- 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

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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

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?

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.

## 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.

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

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

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

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## 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.

## COMMENTS

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.

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.

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 ...

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;

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 ...

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 ...

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 ...

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 ...

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.

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 ...

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.

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.

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 ...

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).

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.

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 ...

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.

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 ...

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.

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 ...

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 ...

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.

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.

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.

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 ...