into the current rules described below, and are advised to do so.

Hours requirements.  The students must complete 39 hours of coursework as follows:

  • At least 30 hours must be in mathematics courses at the 6000-level or higher.
  • At least 9 hours must form the doctoral minor field of study.
  • The overall GPA for these courses must be at least 3.0.
  • These courses must be taken for a letter grade and passed with a grade of at least C.

Minor requirement.  The minor field of study should consist primarily of 6000-level (or higher) coursework in a specific area outside the School of Math, or in a mathematical subject sufficiently far from the student’s thesis work. A total of 9 credit hours is required and must be passed with a grade of B or better. These courses should not include MATH 8900, and must be chosen in consultation with the PhD advisor and the Director of Graduate Studies to ensure that they form a cohesive group which best complements the students research and career goals. A student wishing to satisfy the minor requirement by mathematics courses must petition the Graduate Committee for approval.  Courses used to fulfill a Basic Understanding breadth requirement in Analysis or Algebra should not be counted towards the doctoral minor. Upon completing the minor requirement, a student should immediately complete the  Doctoral Minor form .

Breadth requirements.  The students must demonstrate:

  • Basic understanding of 2 subjects must be demonstrated through passing the subjects' written comprehensive exams.  At least 1 of these 2 exams must be in Algebra or Analysis.
  • Basic understanding of the third subject may be demonstrated either by completing two courses in the subject (with a grade of A or B in each course) or by passing the subject's written comprehensive exam.
  • A basic understanding of both subjects in Area I (analysis and algebra) must be demonstrated.
  • Earning a grade of A or B in a one-semester graduate course in a subject demonstrates exposure to the subject.
  • Passing a subject's written comprehensive exam also demonstrates exposure to that subject.

The subjects.  The specific subjects, and associated courses, which can be used to satisfy the breadth requirements are as follows.

  • Area I subjects:​
  • Area II subjects:​

Special Topics and Reading Courses.

  • Special topics courses may always be used to meet hours requirements.
  • Special topics courses may be used to meet breadth requirements, subject to the discretion of the Director of Graduate Studies.
  • Reading courses may be used to meet hours requirements but not breadth requirements.

Credit Transfers

Graduate courses completed at other universities may be counted towards breadth and hours requirements (courses designated as undergraduate or Bachelors' level courses are not eligible to transfer for graduate credit).  These courses do not need to be officially transferred to Georgia Tech. At a student’s request, the Director of Graduate Studies will determine which breadth and hours requirements have been satisfied by graduate-level coursework at another institution.  

Courses taken at other institutions may also be counted toward the minor requirement, subject to the approval of the Graduate Director; however, these courses must be officially transferred to Georgia Tech.

There is no limit for the transfer of credits applied toward the breadth requirements; however, a maximum of 12 hours of coursework from other institutions may be used to satisfy hours requirements. Thus at least 27 hours of coursework must be completed at Georgia Tech, including at least 18 hours of 6000-level (or higher) mathematics coursework.

Students wishing to petition for transfer of credit from previous graduate level work should send the transcripts and syllabi of these courses, together with a list of the corresponding courses in the School of Math, to the Director of Advising and Assessment for the graduate program.

Comprehensive Examinations

The comprehensive examination is in two phases. The first phase consists of passing two out of seven written examinations. The second phase is an oral specialty examination in the student's planned area of concentration. Generally, a student is expected to have studied the intended area of research but not necessarily begun dissertation research at the time of the oral examination.

Written examinations.  The written examinations will be administered twice each year, shortly after the beginning of the Fall and Spring semesters. The result of the written examination is either pass or fail. For syllabi and sample exams see the  written exams page .

All students must adhere to the following rules and timetables, which may be extended by the Director of Graduate Studies, but only at the time of matriculation and only when certified in writing. Modifications because of leaves from the program will be decided on a case-by-case basis.

After acceptance into the PhD Program in Mathematics, a student must pass the written examinations no later than their fourth administration since the student's doctoral enrollment. The students can pass each of the two written comprehensive exams in separate semesters, and are allowed multiple attempts.

The Director of Graduate Studies (DGS) will be responsible for advising each new student at matriculation of these rules and procedures and the appropriate timetable for the written portion of the examination. The DGS will also be responsible for maintaining a study guide and list of recommended texts, as well as a file of previous examinations, to be used by students preparing for this written examination.

Oral examination.  A student must pass the oral specialty examination within three years since first enrolling in the PhD program, and after having passed the written portion of the comprehensive exams. The examination will be given by a committee consisting of the student's dissertation advisor or probable advisor, two faculty members chosen by the advisor in consultation with the student, and a fourth member appointed by the School's Graduate Director. The scope of the examination will be determined by the advisor and will be approved by the graduate coordinator. The examining committee shall either (1) pass the student or (2) fail the student. Within the time constraints of which above, the oral specialty examination may be attempted multiple times, though not more than twice in any given semester. For more details and specific rules and policies see the  oral exam page .

Dissertation and Defense

A dissertation and a final oral examination are required. For details see our  Dissertation and Graduation  page, which applies to all PhD programs in the School of Math.

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Ph.D. Admissions

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The application window for Fall 2024 is closed.

The Mathematics Department offers two programs to obtain a Ph.D. Applicants can pursue a Ph.D. in  Applied & Interdisciplinary Mathematics or Mathematics.  Please use the "Programs" link at the left to explore our offerings.

  • Three Letters of Recommendation  (May submit up to 5 letters, but only 3 are required.)
  • Curriculum Vitae or Resume
  • Academic Statement of Purpose (concise - no limit)
  • Personal Statement (500 word limit)
  • TOEFL iBT Special Home Edition and IELTS Indicator online test are accepted.
  • Exemption rules:   https://rackham.umich.edu/admissions/applying/tests/
  • List of  International English Exclusive Institutions  approved by Rackham

GRE General Test scores are no longer included in the admission process in accordance with a  policy of the Rackham Graduate School .

GRE Mathematics Subject Test scores are strictly optional. However, if an applicant chooses so, they may submit them as a combined pdf file with their transcript or personal statement.

Application Timeline

The Mathematics Department's graduate programs only accept applications for Fall semesters. 

General Requirements for Admission

A student must have completed a bachelor's degree at an accredited college or university by the time of entry in order to be considered for admission.

Applied & Interdisciplinary Mathematics (AIM) Ph.D. Admissions Requirements

Successful AIM Ph.D. applicants will demonstrate an interest in an interdisciplinary area of applied mathematics in addition to substantial mathematical ability. Two types of students are generally considered for admission to the AIM Ph.D. program:

  • Mathematics majors with excellent grades in mathematics courses and excellent letters of recommendation. The admissions committee will also take into account other scholarly activities such as summer research experience, published papers, or courses in other fields.
  • Non-mathematics majors from the physical, life, or engineering sciences, or from other appropriate areas of study. Such students are expected to have completed at least two upper division mathematics courses, and/or have substantial exposure to mathematics in other courses, and may submit a GRE mathematics subject test score. Other experience in working with mathematics (for instance, summer research positions) will also be taken into account, as well as grade point average and letters of recommendation.

Mathematics Ph.D.  Admission Requirements The undergraduate major need not be mathematics, but a student should have mastered material roughly equivalent to the undergraduate mathematics major at The University of Michigan including:

  • three semesters of calculus
  • one or two semesters of differential equations
  • one semester courses in modern algebra, linear algebra, geometry or topology
  • advanced calculus of one and several variables

In addition, a student should have completed at least three additional mathematics courses and at least two courses in related fields such as statistics, computer science, or the physical sciences. Students with strong records in less comprehensive programs will be considered for admission but if admitted should expect to spend the first one or two semesters in graduate school completing their undergraduate preparation in mathematics. Based on historical data, we expect that successful applicants to the Ph.D. program will have an overall GPA of at least 3.3 on a 4.0 scale.

Application Requirement Details

GRE, TOEFL, and IELTS Tests

  • GRE General test scores are not required. 
  • GRE Mathematics Subject Test scores may be submitted as a combined pdf file with your transcript or personal statement. (Optional)
  • TOEFL or IELTS exam is required for students whose native language is not English
  • TOEFL and IELTS exams should not be older than two years as of the Admission Deadline.
  • Minimum TOEFL and IELTS scores must meet Rackham's requirements here .
  • TOEFL or IELTS Exemptions are only given per Rackham's rules here .
  • ETS school code for the University of Michigan Rackham Graduate School is 1839

Letters of Recommendation

Letters of recommendation play an especially crucial role in the admission process. At least three letters are required, and up to five may be submitted. Applicants should choose as recommenders people who know their strengths and weaknesses relevant to graduate study in mathematics. The most useful letters are those which list in some detail the accomplishments of the student and make direct comparisons with other students who have succeeded at major U.S. graduate schools. International students already in the U.S. should submit letters from their U.S. institution, whenever possible.  Please register your recommenders for the electronic Letters of Recommendation when using the Online Application.  Letters received after the application deadline will be accepted, but should be received within 1 week of that deadline.

Those students who will have completed a Master's degree in Mathematics by the time they begin studies at the University of Michigan must apply to the Ph.D. program. Others may apply to either program. 

Academic Statement of Purpose

Focus your academic statement on your mathematical interests, research experience, published papers, math camps, teaching & tutoring experience etc. Be sure to mention any specific faculty with whom you wish to work.

Personal Statement:

Focus your personal statement on what makes you unique, any struggles you have experienced and overcome, and why you feel U-M Math is the right place for you.  Be sure to include any hardships you have experiencedand how you overcame them. These could be financial, familial, or personal.

Transcript Submission:

The Mathematics Admissions Committee will review uploaded transcripts with university logos during the application process.  While these are considered "unofficial" transcripts because they have been opened from their original sealed envelopes, they are acceptable.  If an applicant receives an offer of admission, an official transcript in a sealed envelope will need to be mailed from the institution directly to the Rackham Graduate School.

Please submit your most current transcript with your online application by the due date.  If you would like the Admissions Committee to see your Fall term scores, you may email them to [email protected] after the due date, and they will be included with your application.

Additonal Application Materials: If you have additional materials you would like to submit with your application, you may email them to [email protected].  Be sure to include your name and umid number in the email and attach files in pdf format.

Note:  All credentials submitted for admission consideration become the property of the University of Michigan and will not be returned in original or copy form.

Additional Information:  Please visit the admissions page of the Rackham Graduate School for additional information regarding admission including: minimum graduate school requirements, residency, and application fees.    Unfortunately, application fee waivers are not available for international students.

Financial Support for Ph.D. Students

Ph.D. Programs

Most students enrolled in the Ph.D. program in Mathematics are granted full financial support including an annual stipend, tuition waiver, and health insurance for a period of five years, subject to satisfactory progress. The Department offers aid in the form of Graduate Student Instructorships, Research Assistantships, and Fellowships.

All entering Ph.D. students will be considered for Graduate Student Instructorships, which normally require four classroom hours of teaching per week plus additional office hours during the Fall and Winter terms. The stipend for such an appointment in 2021-2022 is $11,598 per term. In addition, Graduate Student Instructors receive a full tuition waiver. Teaching duties may involve teaching a section of a first-year calculus or pre-calculus course or serving as an instructor for recitation sections attached to a faculty lecture in multivariable calculus or elementary differential equations. The Department of Mathematics has many fellowship opportunities, including the Copeland, Glover, Rainich, and Shields Fellowships which may provide a stipend, tuition waiver and in some cases a reduced teaching load. Other fellowships administered by the Rackham Graduate School can be found at their  Fellowships office .  The University of Michigan is part of the CIC consortium, which also awards fellowships to outstanding underrepresented applicants. Also available are prestigious Rackham Science Award’s given out by the Rackham Graduate School.

After Admission

All new Graduate Student Instructors are required to attend an orientation and training program which is held the week before classes begin. New Graduate Student Instructors whose Undergraduate Degree is not from an English speaking University must pass an English Evaluation which tests the specific oral skills needed for classroom teaching and are required to attend a three-week cultural orientation program starting in July.

Research Assistantships are awarded mainly to senior Ph.D. students to relieve them of teaching duties during the final part of their dissertation research. Students at this point may also compete for Rackham Dissertation Fellowships, which provide full support for one year, or Research Partnerships. A small number of positions as paper-graders for the larger advanced courses is available each term.

Some additional funds are often available for support during the summer. More advanced students who are actively involved in research may be supported from NSF grants awarded to faculty members. For other students there is a limited number of Departmental fellowships and a few teaching positions are available. No advanced graduate courses are offered in either the Spring or Summer half-terms and students are encouraged to spend some of their summers attending workshops, doing research, working in government, or seeking internships in industry.

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Marjorie Lee Browne (MLB) Scholars Program - an MS bridge to PhD program for diverse students

The Department of Mathematics at the University of Michigan is pleased to offer the Marjorie Lee Browne (MLB) Scholars Program. The program is named for Dr. Marjorie Lee Browne, who in 1949 became the first African-American woman to earn a Ph.D. in Mathematics at the University of Michigan. The MLB Scholars Program is an enhanced option for the M.S. degree in either Mathematics or Applied and Interdisciplinary Mathematics that is designed to give students professional knowledge of pure or applied mathematics in order to prepare them for continuing toward a Ph.D.  Please see this Marjorie Lee Brown Scholars webpage for eligibility and details.

If you have any questions regarding the application process, please contact the Department of Mathematics at [email protected].

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Ph.D. Program

Introduction.

These guidelines are intended to help familiarize graduate students with the policies governing the graduate program leading to the degrees of Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the graduate school requirements found on the  Graduate Student Resources  page and the  Doctoral Degree Policies  of the graduate school. Students are expected to be familiar with these procedures and regulations.

The Doctor of Philosophy program

The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation. This dissertation must exhibit original mathematical contributions that are relevant to a significant area of application.

Course requirements for the Ph.D. program

  • AMATH 561, 562, 563
  • AMATH 567, 568, 569
  • AMATH 584, 585, 586
  • AMATH 600: two, 2-credit readings, each with a different faculty member, to be completed prior to the start of the student's second year.
  • Students must take a minimum of 15 numerically graded courses. At most two of these can be at the 400 level or be cross listed with courses at the 400 level. Graduate level courses previously taken at UW (e.g., during a Master's program) count toward this requirement. Graduate level courses taken outside of UW may count toward the requirement for 15 numerically graded courses with the approval of the Graduate Program Coordinator. The entire course of study of a student and all exceptions to this list must be approved by the Graduate Program Coordinator and the student’s advisor or faculty mentors.

For students who entered the doctoral program autumn 2017 or autumn 2018, please see these degree requirements. For students who entered the doctoral program prior to autumn 2017, please see these degree requirements.  

Faculty mentoring

Upon arrival, incoming students will be assigned two faculty mentors. Until a student settles on an advisor, the faculty mentors aid the student in selecting courses, and they each guide the student through a 2-credit independent reading course on material related to the student’s research interest. The faculty mentors are not necessarily faculty in the Department of Applied Mathematics.

Faculty advisor

By the end of a student’s first summer quarter, an advisor must be determined.  T he advisor provides guidance in designing a course of study appropriate for the student’s research interests, and in formulating a dissertation topic.

A full Supervisory Committee should be formed four months prior to the student’s General Exam. The full Supervisory Committee should have a minimum of three regular members plus the Graduate School Representative , and will consist of at least two faculty members from Applied Mathematics, one of whom is to be the Chair of the Committee. If the proposed dissertation advisor is a member of the Applied Mathematics faculty, then the advisor will be the Chair. The dissertation advisor may be from another department,  or may have an  affiliate  (assistant, associate, full) professor appointment with the Applied Mathematics department  and is then also a member of the Supervisory Committee.

The Dissertation Reading Committee , formed after the General Exam,  is a subset of  at least   three members from the Supervisory Committee   who are appointed to read and approve the dissertation.  Two members of the Dissertation Reading Committee must be from the Applied Mathematics faculty. At least one of the committee members must be a member of the core  Applied Mathematics faculty. It is required that this member is present for both the general and final examination, and is included on the reading committee.

While the principal source of guidance during the process of choosing specialization areas and a research topic is the thesis advisor, it is strongly advised that the student maintain contact with all members of the Supervisory Committee. It is suggested that the student meet with the Supervisory Committee at least once a year to discuss their progress until the doctoral thesis is completed.

Examination requirements for the Ph.D. program

Students in the Ph.D. program must pass the following exams:

  • The  qualifying exam
  • The  general exam
  • The  final exam  (defense)

Satisfactory performance and progress

At all times, students need to make satisfactory progress towards finishing their degree. Satisfactory progress in course work is based on grades. Students are expected to maintain a grade point average of 3.4/4.0 or better. Satisfactory progress on the examination requirements consists of passing the different exams in a timely manner. Departmental funding is contingent on satisfactory progress.   The Graduate School rules regarding satisfactory progress are detailed in Policy 3.7: Academic Performance and Progress .   The Department of Applied Mathematics follows these recommended guidelines of the Graduate School including an initial warning, followed by a maximum of three quarters of probation and one quarter of final probation, then ultimately being dropped from the program.    We encourage all students to explore and utilize the many available  resources  across campus.

Expected academic workload

A first-year, full-time student is expected to register for a full course load, at least three numerically graded courses, typically totaling 12-18 credits. All other students are expected to consult with their advisor and register for at least 10-18 credits per quarter.  Students who do not intend to register for a quarter must seek approved  academic leave  in order to maintain a student status.   Students who do not maintain active student status through course registration or an approved leave request need to request reinstatement to rejoin the program. Reinstatement is at the discretion of the department. Students approved for reinstatement are required to follow degree requirements active at time of reinstatement. 

Annual Progress Report

Students are required to submit an Annual Progress Report to the Graduate Program Coordinator by the second week of Spring Quarter each year. The annual progress report should contain the professional information related to the student’s progress since the previous annual report. It should contain information on courses taken, presentations given, publications, thesis progress, etc., and should be discussed with the student's advisor prior to submission. Students should regard the Annual Progress Report as an opportunity to self-evaluate their progress towards completing the PhD. The content of the Annual Progress Report is used to ensure the student is making satisfactory progress towards the PhD degree.

Financial assistance

Financial support for Doctoral studies is limited to five years after admission to the Ph.D. program in the Department of Applied Mathematics. Support for an additional period may be granted upon approval of a petition, endorsed by the student’s thesis supervisor, to the Graduate Program Coordinator.

Master of Science program

Students in the Ph.D. program obtain an M.Sc. Degree while working towards their Ph.D. degree by satisfying the  requirements for the M.Sc. degree.  

Additional Ph.D. Degree Options and Certificates

Students in the Applied Mathematics Ph.D. program are eligible to pursue additional degree options or certificates, such as the  Advanced Data Science Option  or the  Computational Molecular Biology Certificate .  Students must be admitted and matriculated to the PhD program prior to applying for these options. Option or certificate requirements are in addition to the Applied Mathematics degree requirements. Successful completion of the requirements for the option or the certificate leads to official recognition of this fact on the UW transcript.

Career resources, as well as a look at student pathways after graduation, may be found   here.

FAQs |  Contact the Graduate Program  |  Apply Now

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Ph.D. Program

The degree of Doctor of Philosophy in Applied Mathematics and Computational Science is an advanced degree designed for those who wish to pursue a career involving applied mathematics research. It is conferred in recognition of marked ability and high attainment in advanced applied and computational mathematics, including the successful completion of a significant original research project. The Ph.D. program is designed to guide students, year-by-year , toward becoming researchers in applied mathematics. Typically the program takes four or five years to complete, including the dissertation (although it can be completed in less time, depending on the student).

There are several stages to the Ph.D. program. The first, which is centered on the course requirements and the Written Preliminary Exam, is designed to help the student acquire a broad background in applied mathematics and computational methods. The second stage includes the Ph.D. Oral Exam, and participation in seminars. Depth is one of the goals of this second stage, but the main objective at this point is to assist the student in choosing a field of specialization and in obtaining sufficient knowledge of this specialized field, including recent research developments, to begin to do independent research. Ph.D. students also have an opportunity to earn a masters degree at this stage. The third and key stage of the Ph.D. program is the dissertation (or "Ph.D. thesis"), in which the student will make an original contribution to applied mathematics and computational science. The entire Ph.D. program is designed to help students move toward taking this significant step in creating new mathematics for applications or new applications of mathematics. Along the way, the students are strongly encouraged to acquire some teaching experience, this skill being essential for those entering an academic Mathematics or Applied Mathematics career. As statistics is the language of experimental data analysis, students in the AMCS Ph.D. program are encouraged to satisfy and develope a proficiency in statistics and the analysis of data .  This can be accomplished through successful completion of a statistics course, at the level of STAT 915 or 970.

The program leading to this degree is described below, and may include work completed at the University of Pennsylvania for a Masters degree. (Up to eight courses taken at other universities, while a candidate for a graduate degree, can also be counted toward the Ph.D. requirements.)

Detailed requirements:

  • Admission to candidacy: Admission to Ph.D. candidacy is achieved by passing the Ph.D. Oral Examination. Students must previously have passed the Written Preliminary Exam , and have taken at least six graduate  courses approved by the chair of the graduate group (including those taken elsewhere). 
  • The Ph.D. Oral Examination: The purpose of the oral exam is to assess a student's readiness to transition into full-time research and eventually write his or her dissertation.  It is something of a hybrid between the subject-oriented oral exam administered by the Math department and the thesis proposal used in many fields of science and engineering. As part of this process, the student will choose, with the advice of the Graduate Group Chair, a Thesis Committee to help supervise his/her dissertation research. A detailed description of the exam can be found on the Ph.D. Oral Exam web-page.
  • This PhD Thesis committee is appointed by the Graduate Group Chair after consultation with the student. It consists of three or more faculty members, at least two of whom are full members of the graduate group. 
  • The PhD Oral Exam has two aspects:  
  • The student must prepare a written research proposal, outlining the problem they plan to pursue for their dissertation research. This proposal should be between 10 and 20 double-spaced pages. In any case, not to exceed 20 pages. The proposal should explain the mathematical significance of the proposed research.
  • The student must prepare a syllabus of background material, which is needed to pursue research in their chosen field. The syllabus of background material should be prepared about six months before the exam, and must be approved by the Graduate Group Chair.
  •  The exam itself will consist of a presentation by the student of their thesis proposal, followed by an oral examination covering both the thesis proposal as well as  background material germaine to that proposal.
  • The Graduate Group Chair notifies the AMCS faculty of the exam (date, time, place, committee members, reading lists). All affiliated faculty are to be invited, and are permitted to ask questions, however, only appointed members of the committee will vote on the candidate performance. 
  • If the student has elected to write a Masters Thesis related to the topic of their PhD dissertation research (which is not common), then the oral defense of the Masters thesis may be combined with the  Ph.D. Oral Exam.
  • Scheduling the Ph.D. Oral Exam: To take this exam, the student should have passed the Masters Preliminary Exam and be in good standing. The student also should have taken at least six approved graduate courses (including those taken elsewhere). The student discusses in advance the topics, syllabi and the composition of the oral exam committee with the Graduate Group Chair, whose written approval is needed. Normally, the exam is to be taken by the end of the first semester of the student's third academic year in the program. A one or two semester extension may be requested from the Graduate Group Chair. If the Ph.D. Oral Exam is not passed on the first try, it may be taken just once more, and this must occur before the end of the following semester. Passing the Ph.D. Oral Exam on the second try, at the latest, is a requirement for remaining in the Ph.D. program.
  • Course Requirements: Twenty units of graduate courses, numbered 500 and above (or the equivalent), are required for the Ph.D. degree, including at least twelve courses taken at the University of Pennsylvania.  The bulk of these courses should be drawn from the list of approved courses.  (Independent study courses at Penn may be counted toward the twenty course requirement.) Among the courses, every student must take at least two semesters of graduate courses at the 600 level in each of applied algebra, and applied analysis, at least one semester of probability and stochastic processes, and one semester of computational science.  In general, eight of the courses should be taken in AMCS itself or in the Mathematics department.  After passing the oral exam/thesis proposal requirement, PhD students should register for 3CUs of dissertation research (AMCS 999) until they have accumulated the required 20 CUs. Once they have fulfilled this require they can register for AMCS 995, which carries no credits. To receive the Ph.D. degree a student must have at least a 3.0 cumulative grade point average. Sample programs of study in a range of fields can be found under the Academics menu bar. The Graduate Group Chair may, in exceptional cases, modify the requirement that at least 10 of the 20 graduate courses for the Ph.D. be in AMCS or mathematics. A maximum of 6 of these 20 courses may be reading courses (independent studies).
  • Seminar Requirement: It is expected that all advanced graduate students will regularly attend and participate in at least one seminar series each semester.  First and second year students are required to attend the AMCS colloquium talks, and all students are strongly encouraged to do so.  It is expected that students will give at least one, and hopefully a number of seminar talks to audiences of students and faculty. Guidance in the preparation of these lectures is provided by faculty members in the graduate group. The intention is for the student to gain experience in digesting and presenting advanced material and in fielding questions about it before an audience of scientists, as well as actively participating in research interactions and being a part of the  community of graduate students in the AMCS graduate group.
  • Teaching: In order to gain experience in classroom teaching, students are strongly encouraged  to serve as a teaching assistant or instructor for at least two semesters. Teaching for more than two semesters is encouraged, especially for those students who plan to teach after their Ph.D. Graduate students must participate in a TA training program offered by the Mathematics department before they begin their teaching.
  • The Dissertation: The dissertation, also known as the "Ph.D. thesis", is the heart of the Ph.D. program. It must be a substantial original investigation in a field of applied mathematics and computational science, done under the supervision of a faculty advisor.
  • The Ph.D. Thesis Committee: This committee is appointed by the Graduate Group Chair after consultation with the student, at the time of the PhD Oral Exam. It consists of, at least, three faculty members, including the thesis advisor, and meets at least once a year with the student to discuss his or her progress and to offer guidance.
  • Dissertation Examination: When the dissertation is complete, it must be defended in a Dissertation Exam , at which the student will be expected to give a short public exposition of the results of the thesis, and to satisfactorily answer questions about the thesis and related areas.
  • The Dissertation Exam Committee: This committee is appointed by the Graduate Group Chair after consultation with the student, and consists of three or more faculty members, at least one of whom is a full member of the AMCS graduate group, and at least one of whom is from the area of specialization of the thesis. It will normally include the Thesis committee appointed at the time of the student's PhD Oral Exam.  All AMCS faculty are to be invited to attend the Final Disseration Exam, however only those appointed by the Graduate Group Chair are voting members of the Exam Committee.
  • The student must deliver a finished copy of the Ph.D. thesis to the graduate secretary at least two weeks before the Final Dissertation Exam, so that it will be available for reading by the AMCS faculty.
  • Timing for the Final Dissertation Exam: This must be successfully completed no later than six years after entering the graduate program. It should occur no later than the end of the third academic year after admission to Ph.D. candidacy. In exceptional situations, the Graduate Group Chair may, after consultation with the Graduate Advising Committee, provide an extension.
  • Satisfaction of Requirements: When not otherwise specified, this is determined by the Graduate Group Chair, in consultation with the Graduate Advising Committee and involved faculty members and (in the case of the teaching requirement) the Undergraduate Chair.

General Information

Thank you for your interest in the Applied Mathematics/Mathematics PhD Programs! The Math Department admits new graduate students to the Fall Semester only.  The graduate admissions application for Fall 2024 admission is available as of Wednesday, September 13th, 2023. The deadline to apply is Monday, December 11th, 2023, at 8:59pm Pacific Time.  Access the Graduate Division's Online Application . Please read the information on Graduate Division requirements and information required to complete the application. Copies and "unofficial" transcripts are accepted via the online application system if the name of your institution and your name are on the transcript. Please  do not  mail original transcripts for the review process. We require three letters of recommendation, which should be submitted online. We do not accept mailed letters of recommendation. Letters should be received online by the admissions deadline. To learn more about the program, here is a recording of a recent presentation we held at the 2022 Graduate Diversity Admissions Fair .

Admission to the Ph.D. Program

The Department of Mathematics offers 2 Ph.D. degrees, one in Mathematics and one in Applied Mathematics. Applicants for admission to either Ph.D. program are expected to have preparation comparable to the undergraduate major at Berkeley in Mathematics or in Applied Mathematics. These majors consist of 2 full years of lower-division work (covering calculus, linear algebra, differential equations, and multivariable calculus), followed by 8 one-semester courses including real analysis, complex analysis, abstract algebra, and linear algebra. These eight courses may include some mathematically based courses offered by other departments (e.g., Physics, Engineering, Computer Science, or Economics).

Applicants for admission are considered by the department's Graduate Admissions Committee. The number of students that can be admitted each year is determined by the Graduate Division. In making admissions decisions, the committee conducts a comprehensive review taking into consideration letters of recommendation, level of mathematics preparation, performance in courses, broader impacts (community contributions), research experience, etc.

A Note on the GRE Exams

Due to the COVID-19 pandemic, the  GRE exams will be optional for the Fall 2024 graduate admissions application.  You may still submit GRE scores; however, an absence of GRE scores will not negatively impact your application. For those who choose to take the General GRE and/or the Mathematics Subject GRE exams: to ensure timely reception of official score reports, we recommend you take both exams no later than October; official score reports are due by the admissions deadline. The Educational Testing Service will send your scores to the institutions you specify when you take the exams, please consult their website to see how long it takes for ETS to transmit score reports to institutions. Additional information about the GRE exams, and how to register, can be obtained on the web .

A Note on GPAs

If your undergraduate institution does not use a 4-point grading scale please do not convert your GPA to match the 4.0 scale. Instead, leave the section blank, or write in 0.00. The faculty review committee will be able to see your true academic performance from your uploaded unofficial transcripts. For the "Advanced GPA," our program does not require a GPA calculation spreadsheet.

International Students

All applicants from countries in which the official language is not English are required to submit official evidence of English language proficiency. Please refer to the Graduate Division's admissions page for information on the English language requirement .

For international applicants, we are pleased to offer a limited number of need based  fee  waivers each year to eligible applicants. The waiver is available in the program page of the online application and must be submitted by December 1st. 

The M.A. in Math

The Department of Mathematics no longer accepts applications for the Master's in Mathematics Program. If you are interested in graduate study at UC Berkeley, please apply for the Applied Mathematics or Mathematics Ph.D. program. The MA application is only available to current Ph.D. students at Berkeley interested in a simultaneous MA in Mathematics.

We expect to make final decisions by the end of February or mid-March.

Email Math Graduate Admissions

After reading the above material and our  FAQ  page, if you have further questions on admission to our program you can send an email to  [email protected]

NYU Courant Department of Mathematics

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Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements .

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the  NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September 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. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

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. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

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.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.

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Mathematics PhD

College of arts and sciences, program description.

The Department of Mathematics offers rigorous graduate programs that combine study and research opportunities under the direction of an internationally-known faculty. Students participate in mathematical research in the primary areas of analysis, algebra, applied mathematics and geometry/topology. Area seminars inform faculty and students on current advancements in mathematics. Mathematical training is balanced with faculty mentoring. The goal is to give students the best possible preparation for the many career opportunities available in academia, industry and government.

Jenny Russell 244 Math Building Buffalo, NY 14260 Email: [email protected] Phone: 716-645-8782 Fax: 716-645-5039

Instruction Method

  • In Person   (100 percent of courses offered in person)

Full/Part Time Options

Credits required, time-to-degree, application fee.

This program is officially registered with the New York State Education Department (SED).

Online programs/courses may require students to come to campus on occasion. Time-to-degree and number of credit hours may vary based on full/part time status, degree, track and/or certification option chosen. Time-to-degree is based on calendar year(s). Contact the department for details.

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

  • Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
  • Analysis (examples include MA 711, MA 713, and MA 717)
  • PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
  • Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
  • Topology (examples include MA 721, MA 722, and MA 727)
  • Geometry (examples include MA 725, MA 731, and MA 745)
  • Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
  • Applied Mathematics (examples include MA 750, MA 751, and MA 770)
  • Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
  • Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
  • Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

Watch This Year’s ‘Dance Your PhD’ Contest Winner, a Musical Celebration of Kangaroo Behavior

“Kangaroo Time” took home the competition’s overall prize, while interpretive dances on early life adversity, circadian rhythms and streambank erosion were also honored

Christian Thorsberg

Christian Thorsberg

Daily Correspondent

Weliton Menário Costa dances in the foreground of a grassy plain, while background dancers dressed in orange dance behind him.

An Australian landscape filled with kangaroos, drag queens, ballerinas and twerking may sound like the onset of a fever dream or a carnival—but for Weliton Menário Costa , a behavioral ecologist at Australian National University who goes by Weli, it was the perfect way to create and share a song about marsupial behavior.

“ Kangaroo Time ,” a four-minute music video about Weli’s years studying eastern gray kangaroos in Victoria, is as fun as it is informative—one of the reasons why it was named the overall winner of this year’s “ Dance Your PhD ” competition.

“It’s super incredible,” Weli tells the Guardian ’s Kelly Burke. “To win an international science competition, it’s like Eurovision—except we all have PhDs.”

Though it might sound unreal, the dancing contest for scientists is “ totally serious .” Weli’s winning video explains his thesis research, “ Personality, Social Environment and Maternal-Level Effects: Insights from a Wild Kangaroo Population .” In his work, Weli found that kangaroos develop their personalities early in life , create social groups and dynamics just as humans do and are influenced to act in similar ways as their parents and siblings. As a queer immigrant to Australia, he tells the Guardian that he can relate to how kangaroos modify their behavior in different groups.

“Differences lead to diversity,” he concludes in “Kangaroo Time.” “It exists within any given species; it is just natural.”

The video’s message resonated with the judges, both scientifically and artfully. “There was a sense of surprise and delight in [‘Kangaroo Time’],” judge Alexa Meade tells Science ’s Sean Cummings. “You could tell they were having fun through the process, that it wasn’t this labored, stressful experience.”

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The origins of the “Dance Your PhD” competition can be traced to New Year’s Eve in 2006, when John Bohannon —a microbiologist and director of science at artificial intelligence company Primer—hosted a dance party for his colleagues and friends. The only problem: hardly anyone wanted to boogie.

“It’s very hard to get anyone to dance, particularly scientists,” Bohannon told NPR ’s Barry Gordemer in 2021. “Their parties are not on the dancey side.”

So, like any scientist, he designed an experiment—or, in this case, a dance contest—based on a hypothesis. “One thing you can count on with scientists is they’re competitive and they have a sense of humor about their work, so I thought, let’s just put it all together,” he said to NPR.

The first official contest took place in 2008, and it has been organized every year since by Science magazine and the American Association for the Advancement of Science. For 16 years the competition has made its enduring pitch to scientists globally: “Don’t you wish you lived in a world where you could just ask people to pull out their phones to watch an online video explaining your PhD research through interpretive dance?”

Evidently, many do—dozens of videos each year are submitted to the contest, in four categories of biology, chemistry, physics and social science. Science communication skills are key to a successful video, striking a balance between creativity and sharing new findings.

Weliton Menário Costa, wearing a boa, stands holding a laptop with binoculars around his neck; on the left is a drag queen, looking at the laptop, and two dancers, dressed in purple and black respectively, stand on the right, also looking at the screen.

“It’s actually a real challenge, communicating research results and making a clear link between science and the performing arts,” Weli tells the Guardian .

Weli took home the overall winner’s purse of $2,000, in addition to his $750 social science category prize. The three other winning videos this year focused on how adversity in early life can affect how genes work ( Siena Dumas Ang , Princeton University), treating the loss of neurons by targeting a protein involved with the circadian rhythm ( Xuebing Zhang , City University of Hong Kong) and streambank erosion ( Layla El-Khoury , North Carolina State University). In the social science category, the runner-up behind the kangaroos was a video on the invasive browntail moth  in Maine.

math phd time

Past overall winners have included atmospheric scientists from the University of Helsinki in Finland rapping about cloud formations ; a swing dance about superconductivity from a researcher at the University of Victoria in Canada; and a stylized music video about yeast cells from a researcher at Vilnius University in Lithuania.

For Weli, one of his most meaningful breakthroughs was with his grandmother, who didn’t quite understand his thesis until recently.

“Once I released ‘Kangaroo Time,’ she was like, ‘That’s my grandson! I get it now!’” he tells Science .

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Christian Thorsberg

Christian Thorsberg | READ MORE

Christian Thorsberg is an environmental writer and photographer from Chicago. His work, which often centers on freshwater issues, climate change and subsistence, has appeared in Circle of Blue , Sierra  magazine, Discover  magazine and Alaska Sporting Journal .

What is leap day? Is 2024 a leap year? Everything you need to know about Feb. 29

2024 is a leap year , meaning Thursday, Feb. 29 is a once-in-every-four-year event.

Since leap years typically happen every four years (although there are some exceptions ), our last leap days were in 2020 and 2016, and the next leap year will happen in 2028.

And since this is a day that doesn't come around often, people are celebrating in different ways, with businesses offering special deals in commemoration and others finally celebrating their Feb. 29 birthday .

Here's everything you need to know about leap day, including what is it, why it comes every four years and when it was created.

Leap day deals 2024: Get discounts and free food from Wendy's, Chipotle, Krispy Kreme, more

What is leap day?

Leap day is an extra day that gets added to the calendar. During a leap year, which occurs every four years, leap day falls on Feb. 29, giving the shortest month of the year one added day.

Why is leap day every four years?

The reason there are leap days, and years, is because of the Earth's orbit.

The amount of days it takes for the Earth to complete a full revolution around the Sun is not a whole number. The 365 days we experience is actually  365.242190 days , according to the National Air and Space Museum.

Getting rid of those 0.242190 days adds up.

That fraction allows seasons to correctly line up each year. If leap day was left off the calendar, the months during which we normally experience each season would eventually shift. This would impact other aspects of life, such as the growing and harvesting of crops.

When added, four 0.242190 days roughly equal one full day, which is why Feb. 29 is added to the calendar of most years that are divisible by four, including 2024.

When do we skip leap day?

To make up for decimals of time, we'll sometimes skip leap years, but it's rare. Prepare for a little bit of math: years divisible by 100 but not 400 are skipped, meaning we skipped leap years in 1700, 1800 and 1900 but not 2000. The next leap year we'll skip is quite a ways away, in 2100.

How often is leap year? Here's the next leap day after 2024 and when we'll (eventually) skip one

Who created leap day?

The concept of adding leap days is not new and  has been around for millennia , Britannica reports. Some calendars – such as the Hebrew, Chinese and Buddhist calendars – contained leap months, also known as " intercalary or interstitial months ," according to the History Channel.

While Julius Caesar is often credited for originating leap days, he got the idea from the Egyptians. By the  third-century BCE , Egyptians followed a solar calendar that spanned 365 days with a leap year every four years, National Geographic reports.

In ancient Rome, their calendar varied and included a 23-day intercalary month called " Mercedonius ." But it was not a standalone month. Mercedonius was added to February to account for the difference between the Roman year and solar year, according to the History Channel.

When making the Julian calendar, Caesar took inspiration from the Egyptians and decided to add an extra day to the month of February every four years. The Julian calendar officially began  on Jan. 1 in 45 BCE .

This method would continue over several centuries, but not without issue. Caesar's math of 365.25 days was close, but it wasn't the exact 365.242190 days the solar year contains. To be precise, Caesar " overestimated the solar year by 11 minutes ," the History Channel reports. This meant the Julian calendar would be  short a day every 128 years , according to National Geographic.

By the 16th century, time had shifted again and not in a good way. Major dates had changed, including Easter. The holiday is supposed to occur on the first Sunday following the first full moon on or after  the spring equinox . At the time, Easter's date had moved by  about 10 days .

To fix this, Pope Gregory XIII  introduced the Gregorian calendar , which kept a leap day every four years but eliminated it during centurial years not divisible by 400, according to the History Channel. This is why  1700, 1800 and 1900  were not leap years, but 2000 was.

Despite its accuracy, the Gregorian calendar is not flawless. Instead of being off by one day every 128 years like the Julian calendar, the Gregorian calendar  falls short once every 3,030 years , the History Channel reports.

Upcoming leap days

This year, 2024, is a leap year. Leap day will fall on Thursday, Feb. 29.

The next leap years will be in 2028, 2032 and 2036.

Leap day deals: Where to score on food, products and more Feb. 29

Food chains like Wendy's, Chipotle and Krispy Kreme are offering deals and free food in honor of leap day. Here's where to score on discounts .

What happens if you are born on leap day?

Feb. 29 is the  rarest birthday someone could have . Still, at least 5 million people celebrate their birthday on leap day, according to the History Channel. Your odds of being born on Feb. 29 are  one-in-1,461 .

Many "Leaplings" (or those born on leap day) will celebrate their birthdays on Feb. 28 or March 1 during a typical 365-day year, even though documents will reflect it is on Feb. 29.

25 never looked so good: Oklahoma woman born on leap day celebrates 100th birthday

Meet Mary Lea Forsythe: She turns 100 on Leap Day, but it's only her 25th birthday.

Just Curious for more? We've got you covered

USA TODAY is exploring the questions you and others ask every day. From " What is the olive theory? " to " How many dog breeds are there? " to " How many Zodiac signs are there? " − we're striving to find answers to the most common questions you ask every day. Head to our  Just Curious section  to see what else we can answer.

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Meet the winners of the 2024 dance your phd contest, "one of the main messages i wanted to convey... is that differences lead to diversity.".

Jennifer Ouellette - Feb 29, 2024 5:31 pm UTC

We've been following the annual Dance Your PhD contest for several years now, delighting in the many creative approaches researchers have devised to adapt their doctoral theses into movement—from "nano-sponge" materials and superconductivity to the physics of atmospheric molecular clusters and the science of COVID-19. This year's winner is Weliton Menário Costa of the Australian National University for his thesis "Personality, Social Environment, and Maternal-level Effects: Insights from a Wild Kangaroo Population." His video entry, "Kangaroo Time," is having a bit of a viral moment, charming viewers with its catchy beat and colorful, quirky mix of dance styles and personalities—both human and kangaroo.

As we reported previously , the Dance Your PhD contest was established in 2008 by science journalist John Bohannon. It was previously sponsored by Science magazine and the American Association for the Advancement of Science (AAAS) and is now sponsored by the AI company Primer, where Bohannon is the director of science. Bohannon told Slate in 2011 that he came up with the idea while trying to figure out how to get a group of stressed-out PhD students in the middle of defending their theses to let off a little steam. So he put together a dance party at Austria's  Institute of Molecular Biotechnology , including a contest for whichever candidate could best explain their thesis topics with interpretive dance.

The contest was such a hit that Bohannon started getting emails asking when the next would be—and Dance Your PhD has continued ever since. It's now in its 16th year. There are four broad categories: physics, chemistry, biology, and social science, with a fairly liberal interpretation of what topics fall under each. All category winners receive $750, while Costa, as the overall champion, will receive an additional $2,000.

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A native of Brazil, Costa earned a PhD in ecology from ANU in 2021 after spending several years studying eastern gray kangaroos, using a remote-controlled car to determine their distinct personalities. For example, some were bold and would approach the car out of curiosity; others were shyer and would avoid the car. Among his chief findings: Kangaroos like to socialize in groups but prefer smaller social circles. Kangaroo personalities emerge early, just like in humans, with mothers, offspring, and siblings often having similar personalities. But their personalities are also somewhat flexible; kangaroos will adjust their behavior based on social cues from the kangaroos around them.

When it came time to translate his research into movement, Costa decided to represent the rich diversity of kangaroo behavior with an equally diverse collection of dancers and dance styles: classical ballet, Brazilian funk, and urban styles, to name a few. Everyone was free to improvise their moves, with the only instruction being to mingle with others and slowly unify as a group. Costa joined in, adapting his dance style throughout to match other dancers, thus mimicking how kangaroos adapt their personalities to fit into a group. There's even a behind-the-scenes video, which you can watch here .

"There was a sense of surprise and delight in it," visual artist Alexa Meade, one of the content judges, told Science about why they selected Costa's entry. "You could tell they were having fun through the process, that it wasn't this labored, stressful experience."

Costa is the first ANU researcher to win the contest and only the fourth Australian. "I think it not only shows the incredible might of the research conducted here in Australia but also how creative we are as a nation. Even us scientists," Costa said of his win. "One of the main messages I wanted to convey through this piece of work is that differences lead to diversity, and this is evident throughout the entire video. It's evident with the different dancers that herald from various cultures and backgrounds." Costa is pursuing music as "Dr. WELI," and "Kangaroo Time" is one of four songs on his debut EP, Yours Academically, Dr. WELI . But he'll still be working at ANU as a visiting fellow until early 2025.

Check out the winners of the chemistry, physics, and biology categories on the next page.

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Channel ars technica.

ANU academic and singer-songwriter WELI wins global competition for music video about kangaroo socialisation

A Brazilian academic has won the global Dance Your PhD award for an elaborately produced and choreographed video explaining his academic work studying social behaviour in kangaroos.

A global expert in kangaroo socialisation, 32-year-old Weliton Menário Costa of the Australian National University (ANU) wrote and directed the music video Kangaroo Time (Club Edit).

The Dance Your PhD contest challenges researchers around the world to explain their research in a simple, effective and engaging way to bridge the gap between the scientific community and the general public.

"Winning this contest is the equivalent of winning Eurovision for me," Dr Costa said.

"I think it not only shows the incredible might of the research conducted here in Australia, but also how creative we are as a nation. Even us scientists."

He is the first person from ANU to win the Dance Your PhD competition, and just the fourth person from an Australian institution to do so since the competition began in 2008.

A man in a Bunnings straw hat leans on a white ute.

Known creatively as WELI, the singer-songwriter and biologist's winning video includes a funky beat and features a variety of performers including drag queens, classical ballet dancers, urban street dancers and Brazilian funk dancers.

WELI said including this diversity of performers from a variety of disciplines and cultures was important to reflect the spectrum of personality present in kangaroo populations — the key finding of his research.

"Using diversity to communicate results has been so effective, it makes it so easy for people to clearly see differences when you actually, genuinely sample the differences," he said.

Using a remote-controlled car WELI spent over three years studying the spectrum of behavioural differences in a group of more than 300 wild eastern grey kangaroos in Victoria.

Two ballet dancers posed on a hill.

"We found that kangaroos like to socialise in groups but prefer smaller social circles. Like humans, kangaroo personalities manifest early in life," he said.

"Mothers and their offspring have similar personalities, and so do siblings.

"Kangaroos are very socially aware and will adjust their behaviour based off cues from other roos."

WELI moved from Brazil to Brisbane in 2013 on a Science Without Borders scholarship for undergrad, and after returning to Brazil two years later decided he missed Australia and began applying for PhD positions in the country — eventually landing his kangaroo research with the ANU in 2017.

A group of elaborately dressed performers crowd around a laptop outside.

He said on the surface Kangaroo Time is science communication about his research utilising the creative arts medium, but the video is also a representation of his time in Australia.

"Kangaroo Time is my Australia time, it's the time I came out and lived as a gay man in the workplace for the first time in my life," WELI said.

"I tried to bring all these different aspects of my background — so the Latino WELI, queer WELI, the scientist WELI, the WELI that's popular but [also] the WELI that is sad.

A woman in cultural dress poses on a hilltop.

"There is a very important part of the lyrics that say 'you're surrounded by mates, are you feeling alright?' which shows that sometimes you're in social spaces but you're not feeling quite well."

WELI said his decision to apply for a PhD studying socialisation in mammals came from his upbringing in a conservative space as a queer man and noticing the differences in his behaviour while with others as opposed to alone.

"I think that all comes down from me being queer in a conservative space where I've always felt it's suffocating influence of the people around me, and that was shaping my behaviour in a way that didn't necessarily match what I actually want to be or express."

A man in a Bunnings straw hat and a drag queen lean on a white ute.

WELI said at the core of his video is a message of inclusivity and diversity — something he hopes will be the main takeaway for viewers.

"As a queer immigrant from a linguistically diverse developing country, I understand the challenges of feeling disconnected in certain environments," he said.

"One of the main messages I wanted to convey through this piece of work is that differences lead to diversity, and this is evident throughout the entire video. It's evident with the different dancers that herald from various cultures and backgrounds.

An elaborately dressed dancer stands posed on a hill.

"I think it's extremely important that we celebrate diversity and creating a video explaining kangaroo personality was an excellent medium for me to do this."

After winning the competition WELI plans to stay both in the academic and creative spaces, with a new EP called Yours Academically, Dr WELI being released soon and plans to continue working at ANU as a Visiting Fellow until early 2025.

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Weliton Menario Costa and drag artist Faux Née Phish, who performed in Kangaroo Time.

‘Joyful madness’: ANU scientist wins global prize for ‘dancing his PhD’ about kangaroos

Four-minute video features drag queens, twerking, ballerinas, a classical Indian dancer and a bunch of friends from Canberra

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The former Canberra scientist Dr Weliton Menário Costa, who now goes by the name Weli, said it “felt like winning Eurovision” when he learned he had won the global “Dance Your PhD” competition, for his quirky interpretive take on kangaroo behaviour.

His four-minute video titled Kangaroo Time features drag queens, twerking, ballerinas, a classical Indian dancer, and a bunch of friends Weli acquired from his time studying at the Australian National University.

The video collected the top prize awarded annually by the American Association for the Advancement of Science , Science magazine, and San Francisco-based artificial intelligence company Primer.ai.

The competition encourages scientists to explain complex research to the wider public through dance, music and humour, and attracts dozens of entries from around the world each year.

“It’s super incredible,” Weli told the Guardian on Tuesday. “To win an international science competition, it’s like Eurovision – except we all have PhDs.

“It’s actually a real challenge, communicating research results and making a clear link between science and the performing arts. In Eurovision, you can do anything you want.”

Kangaroo Time narrowly beat an entry from the University of Maine, in which a second-year ecology and environmental science PhD student used the music of Camille Saint-Saëns’s Danse Macabre to convey her research on the invasive browntail moth.

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Weli collected more than A$4,000 (US$2,750), winning the overall prize and the social sciences prize; it was the fourth time an Australian entry had won in the competition’s 17-year history.

In 2009, a University of Sydney entry won for a dance about the use of vitamin D to protect against diabetes. Two years later, a University of Western Australia entry won for a video about why orthopaedic implants fail; and the following year, a University of Sydney entry won once again for a work explaining the “evolution of nanostructural architecture in 7000 series aluminium alloys during strengthening by age-hardening and severe plastic deformation”.

Dr Weliton Menário Costa’s video was described as ‘joyful madness’ by Science magazine

Weli based his entry on his four-year PhD study on animal behaviour, in a video Science magazine described as “joyful madness”. The judging panel of scientists, artists and dancers praised Kangaroo Time for its “sense of surprise and delight” and its accessible explanation of the science of marsupial group dynamics.

Using a remote-controlled car, the ANU graduate studied the behavioural differences and complex personalities of a group of more than 300 wild eastern grey kangaroos in Victoria.

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He found that like humans, kangaroos’ personalities develop in early life and often mirror the personalities of their parents and siblings; he found they take social cues from the group dynamic, and form social circles like humans too.

His conclusion: “Difference leads to diversity. It exists within any given species, it is just natural.”

The Brazilian-born biologist, who gained a scholarship from ANU in 2017, said he drew on his South American roots and a fascination with Australia’s unique fauna to write, produce and perform in the work.

A queer immigrant from a developing country, Weli said he could relate to how the kangaroos modified their behaviour to conform to the wider group.

“I come from a very humble family, a small town where most of the people are not educated,” he said, of his conservative upbringing. “When I came to Australia I came out to my family … in Kangaroo Time I celebrate diversity in my beautiful Canberra community that [mirrors] kangaroo behaviour.”

Since completing his PhD in Canberra in 2021, Weli has abandoned his academic science career and moved his home base to Sydney, where he is seeking to establish himself as a singer-songwriter.

His first EP – Yours Academically, Dr Weli – will be out 1 March.

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