where to get a phd in mathematics

  • 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.

1st Class Honours Master’s degree. Degree must be in Mathematics or Statistics. 2:1 Master’s degree in Mathematics, Statistics or a closely related subject. 2:1 Bachelor’s degree in Mathematics, Statistics or a closely related subject.

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:

UK/EU Full-Time £4,407 £4,327 – £8,589
UK/EU Part-Time £2,204 £2,164 – £4,295
International Full-Time £20,230 £15,950 – £24,531
International Part-Time £10,115 £7,975 – £12,266

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 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

where to get a phd in mathematics

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

where to get a phd in mathematics

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.

Browse PhDs Now

Join thousands of students.

Join thousands of other students and stay up to date with the latest PhD programmes, funding opportunities and advice.

Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

  • Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
  • Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
  • Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
  • Complete a seminar, giving a talk of at least one-hour duration
  • Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
  • Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

  • The firm deadline for applications for Autumn 2025, is December 5, 2024.
  • The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

» » Graduate PhD Program

The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy.

The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government. Admission is limited and highly selective. Successful applicants have typically pursued an undergraduate major in mathematics.

In the first year of PhD studies, students must pass written examinations in the areas of the basic . In the second year an oral examination on two selected topics must be passed. Subsequent years are devoted to seminars, research, and the preparation of a dissertation. Students are required to serve as a teaching assistant or instructor for four years beginning with the second year of study. All students must serve as a primary instructor for at least one semester; all others semesters students will serve as a teaching assistant. En route to the Ph.D., students will earn three degrees: a Master of Arts (after year one), a Master of Philosophy (after year four), and the Doctorate of Philosophy (after a successful thesis defense).

There are also allied doctoral programs in , , and .

The Mathematics Department is housed in a comfortable building containing an excellent , computing and printing facilities, faculty and graduate student offices, a lounge for tea and conversation, and numerous seminar and lecture rooms.

The department has a broad fellowship program designed to help qualified students achieve the PhD degree in the shortest practicable time. Each student admitted to the PhD program is appointed a fellow in the Department of Mathematics for a period of five years, contingent on good progress. A fellow receives a stipend for the nine-month academic year and is exempt from payment of tuition.

A fellow in the Department of Mathematics may hold a fellowship from a source outside Columbia University. When not prohibited by the terms of the outside fellowship, the University supplements the outside stipend to bring it up to the level of the University fellowship. Candidates for admission are urged to apply for fellowships for which they are eligible (e.g., National Science Foundation, Ford and Hertz Foundations).

All students admitted to the PhD program become fellows in the Department and are exempt from tuition. Students may be responsible for certain : a student activity fee and transcript fee.

Students in the PhD program are entitled to affordable University housing near the Department in Morningside Heights. This makes it possible to live comfortably in the University neighborhood on the fellowship stipend.

The PhD program in mathematics has an enrollment of approximately 60 students. Typically, 10-12 students enter each year. While students come from all over the world, they form an intellectually cohesive and socially supportive group.

New York City is America’s major center of culture. Columbia University’s remarkably pleasant and sheltered , near the Hudson River and Riverside Park, is situated within 20-30 minutes of Lincoln Center, Broadway theaters, Greenwich Village, and major museums. Most department members live within a short walk of the University.

Since receiving its charter from King George II in 1754, Columbia University has played an eminent role in American education. In addition to its various faculties and professional schools (such as Engineering, Law, and Medicine), the University has close ties with nearby museums, schools of music and theology, the United Nations, and the city government.

The application deadline is typically early December for admission the following September. Precise details on requirements and deadlines can be found . Applicants must submit all required documents by the posted deadline. Students whose undergraduate degree was not from an English-speaking country must also submit scores from the TOEFL or IELTS.  Applications must be filed .



Graduate School of Arts and Sciences
Columbia University
Office of Student Affairs
107 Low Library, MC 4304
New York, NY 10027

Michael Harris
Director of Graduate Studies
Department of Mathematics
Columbia University
2990 Broadway
509 Mathematics, MC 4406
New York, NY 10027

Graduate Program

Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we urge independent work and research, there exists a real sense of camaraderie among our graduate students. As a result, the atmosphere created is one of excitement and stimulation as well as of mentoring and support. Furthermore, there exists a strong scholarly relationship between the Math Department and the Institute for Advanced Study, located just a short distance from campus, where students can make contact with members there as well as attend the IAS seminar series.  Our program has minimal requirements and maximal research and educational opportunities. We offer a broad variety of advanced research topics courses as well as more introductory level courses in algebra, analysis, and geometry, which help first-year students strengthen their mathematical background and get involved with faculty through basic course work. In addition to the courses, there are several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the Department Colloquium give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students for graduate students, creating a vibrant mathematical interaction among them; and, (3) What’s Happening in Fine Hall (WHIFH) seminar where faculty give talks in their own research areas specifically geared towards graduate students. Working or reading seminars in various research fields are also organized by graduate students each semester. First-year students are set on the fast track of research by choosing two advanced topics of research, beyond having a strong knowledge of three more general subjects: algebra, and real and complex analysis, as part of the required General Examination. It is the hope that one, or both, of the advanced topics will lead to the further discovery of a thesis problem. Students are expected to write a thesis in four years but will be provided an additional year to complete their work if deemed necessary. Most of our Ph.D.'s are successfully launched into academic positions at premier mathematical institutions as well as in industry .

Chenyang Xu

Jill leclair.

PhD in Mathematics

The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD. There are minimal course requirements, and detailed requirements and procedures for the PhD program are outlined in the  PhD Handbook .

Please note that our department alternates recruiting in-coming classes that are focused on either applied or pure mathematics. For the Fall 2024 admissions (matriculation in September 2024), we are focusing on students interested in areas of applied mathematics.

All our professors are active in research, and are devoted to teaching and mentoring of students. Thus, there are many opportunities to be involved in cutting-edge research in pure and applied mathematics. Moreover, the seven other research universities in the Boston area are all within easy reach, providing access to many more classes, seminars and colloquia in diverse areas of mathematical research.

Teaching assistantships are available for incoming PhD students, as well as a limited number of University-wide fellowships. Tufts has on-campus housing for graduate students, but many choose to live off-campus instead.

In addition to the above, PhD students often:

  • Mentor undergraduates as teaching assistants and course instructors, and through graduate-student run programs like the Directed Reading Program.
  • Meet with advisors and fellow students to share research and collaborate with scholars across disciplines
  • Attend professional development workshops and present research at conferences

Ph.D. Degree Programs

The UCSD Mathematics Department admits students into the following Ph.D. programs:

  • Ph.D. in Mathematics -- Pure or Applied Mathematics.
  • Ph.D. in Mathematics with a  Specialization in Computational Science .
  • Ph.D. in Mathematics with a  Specialization in Statistics .

In addition, the department participates in the following Ph.D. programs:

  • Ph.D. in  Bioinformatics .
  • Ph.D. in  Mathematics and Science Education  (joint program between UCSD and SDSU).

For application information, go to  How to Apply (Graduate) .  

Ph.D. in Mathematics

The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at  here . The Ph.D. in Mathematics program produces graduates with a preparation in teaching and a broad knowledge of mathematics. Our students go on to careers as university professors, as well as careers in industry or government.

In the first and second years of study, Ph.D. students take courses in preparation for three written qualifying examinations (quals). One qual must be taken in Algebra or Topology, and another in Real or Complex Analysis. A third qual may be taken in Numerical Analysis or Statistics or one of the remaining topics in the first two groups. All three quals must be passed by the start of the third year. After the qualifying exams are passed, the student is expected to choose an advisor and follow a course of study agreed on by the two of them. At this point, the student chooses a thesis topic, finds a doctoral committee and presents a talk on his or her proposed research topic. If the committee is satisfied with this talk, the student has "Advanced to Candidacy." The student will then pursue their research agenda with their advisor until they have solved an original problem. The student will submit a written dissertation and reconvene his or her committee for a Final Defense. At the Final Defense, the student gives a seminar talk that is very similar to a talk that he or she might give for a job interview.

Nearly every admitted Ph.D. student gets financial support. The financial support is most commonly in the form of a Teaching Assistantship, however, Research Assistantships and other fellowships are also available.

Because of the large faculty to student ratio, graduate students have many opportunities to interact with faculty in courses or smaller research seminars. The graduate students also run their own "Food for Thought" seminar for expository talks as well as a research seminar where they give talks about their research.

UCSD has excellent library facilities with strong collections in mathematics, science, and engineering. Ph.D. students are provided with access to computer facilities and office space.

Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only. The remaining four (4) units can be approved upper-division or graduate-level courses in mathematics-related subjects (MATH 500 may not be used to satisfy any part of this requirement). After advancing to candidacy, Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in MATH 299 (Reading and Research) until they have passed at least two Qualifying Examinations at the PhD or Provisional PhD level, or obtained approval of their faculty advisor.  

Written Qualifying Examinations

Effective Fall Quarter 1998, the department made changes in their qualifying exam requirements with a view to:

  • improving applied mathematics' access to students and the attractiveness of its program to applicants; and
  • broadening the education of our doctoral students and leading more of them towards applied areas.

The department now offers written qualifying examinations in  SEVEN (7)  subjects. These are grouped into three areas as follows:  

Qualifying Examination Subject Areas
Complex Analysis
(MATH 220A-B-C)
Real Analysis
(MATH 240A-B-C)
(MATH 200A-B-C)
Applied Algebra
(MATH 202A-B-C)
(MATH 290A-B-C)
Numerical Analysis
(MATH 270A-B-C)
(MATH 281A-B-C)
  • Three qualifying examinations must be passed. At least one must be passed at the Ph.D. level and a second must be passed at either the Ph.D. or Provisional Ph.D. level.
  • Of the three qualifying exams, there must be at least one from each of Areas 1 and 2. 
  • Students must pass at least two exams from distinct areas with a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass in Real Analysis, Provisional Ph.D. pass in Complex Analysis, M.A. pass in Algebra would  NOT  satisfy this requirement, but a Ph.D. pass in Real Analysis, M.A. pass in Complex Analysis, Provisional Ph.D. pass in Algebra would, as would a Ph.D. pass in Numerical Analysis, Provisional Ph.D. pass in Applied Algebra, and M.A. pass in Real Analysis.) All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies. (Thus, there is no limit on the number of attempts, encouraging new students to take exams when they arrive, without penalty.) Except for this deadline, there is no limit on the number of exams a student may attempt.

After qualifying exams are given, the faculty meet to discuss the results of the exams with the Qualifying Exam and Appeals Committee (QEAC). Exam grades are reported at one of four levels:  

Qualifying Examination Pass Levels
Excellent performance, suitable for continuing towards doctoral work
Marginal performance at doctoral level
Not suitable for continuing towards doctoral work, but satisfactory for terminal M.A. or M.S.
Unsatisfactory for Master's level work

Department policy stipulates that at least one of the exams must be completed with a Provisional Ph.D. pass or better by September following the end of the first year. Anyone unable to complete this schedule will be terminated from the doctoral program and transferred to one of our Master's programs. Any grievances about exams or other matters can be brought before the Qualifying Exam and Appeals Committee for consideration.

Exams are typically offered twice a year, one scheduled late in the Spring Quarter and again in early September (prior to the start of Fall Quarter). Copies of past exams are available on the  Math Graduate Student Handbook .

In choosing a program with an eye to future employment, students should seek the assistance of a faculty advisor and take a broad selection of courses including applied mathematics, such as those in Area 3.  

Master's Transferring to Ph.D.

Any student who wishes to transfer from masters to the Ph.D. program will submit their full admissions file as Ph.D. applicants by the regular closing date for all Ph.D. applicants (end of the fall quarter/beginning of winter quarter). It is the student's responsibility to submit their files in a timely fashion, no later than the closing date for Ph.D. applications at the end of the fall quarter of their second year of masters study, or earlier. The candidate is required to add any relevant materials to their original masters admissions file, such as most recent transcript showing performance in our graduate program. Letters of support from potential faculty advisors are encouraged. The admissions committee will either recommend the candidate for admission to the Ph.D. program, or decline admission. In the event of a positive recommendation, the Qualifying Exam Committee checks the qualifying exam results of candidates to determine whether they meet the appropriate Ph.D. program requirements, at the latest by the fall of the year in which the application is received. For students in the second year of the master's program, it is required that the student has secured a Ph.D. advisor before admission is finalized. An admitted student is supported in the same way as continuing Ph.D. students at the same level of advancement are supported. Transferring from the Master's program may require renewal of an I-20 for international students, and such students should make their financial plans accordingly. To be eligible for TA support, non-native English speakers must pass the English exam administered by the department in conjunction with the Teaching + Learning Commons.  

Foreign Language Requirement

There is no Foreign Language requirement for the Ph.D. in Mathematics.  

Advancement to Candidacy

It is expected that by the end of the third year (9 quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student's appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the C. Phil. degree.  

Dissertation and Final Defense

Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the Ph.D. degree is awarded. When the dissertation is substantially completed, copies must be provided to all committee members at least four weeks in advance of the proposed defense date. Two weeks before the scheduled final defense, a copy of the dissertation must be made available in the Department for public inspection.  

Time Limits

The normative time for the Ph.D. in mathematics is five (5) years. Students must be advanced to candidacy by the end of eleven (11) quarters. Total university support cannot exceed six (6) years. Total registered time at UCSD cannot exceed seven (7) years.  

Ph.D. Program Time Limits
Pass Qualifying Exams
Find thesis advisor
Advance to Candidacy
Final Defense

It may be useful to describe what the majority of students who have successfully completed their Ph.D. and obtained an academic job have done. In the past some students have waited until the last time limit before completing their qualifying exams, finding an advisor or advancing to candidacy. We strongly discourage this, because experience suggests that such students often do not complete the program. Although these are formal time limits, the general expectation is that students pass two qualifying exams, one at the Ph.D. level and one at the masters level by the beginning of their second year. (About half of our students accomplish this.) In the second year, a student begins taking reading courses so that they become familiar with the process of doing research and familiarize themselves with a number of faculty who may serve as their advisor. In surveying our students, on average, a student takes 4 to 5 reading courses before finding an advisor. Optimally, a student advances to candidacy sometime in their third year. This allows for the fourth and fifth year to concentrate on research and produce a thesis. In contrast to coursework, research is an unpredictable endeavor, so it is in the interest of the student to have as much time as possible to produce a thesis.

A student is also a teaching assistant in a variety of courses to strengthen their resume when they apply for a teaching job. Students who excel in their TA duties and who have advanced to candidacy are selected to teach a course of their own as an Associate Instructor. Because there are a limited number of openings to become an Associate Instructor, we highly recommend that you do an outstanding job of TAing in a large variety of courses and advance to candidacy as soon as possible to optimize your chances of getting an Associate Instructorship.

where to get a phd in mathematics

9500 Gilman Drive, La Jolla, CA 92093-0112

(858) 534-3590

Overview of the PhD Program

For specific information on the Applied Mathematics PhD program, see the navigation links to the right. 

What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the  Graduate Policies  pages. 

General Ph.D. Requirements

  • 10 semester-long graduate courses, including at least 8 disciplinary.   At least 5 of the 10 should be graduate-level SEAS "technical" courses (or FAS graduate-level technical courses taught by SEAS faculty), not including seminar/reading/project courses.  Undergraduate-level courses cannot be used.  For details on course requirements, see the school's overall PhD course requirements  and the individual program pages linked therein.
  • Program Plan (i.e., the set of courses to be used towards the degree) approval by the  Committee on Higher Degrees  (CHD).
  • Minimum full-time academic residency of two years .
  • Serve as a Teaching Fellow (TF) in one semester of the second year.
  • Oral Qualifying Examination Preparation in the major field is evaluated in an oral examination by a qualifying committee. The examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in a chosen field and of assessing the student's ability to synthesize knowledge already acquired. For details on arranging your Qualifying Exam, see the exam policies and the individual program pages linked therein.
  • Committee Meetings : PhD students' research committees meet according to the guidelines in each area's "Committee Meetings" listing.  For details see the "G3+ Committee Meetings" section of the Policies of the CHD  and the individual program pages linked therein.
  • Final Oral Examination (Defense) This public examination devoted to the field of the dissertation is conducted by the student's research committee. It includes, but is not restricted to, a defense of the dissertation itself.  For details of arranging your final oral exam see the  Ph.D. Timeline  page.
  • Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee, meet the standards of significant and original research.

Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

  • a Secondary Field (which is similar to a "minor" subject area).  SEAS offers PhD Secondary Field programs in  Data Science and in  Computational Science and Engineering .   GSAS  lists  secondary fields offered by other programs.
  • a Master of Science (S.M.) degree conferred  en route to the Ph.D in one of several of SEAS's subject areas.  For details see here .
  • a Teaching Certificate awarded by the Derek Bok Center for Teaching and Learning .

SEAS PhD students may apply to participate in the  Health Sciences and Technology graduate program  with Harvard Medical School and MIT.  Please check with the HST program for details on eligibility (e.g., only students in their G1 year may apply) and the application process.

In Applied Mathematics

  • First-Year Exploration
  • Areas of Application
  • AM & Economics
  • How to Declare
  • Who are my Advisors?
  • Secondary Field
  • Senior Thesis
  • Research for Course Credit (AM 91R & AM 99R)
  • AB/SM Information
  • Peer Concentration Advisors (PCA) Program
  • Student Organizations
  • How to Apply
  • PhD Timeline
  • PhD Model Program (Course Guidelines)
  • Oral Qualifying Examination
  • Committee Meetings
  • Committee on Higher Degrees
  • Research Interest Comparison
  • Collaborations
  • Cross-Harvard Engagement
  • Clubs & Organizations
  • Centers & Initiatives
  • Alumni Stories

Graduate Programs


The Mathematics program is designed to prepare especially able students for a career in mathematical research and instruction.

A relatively small enrollment of 30 to 40 students permits small classes and close contact with faculty. Applicants should have a good background in undergraduate mathematics, regardless of their majors. Students with backgrounds in advanced mathematics will find our program quite flexible. Visits to Brown and direct communication with the director of graduate study are strongly encouraged.

The core courses are in differentiable manifolds, real functions, complex functions, algebra, and topology. Other courses offered each year are in P.D.E., probability, algebraic geometry, number theory and differential geometry.

Additional Resources

The library contains one of the finest mathematical collections available anywhere. The department has extensive computing facilities.

Application Information

Application requirements, gre subject:.

Not required

GRE General:

Dates/deadlines, application deadline, completion requirements.

Advancement to candidacy determined in part by qualification in the basic and advanced courses; teaching experience; examination on an advanced topic; expository talk based on a research paper in that subject; dissertation; and oral defense.

Alumni Careers


Contact and Location

Department of mathematics, mailing address.

  • Program Faculty
  • Program Handbook
  • Graduate School Handbook

student waving Cal flag

Applied Mathematics PhD

The Department of Mathematics offers both a PhD program in Mathematics and Applied Mathematics.

Students are admitted for specific degree programs: the PhD in Mathematics or PhD in Applied Mathematics. Requirements for the Mathematics and Applied Mathematics PhDs differ only in minor respects, and no distinction is made between the two in day-to-day matters. Graduate students typically take 5-6 years to complete the doctorate.

Continuing students wishing to transfer from one program to another should consult the graduate advisor in 910 Evans Hall. Transfers between the two PhD programs are fairly routine but must be done prior to taking the qualifying examination. It is a formal policy of the department that an applicant to the PhD program who has previous graduate work in mathematics must present very strong evidence of capability for mathematical research.

Students seeking to transfer to the department's PhD programs from other campus programs, including the Group in Logic and the Methodology of Science, must formally apply and should consult the Vice Chair for Graduate Studies.

Contact Info

[email protected]

Berkeley, CA 94720

At a Glance



Admit Term(s)

Application Deadline

December 17, 2024

Degree Type(s)

Doctoral / PhD

Degree Awarded

GRE Requirements

where to get a phd in mathematics

Explore your training options in 10 minutes Get Started

  • Graduate Stories
  • Partner Spotlights
  • Bootcamp Prep
  • Bootcamp Admissions
  • University Bootcamps
  • Coding Tools
  • Software Engineering
  • Web Development
  • Data Science
  • Tech Guides
  • Tech Resources
  • Career Advice
  • Online Learning
  • Internships
  • Apprenticeships
  • Tech Salaries
  • Associate Degree
  • Bachelor's Degree
  • Master's Degree
  • University Admissions
  • Best Schools
  • Certifications
  • Bootcamp Financing
  • Higher Ed Financing
  • Scholarships
  • Financial Aid
  • Best Coding Bootcamps
  • Best Online Bootcamps
  • Best Web Design Bootcamps
  • Best Data Science Bootcamps
  • Best Technology Sales Bootcamps
  • Best Data Analytics Bootcamps
  • Best Cybersecurity Bootcamps
  • Best Digital Marketing Bootcamps
  • Los Angeles
  • San Francisco
  • Browse All Locations
  • Digital Marketing
  • Machine Learning
  • See All Subjects
  • Bootcamps 101
  • Full-Stack Development
  • Career Changes
  • View all Career Discussions
  • Mobile App Development
  • Cybersecurity
  • Product Management
  • UX/UI Design
  • What is a Coding Bootcamp?
  • Are Coding Bootcamps Worth It?
  • How to Choose a Coding Bootcamp
  • Best Online Coding Bootcamps and Courses
  • Best Free Bootcamps and Coding Training
  • Coding Bootcamp vs. Community College
  • Coding Bootcamp vs. Self-Learning
  • Bootcamps vs. Certifications: Compared
  • What Is a Coding Bootcamp Job Guarantee?
  • How to Pay for Coding Bootcamp
  • Ultimate Guide to Coding Bootcamp Loans
  • Best Coding Bootcamp Scholarships and Grants
  • Education Stipends for Coding Bootcamps
  • Get Your Coding Bootcamp Sponsored by Your Employer
  • GI Bill and Coding Bootcamps
  • Tech Intevriews
  • Our Enterprise Solution
  • Connect With Us
  • Publication
  • Reskill America
  • Partner With Us

Career Karma

  • Resource Center
  • Bachelor’s Degree
  • Master’s Degree

Best Doctorates in Mathematics: Top PhD Programs, Career Paths, and Salaries

Given that only a small proportion of the general population holds a PhD in Mathematics, there aren’t many people pursuing doctoral studies in the math field. It requires a high level of intelligence and mathematical ability which a typical person doesn’t possess. It also requires a decent work ethic and the ability to commit five to seven years to research and study.

However, PhD in Mathematics salaries are high. If you’re interested in pursuing a PhD in Mathematics, check out our article to find the best mathematics PhDs and what mathematics jobs you can get. First, let’s find out what a PhD in Mathematics is.

Find your bootcamp match

What is a phd in mathematics.

A PhD in Mathematics is a doctoral degree obtained by a graduate student in mathematics. This kind of mathematics graduate program allows students to develop their research capabilities in mathematics and its potential applications.

PhD in Mathematics can be a Doctor of Philosophy, Doctor of Science, or Doctor of Applied Mathematics degree. Students need to submit their PhD thesis in order to complete the math degree program they are pursuing. Math doctorate programs can take between three and six years to complete, depending on how much time is dedicated to the thesis and its required research.

How to Get Into a Mathematics PhD Program: Admission Requirements

The requirements to get into a mathematics PhD program typically include application fees, school transcripts, a professional resume, three letters of recommendation, and a statement of academic purpose. The admission process for most mathematical PhD programs is similar.

Some schools also require that students have mastered the material roughly equivalent to the undergraduate mathematics major, such as several semesters of calculus and experience with differential equations. Other doctoral math programs require applicants to submit essays or a minimum GPA score as entrance requirements.

PhD in Mathematics Admission Requirements

  • Professional CV or resume
  • Statement of academic purpose
  • Application fee
  • At least three recommendation letters
  • Undergraduate and graduate school transcripts

Mathematics PhD Acceptance Rates: How Hard Is It to Get Into a PhD Program in Mathematics?

It is extremely hard to get into a PhD program in Mathematics. For example, the Harvard PhD acceptance rate is 4.59 percent and the University of Wisconsin has a zero percent PhD acceptance rate over a five-year median. Doctoral studies in mathematics are rigorous and have a low acceptance rate, making it difficult to get into and obtain a Doctorate in Mathematics.

How to Get Into the Best Universities

[query_class_embed] how-to-get-into-*school

Best PhDs in Mathematics: In Brief

School Program Online Option
Columbia University Mathematics PhD No
Harvard University Mathematics PhD No
Massachusetts Institute of Technology Doctor of Philosophy or Doctor of Science Mathematics Degree No
Princeton University Applied and Computational Math PhD No
Rochester Institute of Technology Mathematical Modeling PhD No
Stanford University Mathematics PhD Program No
University of California, Berkeley PhD Program in Applied Mathematics No
University of Michigan – Ann Arbor Applied & Interdisciplinary Mathematics PhD No
University Of Wisconsin Mathematics, PhD No
Yale University PhD in Applied Mathematics No

Best Universities for Mathematics PhDs: Where to Get a PhD in Mathematics

The best universities for mathematics PhDs are Harvard University, Massachusetts Institute of Technology, Princeton University, Stanford University, University of California, Berkeley, and Yale University.

Other universities also have excellent PhD in Mathematics programs that we haven’t mentioned in our list, like Johns Hopkins University, Colorado State University, University of California, Los Angeles, and University of Chicago.

Columbia University is a private Ivy League research university founded in 1754 as King's College. It is among the top five national universities and is known as the oldest institution of higher education in New York. At Columbia University, students can find doctoral studies in biological sciences, astronomy, chemistry, economics, music, psychology, and religion.

Mathematics PhD

The PhD mathematics program is designed for full-time students interested in research and teaching at the university level. It is an intense course also meant for students that seek careers in quantitative research and development in business or government. It covers subjects like analysis and probability, Riemann surfaces, cumulative algebra, and modern geometry.

Mathematics PhD Overview

  • Program Length: 4 years
  • Acceptance Rate: 6%
  • Tuition and Fees: $25,248/semester
  • PhD Funding Opportunities: Department of Defense Funding, NIH Fellowship Parent Funding 

Mathematics PhD Admission Requirements

  • A completed online application form at the Online Application System
  • $120 application fee
  • Statement of purpose
  • A video essay (to be completed in the Online Application System)
  • A current resume or CV
  • Official transcripts from each university you attended
  • Two letters of reference

Harvard University was established in 1636 by the Puritan clergyman John Harvard. It is known as the oldest institution of higher learning in the US and as one of the most prestigious universities in the world. It offers many PhD programs in subjects such as anthropology, statistics, virology, physics, neuroscience, mathematics, immunology, and history of science.

This doctoral program is intended for students who aspire to be research mathematicians and have demonstrated a strong interest in this field. The math graduate courses cover topics like commutative algebra, advanced real analysis, differential geometry evolution dynamics, Riemann surfaces, and Hodge theory.

  • Program Length: 4-5 years
  • Acceptance Rate: 7%
  • Tuition and Fees: $50,928/first two years of study; $13,240/second two years of study
  • PhD Funding Opportunities: Hertz Foundation, National Defense Science and Engineering Graduate Fellowship Program, National Physical Science Consortium for Minorities and Women, National Science Foundation
  • Application
  • $105 application fee 
  • Transcripts
  • Letters of recommendation
  • Demonstration of English proficiency (for non-native speakers)

Massachusetts Institute of Technology (MIT) is a land-grant research university in Cambridge. Founded in 1861, MIT is best known for its programs in physical science and engineering. It offers a wide array of doctoral studies in aeronautics and astronautics, physics, political science, economics, chemical engineering, biology, brain, and cognitive sciences.

Doctor of Philosophy or Doctor of Science Mathematics Degree

In addition to choosing between a Doctor of Philosophy and a Doctor of Science program, students can choose to apply to the Pure or Applied Mathematics programs. Geometry, number theory, algebra, logic, statistics, topology, astrophysics, combinatorics, analysis, probability, numerical analysis, and theoretical physics, are covered in the Pure and Applied Mathematics curricula.

Doctor of Philosophy or Doctor of Science Mathematics Degree Overview

  • Acceptance Rate: N/A
  • Tuition and Fees: $27,755/term
  • PhD Funding Opportunities: Postdoctoral and Senior Research Awards, Faculty Early Career Development Program, Mathematical Sciences Postdoctoral Research Fellowships (MSPRF)

Doctor of Philosophy or Doctor of Science Mathematics Degree Admission Requirements

  • Fill out the online application
  • Transcripts including grades in math/science/engineering courses
  • At least three names and email addresses of recommendation letter writers
  • Educational and work history
  • Statement of objectives
  • Outside financial support and potential outside support
  • Credit/debit card payment of the $75 application fee
  • Self-reported grades
  • Arrange for submission of official transcripts and letters of recommendation

Princeton University is a private Ivy League research university that was founded in 1746. It is known as the fourth-oldest institution of higher education in the US. Princeton University has many PhD programs in subjects like philosophy, mechanical and aerospace engineering, electrical and computer engineering, and neuroscience.

Applied and Computational Math PhD

In this program, students gain a thorough understanding of areas of mathematics critical to scientific and engineering applications, such as numerical analysis and other computational approaches. In the first year, students choose three topics from six applied mathematics categories. At the end of the first year, students need to take a preliminary exam. 

Before the third year, students need to pass the general examination which culminates in a seminar on a research topic. The final requirement for this program is the doctoral dissertation which can be a mathematical contribution to one field of science or engineering.

Applied and Computational Math PhD Overview

  • Tuition and Fees : $58,790/year 
  • PhD Funding Opportunities: University, departmental, and program fellowships, research and teaching assistantships, external financial support

Applied and Computational Math PhD Admission Requirements

  • $75 application fee
  • Recommendation letters
  • Fall semester grades (for students currently enrolled in master’s degree programs)
  • English language tests (for international students)

Established in 1829, Rochester Institute of Technology is known for its excellent technology, engineering, and computing programs. It offers PhDs in Astrophysical Sciences and Technology, Biomedical and Chemical Engineering, Color Science, Imaging Science Sustainability, and many more disciplines.

Mathematical Modeling PhD

Students in this program plan their own trajectory based on required coursework, research, and their selected concentration. They can select from concentrations in the areas of applied inverse problems, biomedical, and discrete mathematics, among others. Some of the program’s courses cover subjects like numerical analysis and computing for mathematical modeling. 

Mathematical Modeling PhD Overview

  • Acceptance Rate: 74%
  • Tuition: $54,176/year 
  • PhD Funding Opportunities: Federal loans, Outside Scholarships, Yellow Ribbon Program, employment through co-ops, internships, or assistantships

Mathematical Modeling PhD Admission Requirements

  • Online graduate application
  • Copies of official transcripts of all previously completed undergraduate and graduate courses
  • Bachelor’s degree from an accredited university or college
  • Current resume/CV
  • Two letters of recommendation
  • Personal statement of educational objectives
  • TOEFL, IELTS, or PTE score (international students)
  • $65 application fee

Stanford University is well-known for its enterprising student population and high return on investment. Founded in 1885 by California senator Leland Stanford, Stanford University is consistently ranking in the top 10 national universities. Stanford offers many PhD programs in its Graduate School of Engineering, including programs in engineering, medicine, and education.

Mathematics PhD Program

Students in this PhD program take courses in algebraic topology, differential topology, differential geometry, algebraic geometry, theory of probability, real analysis, modern algebra, and mathematical methods of imaging. In the first year, the coursework prepares the students for the qualifying examinations which test them on their skills in algebra and real-world analysis. 

Students must have a dissertation advisor and seek candidacy in their second year. Students will take their Area Examination during their third year, which must be completed by the conclusion of the Winter Quarter. In the fourth and fifth years, students are expected to finish their dissertation research.

Mathematics PhD Program Overview

  • Acceptance Rate: 5.7%
  • Tuition and Fees: $56,487
  • PhD Funding Opportunities: Federal programs, university fellowships, research assistantships, teaching assistantships

Mathematics PhD Program Admission Requirements

  • Bachelor’s degree from a regionally accredited US college or university 
  • Unofficial transcripts/academic records
  • Names and contact information of those who can provide between three and six letters of recommendation
  • Online application
  • $125 application fee or fee waiver

University of California, Berkeley was founded in 1868. UC Berkeley is known for strict academic criteria for its undergraduate programs. The school has more than 130 academic departments and 80 multidisciplinary research areas. UC Berkeley is among the top universities in the world.

PhD Program in Applied Mathematics

The applied mathematics program requires doctoral students with previous graduate study in mathematics must demonstrate exceptional mathematical research skills. Students in this course can learn about linear algebra and differential equations, multivariable calculus, and discrete mathematics. There are also major electives like mathematical biology and statistics.

Venus profile photo

"Career Karma entered my life when I needed it most and quickly helped me match with a bootcamp. Two months after graduating, I found my dream job that aligned with my values and goals in life!"

Venus, Software Engineer at Rockbot

PhD Program in Applied Mathematics Overview

  • Program Length: 5-6 years
  • Acceptance Rate: 18%
  • Tuition and Fees: $10,248.75/semester (resident); $17,799.75/semester (non-resident)
  • PhD Funding Opportunities : Berkeley Fellowships, Chancellor’s Fellowships, Cota-Robles Fellowships, Mentored Research Awards, UC Dissertation-Year Fellowships, Conference Travel Grants, Parent and Caregiver Grants

PhD Program in Applied Mathematics Admission Requirements

  • A bachelor’s degree or equivalent from an accredited institution
  • A minimum GPA of 3.0
  • Enough experience in your undergraduate program to complete the program
  • At least three letters of recommendation
  • $120 application fee (California residents); $140 application fee (all other applicants)

The University of Michigan - Ann Arbor is among the top 30 national universities. It was founded in 1817 in Ann Arbor. Some of the most popular majors from this university are business administration, experimental psychology, and economics. It also has good PhD level programs in education, electrical and computer engineering, and computer and information science.

Applied & Interdisciplinary Mathematics PhD

This PhD degree's purpose is to create graduates who are well-prepared to pursue successful careers in the mathematical sciences, whether in government or academia. Students in the applied and interdisciplinary mathematics course can learn about risk management and modeling of financial losses, mathematical theory of probability, and modern mathematics.

Applied & Interdisciplinary Mathematics PhD Overview

  • Program Length: 5-6 years 
  • Acceptance Rate: 26%
  • Tuition and Fees: $25,230.38 (in state); $50,646.38 (out of state)
  • PhD Funding Opportunities: Graduate Student Instructorship (GSI): Mathematics Graduate Student Instructor Teacher Training Program, and Graduate Student Research Assistantship (GSRA)

Applied & Interdisciplinary Mathematics PhD Admission Requirements

  • Three letters of recommendation
  • Personal Statement (500-word limit)
  • TOEFL or IELTS Exam (non-native English speakers)
  • Three semesters of calculus
  • One or two semesters of differential equation courses
  • One semester course in modern algebra, linear algebra, geometry or topology
  • Advanced calculus of one and several variables 
  • $75 application fee (US citizens); $90 application fee (international applicants)

Nelson Dewey, the first governor of Wisconsin, founded the University of Wisconsin in 1848. It has one of the best engineering and business majors. It also has several good graduate degrees from its Department of Mathematics like Doctor of Philosophy, Master of Arts – Foundations of Advanced Studies, and Master of Arts – Foundations for Research.

Mathematics, PhD

The University of Wisconsin’s Doctor of Philosophy program offers a foundation in fundamental and advanced graduate mathematics. Students in this PhD program can learn about linear algebra, abstract algebra, differential equations, knot theory, and real analysis.

Mathematics, PhD Overview

  • Program Length: 5 years
  • Acceptance Rate: 16%
  • Tuition and Fees: $12,176/year (in state); $25,504/year (out of state)
  • PhD Funding Opportunities: Graduate assistantships, fellowships, traineeships, student loans, student jobs, research and travel grants

Mathematics, PhD Admission Requirements

  • Application to the UW–Madison Graduate School
  • Master’s degree in mathematics or a related field
  • Official transcripts
  • Supplementary information form
  • Three academic letters of recommendation and one additional letter
  • Proof of English proficiency (for non-native speakers)
  • One-page statement of purpose

Yale University was founded in 1701 in New Haven, Connecticut. It is among the top 10 national universities and is known for its Ivy League reputation . Yale has many PhD programs like anthropology, applied physics, architecture, biomedical engineering, chemical, and environmental engineering. 

PhD in Applied Mathematics

The applied mathematics program entails the study and application of mathematics to issues prompted by a diverse set of application fields. Students study and apply mathematics concepts to questions driven by a variety of applicable fields.

It covers topics such as discrete algorithms, linear and nonlinear partial differential equations, statistical theory and applications, information theory, econometrics, and classical and modern applied harmonic analysis. This program also covers topics like financial statistics, financial mathematics, econometrics probability theory, and information theory. 

PhD in Applied Mathematics Overview

  • Acceptance Rate: 6.2%
  • Tuition and Fees: $45,700/year
  • PhD Funding Opportunities: Financial aid, university fellowships, dissertation fellowships, teaching fellowships

PhD in Applied Mathematics Admission Requirements

  • A list of all the prior colleges or universities you’ve attended 
  • Unofficial transcripts from each school
  • TOEFL scores (non-native English-speaking applicants)

Can You Get a PhD in Mathematics Online?

Yes, you can get a PhD in Mathematics online. However, there aren’t many online PhD math programs out there because of two reasons. The first reason is that there isn’t a big demand for PhDs in Mathematics, so online universities are not inclined to find ways to make those programs more accessible.

The second reason is that in traditional doctoral studies graduate students in mathematics are used as research and teaching assistants. Usually, math doctoral studies take place within a community in which PhD students are apprentices learning alongside instructors and one another.

Best Online PhD Programs in Mathematics

School Program Length
Atlantic International University Doctorate in Mathematics Custom pace
Edith Cowan University Mathematics PhD 4 years

How Long Does It Take to Get a PhD in Mathematics?

It takes about five years to get a PhD in Mathematics. Depending on the academic institution and the specifications of the program, it can take between three and six years. Some students prefer to have a master’s degree before entering a doctoral program in mathematics, but most programs do not require students to have more than a bachelor’s degree .

Some doctoral mathematics academic programs offer two degrees called dual degree programs. You can begin pursuing a Master’s Degree in Mathematics and begin earning credits for a PhD at the same time.

Is a PhD in Mathematics Hard?

Yes, a PhD in Mathematics is hard. Doctoral studies that require advanced knowledge of mathematics would be extremely difficult for most people. Whether you choose to pursue a PhD in Applied Mathematics or Pure Mathematics, you will encounter complex theoretical concepts.

How Much Does It Cost to Get a PhD in Mathematics?

On average, it costs $12,171 per year to get a PhD in Mathematics . This data is based on the National Center for Educational Statistics’s (NCES) report for the average costs of postgraduate studies at public institutions from 2018 to 2019. According to this data, it would cost a total of $48,684 for four years of studies. The cost to get a PhD in Mathematics has likely risen since 2019.

How to Pay for a PhD in Mathematics: PhD Funding Options

The PhD funding options that students can use to pay for a PhD in Mathematics include research fellowships, teaching assistantships, and tuition waivers. In the previous section, we mentioned the cost of doctoral degrees , but this number is with a deduction in the tuition.

These funding options enable students to lower the cost of tuition. For example, domestic students receive lower tuitions. Without funding options or deductions, a PhD can cost from $20,000 to $30,000 per year.

Best Online Master’s Degrees

[query_class_embed] online-*subject-masters-degrees

What Is the Difference Between a Mathematics Master’s Degree and PhD?

The difference between a Master’s Degree in Mathematics and a PhD is the career opportunities they provide graduates. People who pursue a PhD in Mathematics usually seek jobs in research and academia, while people who pursue master’s degrees are more interested in advancing their professional careers.

A PhD in Math is more research-intensive and focused on historical and current perspectives within the mathematics field. Master’s degrees are a bit broader. Master’s degrees can take up to three years to complete, while PhD can take up to six years. Math PhD students also teach and engage in departmental activities, while master’s students do not.

Master’s vs PhD in Mathematics Job Outlook

It is usually required for postsecondary teachers to have PhDs. According to the Bureau of Labor Statistics (BLS), these professionals have a job outlook of 12 percent , four percent higher than the average for all occupations.

Mathematics and statisticians are usually required to hold a master’s degree and they have a job outlook of 33 percent , nearly three times the average for all occupations. According to these numbers, the job outlook for Master’s Degrees in Mathematics is higher than for PhDs in Mathematics. However, these are just two examples of careers available to master’s and PhD holders.

Difference in Salary for Mathematics Master’s vs PhD

According to PayScale, mathematicians with a master’s degree earn $85,000 per year, and mathematicians with a PhD degree earn $110,000 a year. This is a difference of $25,000 per year for mathematics master’s vs PhD holders.

Related Mathematics Degrees

[query_class_embed] https://careerkarma.com/blog/best-mathematics-bachelors-degrees/ https://careerkarma.com/blog/mathematics-associate-degrees/ https://careerkarma.com/blog/best-mathematics-masters-degrees/

Why You Should Get a PhD in Mathematics

You should get a PhD in Mathematics because it expands your academic career opportunities and salary options. With a PhD in Math, you can work for private businesses or government agencies. Many PhD grads work in engineering, medicine, and software development, where they apply the advanced mathematical knowledge they acquired from their doctoral programs.

Reasons for Getting a PhD in Mathematics

  • Specialized skills. A PhD in Mathematics equips you with highly valuable and marketable skills. Aside from subject-specific abilities, you can obtain several transferable skills that will be beneficial in practically any industry, such as exceptional numeracy, logical ability, holistic deduction, and reasoning skills.
  • Higher salary. A PhD is a terminal graduate degree, meaning it is the highest level of academic certification you can achieve in this field. So with a PhD you will gain the highest skills and knowledge in mathematics. High-level skills and knowledge often translate to a high salary.
  • Career opportunities. One of the best advantages math PhDs have is the option of following a variety of employment pathways. To some extent, all sciences are built on basic mathematical principles, so there are many career opportunities with a PhD in Mathematics. With this kind of degree, you can work in finance, academia, or IT.
  • Research opportunities. Doctoral Degrees in Mathematics cover theoretical mathematics which is one of the best areas for research and research methodology. During your doctoral studies in math, you will study and research with some of the smartest people in the world.

Getting a PhD in Mathematics: Mathematics PhD Coursework

a female PhD Student solving a mathematical test

Getting a PhD in Mathematics is not an easy task. Students need to learn different math courses, some of which require advanced knowledge of mathematics. There is some standard mathematics PhD coursework, like classes in mathematical analysis or mathematical logic. Find out more details on common mathematics PhD courses below.

Mathematical Analysis

These kinds of courses explain the principles of mathematical analysis, including differentiability, continuity, sequence and series convergence, the Riemann integral, function sequences, and series. Students can also learn real applications of real-world analysis, including the estimation of indeterminate integrals, Laurent series, WKB theory, Cauchy theorem, and residual theorem.

Differential Topology

Courses in differential topology are a part of the theory of differential forms and De Rham’s theory. Somer differential topology courses teach about multilinear algebra, Stokes’ theorem, and an introduction to cohomology. But, in most cases, these courses teach about winding numbers, vector fields, index, smooth maps, transversality, and differential manifolds.

Discrete Mathematics

Courses in discrete mathematics usually cover finite geometry, finite groups, finite topology, finite fields, fundamental algebraic topology, combinatorics, and graph theory. Students can learn about the symmetry group of the regular icosahedron because it is a reoccurring subject throughout the course.

Theory of Probability

Theory of probability courses introduce students to discrete and continuous random variables, independent random variables, conditional probability, distribution functions, Poisson distributions, Bayes theorem, and joint distribution. Students in this course will learn how to use math principles in the analysis of random phenomena.

Algebraic Geometry

In most cases, algebraic geometry courses teach students about complex algebraic varieties, cohomology, affine, and projective algebraic geometry. They also cover the fundamental concepts of complex analytic varieties, Bezout’s theorem, algebraic curves, and surfaces, the language of schemes, and properties of morphisms.

Best Master’s Degrees

[query_class_embed] *subject-masters-degrees

How to Get a PhD in Mathematics: Doctoral Program Requirements

Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs. Keep reading to find out more.

PhD students must finish eight or nine-term courses at the graduate level, in most cases maintaining at least a C average grade. The time for completion of a PhD math coursework is four to five years.

The residency requirement can vary from university to university. For most math PhD candidates, the usual residency requirement is around three years. The whole point of residency is to continue the education and training of students in a specialized field of mathematics.

A committee of three faculty members administers the Qualifying Examination, which is an oral test. Each student selects three qualifying test subjects and discusses them with appropriate examiners. Subjects must be in separate, reasonably broad mathematical fields. 

Typically, the primary topic is decided in cooperation with the potential thesis advisor. After completing the qualifying test, students must choose a thesis advisor, who is usually the primary topic examiner.

In academic positions, teaching is important, especially in mathematical doctoral studies. Many people in math PhD programs aspire to academic positions, so teaching is one of the best ways to learn about the mathematics academic profession. It is an excellent way to learn public presentation skills by completing at least one semester of classroom teaching.

Writing and defending a thesis for a PhD in Mathematics is the culmination of this graduate program. Usually, a thesis is anticipated to contain original research of a high enough quality to be published in a high-level research journal. The defense is usually held in the classroom of the Institute and is presented to the Thesis Examination Committee.

Potential Careers With a Mathematics Degree

[query_class_embed] how-to-become-a-*profession

PhD in Mathematics Salary and Job Outlook

People with a PhD in Mathematics earn above the average annual salaries and have careers with above the average job growth. For example, actuaries have a 24 percent job growth till 2030. According to the Bureau of Labor Statistics, the average job growth rate for all occupations is 7.7 percent .

Earning a mathematics PhD is difficult but you will graduate with a wide range of job opportunities. People with a PhD in Math earn between $82,360 to $108,660 per year. Overall, people with PhDs in Mathematics have a good salary and job outlook.

What Can You Do With a PhD in Mathematics?

With a PhD in Mathematics, you can work in education or IT and for private, corporate, or government corporations. You can work as a postdoctoral research associate, a math professor in postsecondary or higher education, a director of analytics, a research scientist, a principal software engineer, or an asset manager.

Best Jobs with a PhD in Mathematics

  • Data Scientist
  • Mathematicians and Statistician
  • Operations Research Analyst

What Is the Average Salary for a PhD in Mathematics?

The average salary for a PhD in Mathematics is $110,000 , according to PayScale. The salary range for doctorate-level degree mathematics jobs ranges from $48,690 to $167,040 per year. Lower-earning operations research analysts make an average of $48,690 , while top-earning data scientists earn $167,040 annually, according to the Bureau of Labor Statistics.

Highest-Paying Mathematics Jobs for PhD Grads

Mathematics PhD Jobs Average Salary
Data Scientist
Mathematician or Statistician
Operations Research Analyst

Best Mathematics Jobs with a Doctorate

There are many jobs you can find with a math PhD. The skills you will gain are applicable to almost any field. Find out more about the best PhD in Mathematics jobs below.

Data scientists are specialists who know how to extract and interpret data. They know how to use models and algorithms to analyze massive data repositories. They use various strategies to determine the optimal methods for developing a data model for a business. Data scientist is one of the most in-demand and highest-paid jobs in 2022. 

  • Salary with a Mathematics PhD: $108,660
  • Job Outlook: 22% job growth from 2020 to 2030
  • Number of Jobs: 105,980
  • Highest-Paying States: Washington, California, Delaware, New York, New Jersey

Actuaries are more concerned with the financial implications of risk and uncertainty. Actuaries are financial analysts who analyze past and present financial data and forecast future risks. They assess risk using financial theory, statistics, and math and develop plans that reduce the cost of risk.

  • Salary with a Mathematics PhD: $105,900
  • Job Outlook: 24% job growth from 2020 to 2030
  • Number of Jobs: 27,700
  • Highest-Paying States: Georgia, New Hampshire, New York, Connecticut, Vermont

Some of the main responsibilities economists have are to predict the customer demand for the firm's products and the firm's product sales. They deal extensively with microeconomic issues while researching trends, collecting, evaluating, and analyzing data. Economists also investigate how to efficiently allocate resources like raw materials, labor, land, or machines.

  • Salary with a Mathematics PhD: $105,630
  • Job Outlook: 13% job growth from 2020 to 2030
  • Number of Jobs: 18,600
  • Highest-Paying States: New York, District of Columbia California, New Hampshire, Illinois

In most cases mathematicians and statisticians work in academia and government. Usually, both of the positions require the use of analyzing data or applying statistical and mathematical techniques that help solve problems. 

Statisticians are increasingly involved in statistics and research methodology. Mathematicians are more involved in researching mathematical models or abstractly measuring values and creating results. Mathematics and statistics are the best duos that understand the principles of probability.

  • Salary with a Mathematics PhD: $96,280
  • Job Outlook: 33% job growth from 2020 to 2030
  • Number of Jobs: 44,800
  • Highest-Paying States: District of Columbia, New York, New Jersey, Virginia, Maryland

Operations research analysts utilize mathematics and logic to assist businesses in making informed decisions and solving complex problems. They are high-level problem solvers that use sophisticated approaches such as mathematical modeling and statistical analysis to help companies operate more economically.

  • Salary with a Mathematics PhD: $82,360
  • Job Outlook: 25% job growth from 2020 to 2030
  • Number of Jobs: 104,100
  • Highest-Paying States: Virginia, Alabama, Maryland, Hawaii, New York

Is a PhD in Mathematics Worth It?

Yes, a PhD in Mathematics is worth it if you are interested in solving math problems and analytical thinking. You also have to be willing to commit to the long educational journey and research required to achieve this level of degree.

Exploring the mathematical fields is challenging and demanding but with time it provides excellent career opportunities. Math positions are respected and well-paid with positive job outlooks. Other than its academic difficulty, there aren’t many downsides when it comes to doctoral math degrees because you can go on to work in many fields.

Additional Reading About Mathematics

[query_class_embed] https://careerkarma.com/blog/best-schools-for-mathematics/ https://careerkarma.com/blog/mathematics-for-computer-science/ https://careerkarma.com/blog/jobs-that-use-math/

PhD in Mathematics FAQ

Yes, a math PhD is useful because it will help you acquire some transferable skills that will be useful in virtually any industry. It is also useful for those interested in mathematics research or academia. If you wonder what you can do with a math degree , a PhD will equip you with many valuable skills.

Yes, a PhD in Mathematics is difficult to learn. It is difficult to be admitted to a doctoral program in mathematics, and it is also difficult and too abstract for most people to grasp advanced mathematical principles taught in PhD studies. Doctoral math studies are objectively difficult, even for those who are naturally strong at math and have excelled at it their whole life.

Mathematicians need several skills like active learning, complex problem-solving, critical thinking, and analytical skills. A good mathematician also needs information ordering and inductive and deductive reasoning abilities.

Mathematicians mainly explore mathematical principles or models and create their own mathematical theories and concepts. Most of the work they do is in the theoretical realm, that is why they mainly want to work in IT, social science, engineering, or financial fields.

About us: Career Karma is a platform designed to help job seekers find, research, and connect with job training programs to advance their careers. Learn about the CK publication .

What's Next?


Get matched with top bootcamps

Ask a question to our community, take our careers quiz.

Hristijan Josifovski

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Apply to top tech training programs in one click

Mathematics Education PhD

Doctor of philosophy.

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

A graduate student has an animated conversation with his peers at TC.

Admissions Information

Displaying requirements for the Spring 2024, Summer 2024, and Fall 2024 terms.

  • Points/Credits: 75
  • Entry Terms: Spring, Summer, Fall

Application Deadlines

Entry Term AvailablePriority DeadlinesFinal DeadlinesExtended Deadlines
SpringNovember 15, 2023November 15, 2023N/A
SummerDecember 1, 2023June 1, 2024N/A
FallDecember 1, 2023July 1, 2024N/A

For details about rolling deadlines , visit our admission deadlines page.

Select programs remain open beyond our standard application deadlines , such as those with an extended deadline or those that are rolling (open until June or July). If your program is rolling or has an extended deadline indicated above, applications are reviewed as they are received and on a space-available basis. We recommend you complete your application as soon as possible as these programs can close earlier if full capacity has been met.

Application Requirements

  , including Statement of Purpose and Resume
 Results from an accepted (if applicable)
 $75 Application Fee
 Two (2) Letters of Recommendation

Requirements from the TC Catalog (AY 2023-2024)

Displaying catalog information for the Fall 2023, Spring 2024 and Summer 2024 terms.

View Full Catalog Listing

Doctoral Degrees

All candidates for the Ed.D., Ed.D.C.T., or Ph.D. degrees are expected to demonstrate both mathematics and mathematics education competencies through a series of certification examinations taken upon the completion of 60 graduate points. Certification examinations test the student’s knowledge of current research and theory in mathematics education and mathematics content. Examinations are offered once in the fall, spring, and summer terms. Courses recommended as preparation for the examinations in mathematics education include MSTM 6037,  MSTM 4019, and other mathematics education courses; Courses recommended as preparation for the examinations in mathematics are 6000- level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Alternatively, they may register for advanced content courses and, with permission of the program, sit for the content area certification examination upon completion of the course. Incoming doctoral candidates should register for MSTM 6037 Professional Seminar in Mathematics during the first year of doctoral studies.

Doctoral students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Doctor of Philosophy in Mathematics Education

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree program requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Candidates are encouraged to develop an association with a faculty member early in their studies to identify a problem area of mutual interest to plan a course of studies that leads to the competencies needed to complete dissertation research and prepare for a professional role. Further details are available in the brochures on doctoral studies and in the general descriptions of doctoral programs available from the Office of Doctoral Studies (ODS).

A program of study for the Doctor of Philosophy degree must include at least 45 points taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 60 points in mathematics, mathematics education, statistics, and computing. At least 35 points should be in advanced courses – including research courses (MSTM 6500 or 6501 and MSTM 7500). (Any Teachers College course at the 6000 level or above, any Columbia University Graduate School of Arts and Sciences course with a “G” prefix, any “W” course numbered above 4000, or any transferred course with a graduate-level prerequisite will be considered an advanced course.) Further, 15 points in the philosophical, psychological, and curricular foundations of education must be included in every Ph.D. degree program. Students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Candidates for the Ph.D. degree are required to demonstrate competency in two languages chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the program to request one substitution. Students in mathematics may not use computer languages or statistics to satisfy the language requirement.

The Ph.D. dissertation is a scholarly study contributing new theoretical knowledge to the field and should be planned early in the program when sufficient advanced courses have been completed to permit the candidate to enroll in relevant research courses. Ph.D. dissertations in mathematics education should be (1) experimental studies in learning, (2) analytical studies in policy theory in mathematics education, or (3) other scholarly investigations of problems and issues of broad significance in the field.

The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.

  • View Other Degrees

Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

Phone: (212) 678-3381 Fax: (212) 678-8319

Email: tcmath@tc.edu

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

How to get into a top mathematics PhD program?

I'm a first year student undergraduate at a top US university, and I'm going to major in math. Of course, I still don't really know what I want to do with my life, but I'm really excited about going on to a PhD in math. What does one have to do to get into a top PhD program in mathematics? When I say top, I mean absolute top - like Princeton or MIT. Please understand that I'm not being presumptuous in asking this: I don't know whether I'll ever be good enough to do a PhD at an institution such as these, but I'm just asking for reference - and out of curiosity.

I've read a lot of threads about similar topics, but answers there are fairly vague ("good letters of recommendation", "advanced coursework", etc). What exactly do these terms mean, and what should I - as a first year student - already start doing to at least stand a chance sometime in the future to even dream of being in a program such as the ones I mentioned?

  • graduate-admissions
  • mathematics
  • undergraduate
  • research-undergraduate

gtoques's user avatar

  • 1 Get good grades and apply when you have finished final year... –  Solar Mike Commented Mar 28, 2019 at 6:28
  • 6 Let me be blunter than I or most mathematicians would like to be. There is such a thing as mathematical talent, and, starting where you are and given the level you're aiming for, it matters (though many other things also matter!) Let me make an analogy to making the NBA. One could make a list of things that most basketball players have to do to make the NBA, but almost all of the basketball players who try to do most of these things still won't make the NBA. In fact, so few of them will make it that calling such a list a guide to making the NBA would be ridiculous. –  Alexander Woo Commented Mar 28, 2019 at 8:00
  • 2 I think a lot of it has to do with opportunities taken at a young age. Enrolling in a program to skip part of high school and start college early is an example. Basically, one initial requirement would probably be access to math beyond what one typically sees. Another example is participating in the Ross program. Or working with highly motivated students on challenging math. If you can forgo everything and focus on math, that would probably help. Go to a top college and take as much math as possible. It helps to have mathematician parents. –  user74089 Commented Mar 28, 2019 at 9:05
  • 1 @AlexanderWoo The problem with the NBA analogy is that there are much clearer ways to measure talent and performance in basketball than in mathematics. Even if "mathematical talent" were a one-parameter quantity, it's more than a little dubious that Princeton and MIT are particularly good at identifying it. –  Elizabeth Henning Commented Mar 28, 2019 at 17:11

2 Answers 2

First off, I have a PhD in a top 20 - not top 3. I believe my school was 16 or 17 when I was doing my PhD. So I'm below what you are aiming for. So feel free not to read this post.

First of all, I'm puzzled by your comment:

fairly vague ("good letters of recommendation", "advanced coursework", etc). What exactly do these terms mean, and what should I - as a first year student - already start doing to at least stand a chance sometime

Good letters of recommendation: You will need to get about 3 profs to write good letters of recommendation when you apply to grad school. That means you need them to say you are smart as in PhD-smart.

Advanced coursework: Take ALL the higher level courses if possible. Take some graduate level courses if possible.

Now about grad school: don't think about the top 1 or 2 or even 3 for now. If your goal is math, then your goal is math, not the school. Just focus on math for now.

I do not know you, so whatever I said below might be useless and meaningless.

What can you do as a first year student? Get a good GPA, as close to 4.0 as you can. You want to take as many math courses as you can right? So do some self-study and test out of your gen ed courses. I had a student who tested out about 8 so that he can have time to take ALL the higher level courses.

Are you taking any math courses now? Then focus on them and do well. Doing well does not mean just getting an A. It means being near the top of the class. Your prof knows. Not all profs will take note. But some do.

You have to figure out which profs are interested in growing PhD students. Profs who care will be open to chat with you and guide you. The only way you can catch their attention and learn from them is to be at the top of your class. Ask questions in class (if possible, when appropriate). Do you study ahead? Talk to them during office hours and ask questions so that they know you are interested and are studying your textbook ahead of the class.

When I was an undergraduate I always study ahead. While studying all the courses, I will pick one book and study ahead until I'm done with the book for that course. Then I'll pick another one and study ahead. Etc. Don't just read the book. Do the problems.

It's also a good idea to think about your favorite area in math and study it on your own. Unfortunately if you are not very deep into math, you might not know where to go with this. That's why knowing a prof well will help. He can guide you.

If you have time and if you have not done so, I suggest you look at the textbooks for math olympiads. Study them and do all the problems. Try to finish as much as you can so that you have some time to try some putnam competition books. Math problems in the math olympiad and the putnam are very different from the type of problems you will solve in your regular math classes. In many ways they are closer to research-type math problems. Again, I do not know you. Maybe you have already done lots of math olympiad training.

Another very important thing to note is that it is your responsibility to keep your level of interest in your area (i.e. math) as high as possible. That means spending some time reading up on the biographies of famous mathematicians. Don't do too much of that since you do have to study math.

Books are the most important resource for you right now. Ask your profs for good recommendations. Do not be surprised that your class textbook might not be the best textbook on that subject. It's just one that's convenient and easy to use. I have no idea where you are in your math education. But if you are in Calculus, then you can for instance study "Calculus" by Michael Spivak. If you are very strong in math and have already studied that, you can go on to other books.

Check your math library and see if you can find magazines you can understand. Try the American Mathematical Monthly and the Mathematical Intelligencer.

See if there's a math club you can join. Make sure it's a math club and not just a social gathering for math majors. Nothing wrong with socializing, but if the club does not have math related activities, then it won't help your goal.

If you work very hard in the first 2 years, you might know what area you want to go into. (But it might change.) And if you take some grad level course(s) in that area in your third year, you might be able to attend the research seminar in that area, which might be a weekly meeting. You might be able to start doing some research during your senior year.

spoock7824's user avatar

  • 4 This is good advice except the part about math competitions. Those questions are nothing like research problems. –  Tobias Kildetoft Commented Mar 29, 2019 at 5:43

Roughly: good grades (3.8+ GPA) in difficult courses, good test scores (80+ percentile on math GRE subject test [not the regular GRE math, which you should get a ~perfect score on without studying]), strong research background and good letters corresponding to it.

That will get you into schools in the top ~30. To get into the very top programs, you will need to meet this standard and also have either (1) a very nice research background / letters, or (2) something "interesting", such as impressive accomplishments outside of math

Disclaimer: not a mathematician

cag51's user avatar

  • 1 Can the downvoters explain? Not a mathematician, will delete if I'm off-base, but I got into a top-10 physics program with basically this formula... –  cag51 ♦ Commented Mar 28, 2019 at 5:52
  • 1 I understand that. What exactly do you mean by accomplishments "outside of math" though? What kind of accomplishments? –  gtoques Commented Mar 28, 2019 at 6:18
  • 4 Voted this up - can't see why it gets downvotes... –  Solar Mike Commented Mar 28, 2019 at 6:50
  • 7 This advice is far too generic. Good grades (3.8 GPA)? There is no mention of the caliber of courses. Median Princeton admit probably has a 4.0 GPA with stellar performance in numerous graduate level courses like differential geometry or algebraic topology. 95+ percentile on GRE is probably a given although I doubt top programs put much weight on it at all. Most importantly, it really helps if a respected mathematician gives an absolutely glowing recommendation regarding your research potential. Impressive accomplishments outside math count for very little. –  zoidberg Commented Mar 28, 2019 at 7:06
  • 3 @zoidberg surely the advice has to be generic - the OP is nowhere near completion, has no grades to speak of and not applied to any institution yet.... –  Solar Mike Commented Mar 28, 2019 at 7:14

You must log in to answer this question.

Not the answer you're looking for browse other questions tagged phd graduate-admissions mathematics undergraduate research-undergraduate ..

  • Featured on Meta
  • Upcoming sign-up experiments related to tags

Hot Network Questions

  • What was the submarine in the film "Ice Station Zebra"?
  • Would a PhD from Europe, Canada, Australia, or New Zealand be accepted in the US?
  • Who is a "sibling"?
  • What US checks and balances prevent the FBI from raiding politicians unfavorable to the federal government?
  • Is "ROW_NUMBER() OVER(ORDER BY xml.node)" well defined?
  • Can a unique position be deduced if pieces are replaced by checkers (can see piece color but not type)
  • Do I need to staple cable for new wire run through a preexisting wall?
  • Short story about soldiers who are fighting against an enemy which turns out to be themselves
  • Mōnstrō and mōnstrum - how exactly are they related?
  • Definition of "Supports DSP" or "has DSP extensions" in a processor
  • Traveling between two Schengen Countries using a Verlustanzeige?
  • Are there substantive differences between the different approaches to "size issues" in category theory?
  • If a reference is no longer publicly available, should you include the proofs of the results you cite from it?
  • Hard-to-find historical grey literature - any tips?
  • C# Linked List implementation
  • What is a curate in English scone culture?
  • Does a publication similar to the American Mathematical Monthly exist in Theoretical Computer Science?
  • Forcing QGIS to export using left hand rule
  • Idiom for a situation where a problem has two simultaneous but unrelated causes?
  • Creating a command to display blackboard font
  • I'm on a windows 10 machine and trying desperately to see when the last dns flush took place
  • A puzzle from YOU to ME ;)
  • Can a contract require you to accept new T&C?
  • Comprehensive Guide to saying Mourners' Kaddish

where to get a phd in mathematics

Get the Reddit app

This subreddit is for anyone who is going through the process of getting into graduate school, and for those who've been there and have advice to give.

Which Master's to Choose for PhD Admissions (Mathematics)

Hey everyone,

I'm really interested in pursuing a PhD in either mathematics or statistics and am contemplating the best master's degree to enroll in to strengthen my application credentials. For context, I studied economics with a math minor and completed a master's in GIS since I was originally going down the urban planning route. I completed calc I-III, differential equations, abstract algebra, undergrad linear algebra, a graduate linear algebra course, a proofs course, a graduate real analysis course, a statistics course, and two econometrics courses. So, it's not so much that I am terribly behind on content, but I definitely would like to supplement what I've taken through an affordable degree. I live in NYC and not open to relocating due to my job, so I was looking into Hunter College 's MA in Pure Math since it seems that classes are held in the evening. I was also contemplating online programs of comparable rigor such as the University of Southern Mississippi 's MS program and the University of North Alabama 's MS program. Both programs have comparable courses and course content to Hunter's and are similar in price. UNA and Hunter both have comprehensive exams, but USM has a year-long thesis sequence that few other programs I've found offer, which would give me the opportunity to publish mathematical research. I'm just curious to see what others would recommend in this situation, or if you have other programs worth considering.


  1. PhD in Mathematics

    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.

  2. Admissions

    Harvard Kenneth C. Griffin Graduate School of Arts and Sciences (Harvard Griffin GSAS) Mathematics Graduate Studies. Admissions. Financial Support. Graduate Program Administrator. Marjorie Bell (she/her) 617-496-5211. [email protected]. Science Center Room 331.

  3. Ph.D. Program

    In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ...

  4. Requirements for the Ph.D. Degree

    In order to qualify for the Mathematics Ph.D., all students are required to: Complete eight term courses at the graduate level, at least two with Honors grades. Pass qualifying examinations on their general mathematical knowledge; Submit a dissertation prospectus; Participate in the instruction of undergraduates;

  5. PhD Program

    PhD Program. More information and a full list of requirements for the PhD program in Mathematics can be found in the University Bulletin. 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 ...

  6. Guide To Graduate Study

    Guide to Graduate Studies. The PhD Program. The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in ...

  7. Mathematics PhD Program

    The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both ...

  8. 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 ...

  9. Department of Mathematics at Columbia University

    website creator . Program of Study. The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy. The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government.

  10. Graduate Program

    Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we ...

  11. PhD in Mathematics

    The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD.

  12. Ph.D. in Mathematics

    The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at here.

  13. Harvard Mathematics Department Graduate Information

    Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences. ... Department of Mathematics Science Center Room 325 1 Oxford Street Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main ...

  14. Ph.D. in Mathematics

    Overview of Graduation Requirements. To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements: If you have a Master's degree in mathematics at UConn, then 30 credits are required, including 15 doctoral dissertation research credits. Pass three preliminary exams and two core courses (details below).

  15. PhD in Applied Mathematics

    a Secondary Field (which is similar to a "minor" subject area). SEAS offers PhD Secondary Field programs in Data Science and in Computational Science and Engineering. GSAS lists secondary fields offered by other programs. a Master of Science (S.M.) degree conferred en route to the Ph.D in one of several of SEAS's subject areas.

  16. PhD 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 ...

  17. Mathematics

    Mathematics. Ph.D. The Mathematics program is designed to prepare especially able students for a career in mathematical research and instruction. A relatively small enrollment of 30 to 40 students permits small classes and close contact with faculty. Applicants should have a good background in undergraduate mathematics, regardless of their majors.

  18. Applied Mathematics PhD

    Requirements for the Mathematics and Applied Mathematics PhDs differ only in minor respects, and no distinction is made between the two in day-to-day matters. Graduate students typically take 5-6 years to complete the doctorate. Continuing students wishing to transfer from one program to another should consult the graduate advisor in 910 Evans ...

  19. Best PhDs in Mathematics

    How to Get a PhD in Mathematics: Doctoral Program Requirements. Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs.

  20. Mathematics Education PhD

    Mathematics Education PhD; Doctor of Philosophy. The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching ...

  21. How Long Does It Take To Get a PhD in Math?

    Typically, it takes about five years to get a Ph.D. in math. This amount of time is in addition to your undergraduate education, which usually takes about four years to complete. You don't necessarily have to get a master's degree, which takes about two years to complete, to pursue a Ph.D. in math. However, many students choose to earn a master ...

  22. Graduate Admissions

    For non-Stanford applicants, the Mathematics Department offers admission to the PhD program only. Please see the Explore Graduate Programs page for other departments that offer a Master's degree. For current Stanford undergraduate students only: The department accepts applications to the Coterminal Master's degree program.

  23. graduate admissions

    0. Roughly: good grades (3.8+ GPA) in difficult courses, good test scores (80+ percentile on math GRE subject test [not the regular GRE math, which you should get a ~perfect score on without studying]), strong research background and good letters corresponding to it. That will get you into schools in the top ~30.

  24. Required Exams for PhD Students

    Students in the PhD program in Mathematics must fulfill one of the following two options within the time frame described in the graduate catalog. Option 1: Pass two written qualifying exams from five subjects. Written qualifying exams are given twice a year, in January and August respectively, lasting four hours each.

  25. Which Master's to Choose for PhD Admissions (Mathematics)

    I'm really interested in pursuing a PhD in either mathematics or statistics and am contemplating the best master's degree to enroll in to strengthen my application credentials. For context, I studied economics with a math minor and completed a master's in GIS since I was originally going down the urban planning route. I completed calc I-III ...