after phd in mathematics what next

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

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

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.

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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 knowledge in algebra and real analysis.

Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics:

real analysis
geometry and topology
applied mathematics

Course Requirements for students starting prior to Autumn 2023

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

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

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry
Math 216A, B, & C: Introduction to Algebraic Geometry
Math 230A, B, & C: Theory of Probability
3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

Course Requirements for students starting in Autumn 2023 and later

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

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

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

Years 4&5

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

Throughout the PhD Program

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

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

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Research Programmes

Prospective Students
Postgraduate Study

The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.

Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.

Programme	Duration	Department
	3-4 years	DAMTP
	3-4 years	DPMMS
	4 years; with a structured first year	DAMTP and DPMMS
(by thesis)	12 months full-time, or 2 years part-time	DAMTP and DPMMS

Research Areas and Potential Supervisors

Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.

We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.

Before making an application to study with us we recommend you:

Investigate our areas of research and consider how they fit with your interests and ambitions.

A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.

Identify 2 or 3 appropriate supervisor(s) with whom you might work.

Applicants should indicate one or more proposed supervisor(s) in their application. The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.

If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.

Give some thought to your intended research and why you want to study with us.

On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.

Research areas

Click on a research area to find out more about available supervisors and their research:

DAMTP	DPMMS

Please note that a large majority of the successful applicants for PhD studentships with the High Energy Physics, and General Relativity & Cosmology (GR) groups will have taken Part III of the Mathematical Tripos.

Funding Opportunities

Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.

[Funding opportunities across the University and Colleges]

[Includes Gates Cambridge and Cambridge Trusts]

The following opportunity is for MPhil applicants only:

The following opportunities are for doctoral applicants only:

[HEP, GR and Cosmology]

: Atmosphere-Ocean Dynamics, Theoretical Geophysics, and certain areas of Fluid and Continuum Mechanics [ ]

[via DPMMS]

All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:

16 October 2024

Gates Cambridge Scholars (US citizens only)

15 December 2024

(for doctoral applicants only)

7 January 2025

All other applications for admission in October, including Gates for non-US citizens.

This is our funding deadline. Applications received by this date will be considered for nomination to the University’s Postgraduate Funding Competition.

Note for PhD applicants:

We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.

Note for MPhil applicants:

We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Most interviews are expected to take place in the second half of January.

The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.

Not all applicants will be selected for interview.

If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:

the location of the interview (it may be in-person or on-line dependent upon interviewer availability, your distance from Cambridge, as well as individual preferences),
the interview format and whether you should prepare anything specific in advance,
the approximate duration of the interview,
who you will be meeting.

Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.

Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.

Decision timeline

Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.

To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.

Communication of outcomes

You will be notified of the formal outcome of your application via the Applicant Portal.

Following an interview, you can normally expect to receive notification of the outcome within a week or two.

If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.

We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.

Take a look at our frequently asked questions for PhD applicants.

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Find Graduate Programs in the Mathematical Sciences offers comparative information on graduate programs in the mathematical sciences for prospective graduate students and their advisers. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information. Currently 276 graduate programs are listed.

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Program type, masters programs (check all that apply), phd specialties (check all that apply), financial support available, gre required, online options available, skills training resources (check all that apply), number of phds awarded in the last year, enrollments, canadian province, list or edit your graduate program in the mathematical sciences.

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Find Graduate Programs Find the right graduate program in the mathematical sciences

Find Graduate Programs (FGP) in the Mathematical Sciences offers comparative information on over 500 graduate programs in the mathematical sciences in the US and Canada. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information. Currently 736 graduate programs are listed.

Bridge / Postbaccalaureate Programs

Masters Programs

Doctoral Programs

Certificate Programs

In the wake of the pandemic, many mathematical sciences departments have made at least short-term changes in their requirements regarding the GRE for individuals applying for admission to graduate programs. The Google doc USA/Canada Math PhD Programs: GRE requirements and Qualifying Exams , curated by Brown University graduate student Emily Winn, provides a list of those current requirements.

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:


Complex Analysis (MATH 220A-B-C)	Real Analysis (MATH 240A-B-C)
Algebra (MATH 200A-B-C)	Applied Algebra (MATH 202A-B-C)	Topology (MATH 290A-B-C)
Numerical Analysis (MATH 270A-B-C)	Statistics (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.

$after phd in mathematics what next$

9500 Gilman Drive, La Jolla, CA 92093-0112

(858) 534-3590

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.

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.

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

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

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

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

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

The pure math PhD admissions application is open. The application submission deadline is December 15, 2024.

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

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

Note for Harvard College Undergraduates

Since it is better for a student’s mathematical development to learn mathematics at different institutions so as to be exposed to a broader range of mathematical perspectives, ordinarily applications for the mathematics PhD program from Harvard College undergraduates are not considered. If exceptional circumstances warrant an application from a Harvard undergraduate, an advisor or mentor of that student should seek approval from the Director of Graduate Studies before the student submits an application.

$Graduate Students 2018-2019$

The department offers programs covering a broad range of topics leading to the Doctor of Philosophy and the Doctor of Science degrees (the student chooses which to receive; they are functionally equivalent). Candidates are admitted to either the Pure or Applied Mathematics programs but are free to pursue interests in both groups. Of the roughly 125 Ph.D. students, about 2/3 are in Pure Mathematics, 1/3 in Applied Mathematics.

The two programs in Pure and Applied Mathematics offer basic and advanced classes in analysis, algebra, geometry, Lie theory, logic, number theory, probability, statistics, topology, astrophysics, combinatorics, fluid dynamics, numerical analysis, mathematics of data, and the theory of computation. In addition, many mathematically-oriented courses are offered by other departments. Students in Applied Mathematics are especially encouraged to take courses in engineering and scientific subjects related to their research.

All students pursue research under the supervision of the faculty , and are encouraged to take advantage of the many seminars and colloquia at MIT and in the Boston area.

Degree Requirements

Degree requirements consist of:

Oral qualifying exam
Classroom teaching
Original thesis and defense

Prospective students are invited to consult the graduate career timeline for more information, and to read about the application procedure .

Graduate Co-Chairs

Graduate Student Issues, math graduate admissions

Jonathan Kelner , Davesh Maulik , and Zhiwei Yun

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» » 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
212-854-6729

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

PhD in Applied Mathematics

Phd in applied mathematics degree.

Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities. The program has focuses on understanding nature through the fusion of Artificial Intelligence, Computing (classical to quantum), and Mathematics. We value foundational contributions, societal impact, and ethics in our work. Our program uniquely interfaces with diverse fields, including physics, neuroscience, materials science, economics, biology and fluid mechanics, to tackle some of the most pressing challenges of our time, such as sustainability, responsible digital transformations, and health and well-being.

Working individually and as part of teams collaborating across the University and beyond, you will partner with faculty to quantitatively describe, predict, design and control phenomena in a range of fields. Projects current and past students have worked on include collaborations with mechanical engineers to uncover some of the fundamental properties of artificial muscle fibers for soft robotics and developing new ways to simulate tens of thousands of bubbles in foamy flows for industrial applications such as food and drug production.

Our core mission is to provide students with individualized programs tailored to their interests, needs, and background. We welcome students from diverse technical backgrounds. Our program is dedicated to the principles of diversity, equity, and inclusion. We celebrate and value differences among our members, and we strive to create an equitable and inclusive environment for people of all backgrounds.

APPLY NOW >

Applied Mathematics PhD Degree

Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics conferred through the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences . Doctoral students may earn the masters degree en route to the Ph.D. Prospective students apply through Harvard Griffin GSAS; in the online application, select “Engineering and Applied Sciences” as your program choice and select “PhD Applied Math” in the Area of Study menu.

The Applied Mathematics program does not offer an independent Masters Degree.

Applied Mathematics PhD Career Paths

Our graduates have gone on to careers such as start-up pioneers, social innovators, and a range of careers in industry in organizations like the Kingdom of Morocco, Meta, and Bloomberg. Others have secured faculty positions at Dartmouth, Imperial College in London, and UCLA. More generally, students with a PhD in Applied Mathematics can go on to careers in academia, banking, data science, bioinformatics, management consulting, government/military research, and more. Also, r ead about some of our Applied Mathematics alumni .

Admissions & Academic Requirements

Please review the admissions requirements and other information before applying. Our website also provides admissions guidance , program-specific requirements , and a PhD program academic timeline .

Academic Background

Applicants typically have bachelor’s degrees in the natural sciences, mathematics, computer science, or engineering.

Standardized Tests

GRE General: Not Accepted

Applied Mathematics Faculty & Research Areas

View a list of our Applied Mathematics faculty and applied mathematics affiliated research areas , Please note that faculty members listed as “Affiliates" or "Lecturers" cannot serve as the primary research advisor.

Applied Mathematics Centers & Initiatives

View a list of the research centers & initiatives at SEAS and the Applied Mathematics faculty engagement with these entities .

Graduate Student Clubs

Graduate student clubs and organizations bring students together to share topics of mutual interest. These clubs often serve as an important adjunct to course work by sponsoring social events and lectures. Graduate student clubs are supported by the Harvard Kenneth C. Griffin School of Arts and Sciences. Explore the list of active clubs and organizations .

Funding and Scholarship

Learn more about financial support for PhD students.

How to Apply

Learn more about how to apply or review frequently asked questions for prospective graduate students.

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
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 student stories
Undergraduate Student Stories

Graduate News

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Harvard SEAS student Susannah Su with a poster for her master's student capstone project

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Speeding up document analysis ahead of negotiations

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Harvard SEAS students Samantha Nahari, Rama Edlabadkar, Vlad Ivanchuk with a poster for their computational science and engineering capstone project

Master's student capstone spotlight: A Remote Sensing Framework for Rail Incident Situational Awareness Drones

Using drones to rapidly assess disaster sites

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A Guide to Postgraduate Maths

30 th January 2023

A mathematics student solving a problem on a whiteboard in a library

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Thinking about taking a degree in mathematics at the postgraduate level? Not sure where to start? Then you're in the right place – we have created this subject guide to mathematics to help students achieve their postgraduate education goals in the topic.

This subject offers up a wealth of fascinating areas or study as well as a variety of job opportunities for sucessful graduates. The skills developed on these courses can also be used in a wide range of industries and sectors, making it a value degree to pursue.

Read on to find out more about postgraduate mathematics programmes, the opportunities the degree can offer and how you can expect to be taught on a course.

Why do a mathematics degree?
What qualifications can you get?
What jobs can you do with a mathematics degree?
What are the mathematics degree entry requirements?
What mathematics courses are there?
What topics does a mathematics degree cover?
How will you be taught and assessed?
How long is a mathematics degree?
Where can you study mathematics?
What similar subjects are there to mathematics?

Why do a mathematics degree?

Mathematics is a highly popular subject for postgraduate study, as it has a lot of scope for development and offers to build knowledge that will be relevant to a wide variety of sectors for decades to come.

Alongside the mathematical intelligence that the course will develop, you’ll strengthen a host of other skills during a mathematics degree. You’ll learn how to be more analytical and interpret difficult data, which will improve your decision making and problem-solving skills. Time management, organisation, communication and teamwork competency will also play a part.

The combination of transferable skills and mathematical expertise will make you an attractive prospect for companies looking to hire proficient employees in related and unrelated careers.

What qualifications can you get?

There are a variety of qualifications that students can get in mathematics, depending on previous experience in the subject and the desired career route they are looking to take.

Students wanting to take a traditional style of course will be to get a taught master’s degree in mathematics. These can cover a general selection of topics within the subject or can be more specific on certain topics if a student has a particular interest in data science or statistics, for example. These courses are mostly MSc degrees, though some MA degrees are available.

Research-based degrees are also available for mathematics, including Mres, PhD and doctorate programmes. These will offer students the chance to make developments in their chosen field and operate with a stronger sense of independence compared to other qualifications.

Students looking to quickly gain knowledge and experience in mathematics should look to take a PGDip or PGCert, as these courses are much shorter than others.

What jobs can you do with a mathematics degree?

Mathematics graduates are highly valued in a number of industries. Many students go on to work in the financial sector, taking advantage of their skill and understanding of numbers and data. Graduates from PhD courses could use their expertise to aim for a career in scientific research. A host of IT companies are always looking for accomplished mathematicians to help develop the latest technology.

There is also the option for students to help create the next generation of mathematics specialists by becoming a teacher. There are many incentives available for primary and secondary school mathematics teachers, which can make it an attractive opportunity.

What are the mathematics degree entry requirements?

Although the requirements change based on the university and the type of course you want to do, ideally you need some sort of mathematical background to do join a mathematics postgraduate programme. This could include qualifications in subjects like physics, engineering or computer science. It’s likely that you’ll need a 2:1 degree to get a place on a mathematics master’s or PhD course in a related field.

What mathematics courses are there?

When looking for a mathematics degree, you will find there are several different types of course you can take. These can range from generic mathematics programmes to ones that focus on particular areas of the field. Here are a few examples of the courses you could take...

Mathematics MSc
MSc Applied Mathematical Sciences
Mathematical Trading and Finance MSc
Mathematical Modelling (Fluid Dynamics) MSc
Data Analytics MSc

What topics does a mathematics degree cover?

The topics covered on a mathematics postgraduate degree can vary from university to university. To give you an idea of what you could be study, take a look at these modules below...

Mathematical Ecology
Statistical Modelling in Space and Time
Stochastic Calculus and Pricing Derivatives
Partial Differential Equations
Quantitative Data Analysis

How will you be taught and assessed?

Many mathematics postgraduate courses will rely on lectures and coursework to help develop skills and knowledge in the subject. Students can also expect to do their own research into different areas of mathematics, particularly those doing a PhD or doctorate. Some courses will feature placements in different industries to help students get an idea for how their work can be applied across sectors and in businesses. Assessments can take the form of coursework, examinations and dissertations.

How long is a mathematics degree?

The length of a mathematics degree will vary depending on the qualification it awards as well as whether it’s being studied full-time or part-time. Master’s degrees can take one or two years, while PhDs can take four or more years. If studied part-time, it is likely to take double the amount of time to complete the course.

Where can you study mathematics?

Mathematics is a popular subject at the postgraduate level, so there are many universities which offer courses in it. To browse all the available universities and courses, please use our handy University Search tool or Course Search tool.

What similar subjects are there to mathematics?

If mathematics isn’t quite the right subject for you, but you’d still like to study in the same sort of area, take a look at these subjects instead...

Finance
Physics
Computer Science
Engineering
Accountancy

Next: Search for mathematics courses

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Applied statistics msc, birkbeck, university of london, mathematics msc, northumbria university, newcastle, mres mathematical sciences, nottingham trent university, computing and mathematical sciences, msc by research, university of greenwich, computer science phd, mphil - algebraic and categorical structures and methods, university of leicester, your next steps.

Doctor of Philosophy in Mathematics (PhD)
Graduate School
Prospective Students
Graduate Degree Programs

Go to programs search

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics. The PhD program trains students to operate as research mathematicians. The focus of the program is on substantial mathematical research leading to the PhD dissertation. Students also develop their skills in presenting and teaching mathematics and its applications.

For specific program requirements, please refer to the departmental program website

What makes the program unique?

UBC has one of the largest and most vigorous departments of mathematics in Canada. Our faculty routinely win national and international awards for their research and teaching achievements. We have an engaged and sociable cohort of graduate students who are essential members of a broad selection of active research groups. Each group holds a variety of seminars and events that allow graduate students, postdoctoral fellows, visitors and faculty to enjoy regular interaction.

UBC is the headquarters for the Pacific Institute of Mathematical Sciences (PIMS). PIMS hosts a plethora of mathematical events such as conferences and summer schools, greatly enriching the scientific environment in the quantitative sciences at UBC. Our mathematics students are also regular participants at the nearby Banff International Research Station for Mathematical Innovation and Discovery. Finally, our Institute for Applied Mathematics provides options for interdisciplinary studies for PhD students who wish to work in applied and computational mathematics.

UBC's math program has a high reputation and there are many renowned professors in the department. This was a selling point of the UBC math graduate program for me.

Pardis Semnani

Quick Facts

Program enquiries, admission information & requirements, 1) check eligibility, minimum academic requirements.

The Faculty of Graduate and Postdoctoral Studies establishes the minimum admission requirements common to all applicants, usually a minimum overall average in the B+ range (76% at UBC). The graduate program that you are applying to may have additional requirements. Please review the specific requirements for applicants with credentials from institutions in:

Canada or the United States
International countries other than the United States

Each program may set higher academic minimum requirements. Please review the program website carefully to understand the program requirements. Meeting the minimum requirements does not guarantee admission as it is a competitive process.

English Language Test

Applicants from a university outside Canada in which English is not the primary language of instruction must provide results of an English language proficiency examination as part of their application. Tests must have been taken within the last 24 months at the time of submission of your application.

Minimum requirements for the two most common English language proficiency tests to apply to this program are listed below:

TOEFL: Test of English as a Foreign Language - internet-based

Overall score requirement : 100

IELTS: International English Language Testing System

Overall score requirement : 7.0

Other Test Scores

Some programs require additional test scores such as the Graduate Record Examination (GRE) or the Graduate Management Test (GMAT). The requirements for this program are:

The GRE is not required.

2) Meet Deadlines

3) prepare application, transcripts.

All applicants have to submit transcripts from all past post-secondary study. Document submission requirements depend on whether your institution of study is within Canada or outside of Canada.

Letters of Reference

A minimum of three references are required for application to graduate programs at UBC. References should be requested from individuals who are prepared to provide a report on your academic ability and qualifications.

Statement of Interest

Many programs require a statement of interest , sometimes called a "statement of intent", "description of research interests" or something similar.

Supervision

Students in research-based programs usually require a faculty member to function as their thesis supervisor. Please follow the instructions provided by each program whether applicants should contact faculty members.

Instructions regarding thesis supervisor contact for Doctor of Philosophy in Mathematics (PhD)

Citizenship verification.

Permanent Residents of Canada must provide a clear photocopy of both sides of the Permanent Resident card.

4) Apply Online

All applicants must complete an online application form and pay the application fee to be considered for admission to UBC.

Tuition & Financial Support

Fees	Canadian Citizen / Permanent Resident / Refugee / Diplomat	International
	$114.00	$168.25
Tuition *
Installments per year	3	3
Tuition	$1,838.57	$3,230.06
Tuition (plus annual increase, usually 2%-5%)	$5,515.71	$9,690.18
Int. Tuition Award (ITA) per year ( )		$3,200.00 (-)
Other Fees and Costs
(yearly)	$1,116.60 (approx.)
	Estimate your with our interactive tool in order to start developing a financial plan for your graduate studies.

Financial Support

Applicants to UBC have access to a variety of funding options, including merit-based (i.e. based on your academic performance) and need-based (i.e. based on your financial situation) opportunities.

Program Funding Packages

All full-time students who begin a UBC-Vancouver PhD Mathematics program in September 2018 or later will be provided with a funding package of at least $24,256 for each of the first four years of their PhD. The funding package may consist of any combination of internal or external awards, teaching-related work, research assistantships, and graduate academic assistantships.

Average Funding

52 students received Teaching Assistantships. Average TA funding based on 52 students was $13,784.
48 students received Research Assistantships. Average RA funding based on 48 students was $11,580.
3 students received Academic Assistantships. Average AA funding based on 3 students was $1,814.
54 students received internal awards. Average internal award funding based on 54 students was $13,279.
4 students received external awards. Average external award funding based on 4 students was $27,083.

Scholarships & awards (merit-based funding)

All applicants are encouraged to review the awards listing to identify potential opportunities to fund their graduate education. The database lists merit-based scholarships and awards and allows for filtering by various criteria, such as domestic vs. international or degree level.

Graduate Research Assistantships (GRA)

Many professors are able to provide Research Assistantships (GRA) from their research grants to support full-time graduate students studying under their supervision. The duties constitute part of the student's graduate degree requirements. A Graduate Research Assistantship is considered a form of fellowship for a period of graduate study and is therefore not covered by a collective agreement. Stipends vary widely, and are dependent on the field of study and the type of research grant from which the assistantship is being funded.

Graduate Teaching Assistantships (GTA)

Graduate programs may have Teaching Assistantships available for registered full-time graduate students. Full teaching assistantships involve 12 hours work per week in preparation, lecturing, or laboratory instruction although many graduate programs offer partial TA appointments at less than 12 hours per week. Teaching assistantship rates are set by collective bargaining between the University and the Teaching Assistants' Union .

Graduate Academic Assistantships (GAA)

Academic Assistantships are employment opportunities to perform work that is relevant to the university or to an individual faculty member, but not to support the student’s graduate research and thesis. Wages are considered regular earnings and when paid monthly, include vacation pay.

Financial aid (need-based funding)

Canadian and US applicants may qualify for governmental loans to finance their studies. Please review eligibility and types of loans .

All students may be able to access private sector or bank loans.

Foreign government scholarships

Many foreign governments provide support to their citizens in pursuing education abroad. International applicants should check the various governmental resources in their home country, such as the Department of Education, for available scholarships.

Working while studying

The possibility to pursue work to supplement income may depend on the demands the program has on students. It should be carefully weighed if work leads to prolonged program durations or whether work placements can be meaningfully embedded into a program.

International students enrolled as full-time students with a valid study permit can work on campus for unlimited hours and work off-campus for no more than 20 hours a week.

A good starting point to explore student jobs is the UBC Work Learn program or a Co-Op placement .

Tax credits and RRSP withdrawals

Students with taxable income in Canada may be able to claim federal or provincial tax credits.

Canadian residents with RRSP accounts may be able to use the Lifelong Learning Plan (LLP) which allows students to withdraw amounts from their registered retirement savings plan (RRSPs) to finance full-time training or education for themselves or their partner.

Please review Filing taxes in Canada on the student services website for more information.

Cost Estimator

Applicants have access to the cost estimator to develop a financial plan that takes into account various income sources and expenses.

Career Outcomes

88 students graduated between 2005 and 2013: 1 is in a non-salaried situation; for 19 we have no data (based on research conducted between Feb-May 2016). For the remaining 68 graduates:

$after phd in mathematics what next$

Sample Employers in Higher Education

Sample employers outside higher education, sample job titles outside higher education, phd career outcome survey, career options.

A great majority of our PhD graduates move on to postdoctoral fellowships and faculty positions at universities and research institutes in North America and around the world. However, a significant fraction of students move into careers in industry. Students considering non-academic careers are encouraged to complete an industrial internship (for instance through the Mitacs Accelerate program - headquartered at UBC) during their studies.

Enrolment, Duration & Other Stats

These statistics show data for the Doctor of Philosophy in Mathematics (PhD). Data are separated for each degree program combination. You may view data for other degree options in the respective program profile.

ENROLMENT DATA

	2023	2022	2021	2020	2019
Applications	155	167	176	176	114
Offers	30	21	27	29	22
New Registrations	12	11	17	13	17
Total Enrolment	72	68	64	65	72

Completion Rates & Times

Upcoming doctoral exams, tuesday, 17 september 2024 - 2:00pm - room 203.

Research Supervisors

Advice and insights from UBC Faculty on reaching out to supervisors

These videos contain some general advice from faculty across UBC on finding and reaching out to a supervisor. They are not program specific.

This list shows faculty members with full supervisory privileges who are affiliated with this program. It is not a comprehensive list of all potential supervisors as faculty from other programs or faculty members without full supervisory privileges can request approvals to supervise graduate students in this program.

Adem, Alejandro (Cohomology of finite groups, orbifolds, stringy topology, algebra, sporadic simple group, group actions, arithmetic groups, K-theory, homotopy theory, spaces of homomorphisms)
Alacaoglu, Ahmet
Angel, Omer (Probability theory, percolation, random graphs, random walks, particle processes, scaling limits)
Bachmann, Sven (Mathematics and statistics; Mathematical Analysis; quantum phenomena; Mathematical physics; Quantum statistical physics; Topological states of matter)
Balmforth, Neil (Fluid mechanics, nonlinear dynamics and applied partial differential equations)
Behrend, Kai (Moduli spaces, Gromov-Witten invariants, string theory, Donaldson-Thomas invariants, Euler characteristics, categorification)
Bennett, Michael (Number Theory, Diophantine Approximation and Classical Analysis)
Bryan, Jim (Algebraic and differential geometry; Algebraic geometry, moduli spaces, enumerative invariants related to theoretical physics.)
Cautis, Sabin (Mathematics and statistics; Geometry)
Chau, Albert (Differential Geometry and Partial Differential Equations)
Chen, Jingyi (Algebraic and differential geometry; Differential Geometry, Partial Differential Equations)
Colliander, James (hamiltonian dynamical systems; partial differential equations; harmonic analysis)
Coombs, Daniel (Mathematical biology; Cellular immunology; Complex physical systems; Epidemiology (except nutritional and veterinary epidemiology); Cell Signaling and Infectious and Immune Diseases; Cell biophysics; Disease models; Epidemiology; Immune cell signalling; Mathematics)
Cytrynbaum, Eric (Bacterial cell division, Microtubule and cellular organization, Wave propagation in excitable media)
Dao Duc, Khanh (Genomics; Mathematical biology; Neurocognitive patterns and neural networks; Agricultural spatial analysis and modelling; combine mathematical,computational and statistical tools to study fundamental biological processes; regulation and determinants of gene expression and translation; Machine Learning for Biological Imaging and Microscopy; Database development and management; Biological and Artificial Neural Networks for geometric representation)
Doebeli, Michael Walter (Mathematical ecology and evolution, evolution of diversity, adaptive speciation, evolution of cooperation, game theory, experimental evolution in microorganisms)
Feng, James (Chemical engineering; Mathematics and statistics; Biophysics; Complex fluids; Fluid mechanics; Mathematical biology)
Fraser, Ailana (Differential Geometry, Geometric Analysis)
Friedlander, Michael (numerical optimization, numerical linear algebra, scientific computing, Scientific computing)
Frigaard, Ian (Fluid mechanics (visco-plastic fluids))
Ghioca, Dragos (Drinfeld modules, isotrivial semiabelian varieties, Lehmer inequality)
Gordon, Julia Yulia (Representation theory of p-adic groups and motivic integration; Trace Formula and its applications)
Gustafson, Stephen James (Mathematics and statistics; Mathematical Analysis; Differential Equation; Global and Non-Linear Analysis; Mathematical physics; Nonlinear partial differential equations; Nonlinear waves; Topological solitons)
Hauert, Christoph (Mathematics and statistics; Modelization and Simulation; Evolution and Phylogenesis; Biological Behavior; dynamical systems; evolution; game theory; social dilemmas; stochastic processes)
Hermon, Jonathan (probability theory; Markov chains and the cutoff phenomenon; particle systems; percolation)

Doctoral Citations

Year	Citation
2024	Dr. Oliveira studied a new class of surfaces of interest to researchers in different areas of mathematics and provided many previously unknown examples. His research contributes to an understanding of the deeper relationships between seemingly separate subjects.
2024	Dr. Gheorghiu has made a contribution to algebra. One of the simplest algebraic structures are groups. Cohomology is an algebraic tool that can discern geometric objects by looking at their "holes". Then group cohomology is a tool that can discern different groups. Dr. Gheorghiu has developed a generalization of a specific form of group cohomology.
2024	Dr. Hamidi studied elliptic curves over quadratic imaginary fields. Using a new and robust technique, Dr. Hamidi proved significant results about the vanishing and bounding of certain invariants. His results could have applications in number theory, cryptography, and other areas of mathematics.
2024	Dr. Bajpai made theoretical and algorithmic contributions to the study of integer solutions to polynomial equations. He developed methods to resolve several new families of such equations, and applied these methods to prove novel results on approximations to complex numbers.
2023	Dr. Huet developed numerical tools that allow fast and accurate simulations of complex fluid systems, ranging from rockfall dynamics to cell-resolved biological flows. His open-source software contributions can be used to better design microfluidic cell-sorting devices, thus speeding up many labour intensive tasks in biotechnology research.
2023	Dr. Zhang developed the gluing method to construct the bubble tower of the ancient solutions and infinite time blow-up solutions for the critical heat equations, and finite time blow-up solutions simultaneously at any prescribed N points for the Landau-Lifshitz-Gilbert equation.
2023	Dr. Jana rigorously investigated algebraic invariants of two spaces: Classifying space for commutativity and Unordered flag manifolds. Their research explored algebraic topology, employing algebraic methods to analyze shapes. The core of the research lies in the pursuit of simplification through decomposition, marking its fundamental significance.
2023	Dr. Michta studied how phase transitions occur in finite volume for some classical models from statistical physics. This work contributes to a better and rigorous understanding of finite-size scaling theory in high dimensions. This is useful to the wide spectrum of people working at the interface between physics and mathematics.
2023	Counting sums and differences between sets is a central part of many questions in additive combinatorics. Dr. White developed a new technique combining harmonic analysis and optimization to nearly resolve a longstanding question in this field. He expects that his new method can be extended to other problems in additive combinatorics.
2023	Dr. Lawrence unified elements from reinforcement learning and control theory to solve industrially relevant problems. His framework enables learning stable control policies directly from data. This ensures that maintaining controllers in an industrial setting is efficient, safe, and automated.

Sample Thesis Submissions

Set-restricted isometry for sub-Gaussian matrices and inversion of deep generative models
On problems of regularity and existence for critical drift elliptic equations and Navier-Stokes equations
Symmetry-breaking bifurcations in compartmental-reaction diffusion systems with comparable diffusivities
The polynomial method over finite rings and fields
Global well-posedness and localized patterns of several reaction-diffusion systems involving advection
Topics in arithmetic combinatorics
Free boundary minimal submanifolds in geodesic balls of simply connected space forms
On a completion of cohomological functors generalizing Tate cohomology
Distribution of integral points on varieties
Effective and explicit S-unit equations with many terms
Classifying space for commutativity and unordered flag manifolds
Finite-size scaling of a few statistical physics models in high dimensions
Residual supersingular Iwasawa theory and μ-invariants for Zₚ²-extensions
Numerical methods for biological flows laden with deformable capsules and solid particles
The construction of blow-up solutions for some evolution equations

Related Programs

Same specialization.

Master of Science in Mathematics (MSc)

At the UBC Okanagan Campus

Further information, specialization.

UBC Calendar

Program website, faculty overview, academic unit, program identifier, classification, social media channels, supervisor search.

Departments/Programs may update graduate degree program details through the Faculty & Staff portal. To update contact details for application inquiries, please use this form .

Nicholas Richardson

Having grown up outside of Toronto and completed my undergrad and master's degree at the University of Waterloo, I was ready to change the scenery and go study somewhere else. I joke that is it the farthest I could move without leaving Canada, but more truthfully it was the campus that felt "right...

Gabriel Currier

I quite like the kind of math that people do here, and enjoy working with my supervisors. The campus is also a beautiful place and the graduate student community is pretty laid back and friendly.

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Many factors contributed to my choice of UBC for graduate school. I was attracted to Vancouver’s geographical similarities to Portland in the pacific northwest. Also, I have family in the area. However, most importantly, I was intrigued and inspired by my professors and advisors to take on the...

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Department of Mathematics

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 ;
Be in residence for at least three years;
Complete a dissertation that clearly advances understanding of the subject it considers.

All students must also complete any other Graduate School of Arts and Sciences degree requirements as they appear in the Programs and Policies bulletin.

The normal time for completion of the Ph.D. program is five to six years. Requirement (1) normally includes basic courses in algebra, analysis, and topology. Students typically complete the eight-course requirement by the end of their third year. The Honors grades of (1) must be achieved within the first two years. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term. All qualifying examinations must be passed by the end of the second year. There is no limit to the number of times that students can take the exams, and so they are encouraged to take them as soon as possible.

The dissertation prospectus should be submitted during the third year.

The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)–(5) and obtaining an adviser.

In addition to all other requirements, students must successfully complete MATH 991a, Ethical Conduct of Research, prior to the end of their first year of study. This requirement must be met prior to registering for a second year of study.

Master’s Degrees :

The M.Phil. and M.S. degrees are conferred only en route to the Ph.D.; there is no separate master’s program in Mathematics.

M.Phil. Please refer to the Graduate School Degree Requirements

M.S. A student must complete six term courses with at least one Honors grade, perform adequately on the general qualifying examination, and be in residence at least one year.

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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

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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.

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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

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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

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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.

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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

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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
Actuary
Economist
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

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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.

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Ph.D. (Mathematics)

Career Options after a Doctorate Degree in Mathematics

Employment Outlook for Ph.D. Holders?

Ph.D. Holders in mathematics are mainly catering to the education industry and due to the laws of UGC one position of Head of Department is always secured for Ph.D. holders only. As the UGC States that to conduct PG classes in Mathematics every university needs to hire a HOD who compulsorily needs to be doctorate.

Employment of Mathematician in India is prospected to grow by 23% as the surging demand of knowledge and expertise in private sector analytics firm. Although the population is less average number of new jobs being generated every year is 3000 in the period of five years.

Students Getting Ph.D. from Low and Middle range Colleges: Employment numbers for the students graduating from middle range colleges may feel crunch in getting a job but private sector can offer them better pay and opportunities. Package can also increase if they add advance computing skills and statistical tools in their profile.

Job Title	No of Employment 2014	No of Employment 2020	Change 2014-2022
Job Title	No of Employment 2014	No of Employment 2020	Percent	Numeric
Scientist	5000	8000	60	3000
Consultant	3500	6300	80	2800
Professor	1200	2800	103	1600
Top Recruiters	Amazon	McKinsey	Goldman Sachs	Universities and Colleges

As the amount of data stored digitally is increasing the next decade and analysis will help companies improve their business process, design and develop new products and even target potential customers. The next decade is more lucrative for upcoming mathematics wizards

Fields to Work after Ph.D. Maths?

I.Expand Knowledge of Mathematics in Several areas with further research in private or government scientific and engineering Research Institutions like Tata Innovation Foundation

II.Becoming Professor or an Associate Professor in Leading Educational Institutions

III.Joining a Big Manufacturing or KPO to apply Mathematical models in increasing output and profitability

IV.Opening their own consulting firm or join government agencies as a consultant

Ph.D. Mathematics: Salary Trends

How Much a Doctorate Holders in Mathematics get paid?

The Indian market is quite welcoming for the Mathematicians, the median salary of a Doctorate holder in India is 8.14 Lacs. Median Package means that half of the Ph.D. holders have get more than 8.14 lacs and another half have get less than 8.14 lacs.

The least 10 percent have got average package of 3.5 LPA and Highest 10 percent have got 30 LPA. Private Industry always offers better pay than government agencies as the job opportunities is equal in both the sectors.

Field of Work	% Employed	Average Package
Private and Government Educational Institutions	47	16.5 LPA
Government and Private Research Labs	12	10 LPA
Manufacturing Firms	8-10	9 LPA
Consulting and Management Companies	5-6	14 LPA
Government Agencies (Ex. NSSO)	4-5	20 LPA

Ph.D. (Chemistry)

Ph.d. (physics), ph.d. (biotechnology), ph.d. (zoology), ph.d. (botany), ph.d. (english), master of science [ms], master of science [m.sc] (biotechnology), ph.d. (mathematics) colleges in india.

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COMMENTS

A Discussion on Opportunities for Math PhDs : r/math
A Discussion on Opportunities for Math PhDs. Gone are the days of the mid 1900s, where fresh PhD graduates could reasonably expect to land a couple postdocs and then get a tenure track positions, or easily pivot to industry with handsome compensation. According to the AMS, 860 Math PhDs were awarded in 1982, but 2017 saw 1,957 Math PhDs awarded.
PhD in Mathematics
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: Situation. Typical Fee (Median) Fee Range.
Is a PhD in mathematics worth it? : r/math
Revlong57. •. Honestly, if you're looking at doing a PhD in applied math, it will probably have value in a future career outside of academia. Pure math is basically only useful for academic jobs. Now, let's look at the pros and cons of getting a PhD in applied math. Source, I'm getting a PhD in an applied math area.
Guide To Graduate Study
Guide to Graduate Studies. 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 one's own way.
What are the career options after PhD in mathematics?
What are the career options after PhD in mathematics? Interested students in mathematics subject can pursue the highest degree in the field. Doctorate In Mathematics can provide students lucrative career options. If students have a talent for numbers, they can get the chance to use their degrees in a variety of ways after graduation.
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 ...
Research Programmes
The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes. Select a course below to visit the University's Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines. 12 months full-time, or 2 years part-time.
AMS :: Find Graduate Programs
Edit existing listing. Find Graduate Programs (FGP) in the Mathematical Sciences offers comparative information on over 500 graduate programs in the mathematical sciences in the US and Canada. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information.
PDF Graduate Schools and Fellowships in Mathematics
Unlike what many people think, you don't need to pay to go to graduate school in mathematics. Grad students are usually paid (albeit not much) to study. There are several ways post-graduate education in mathematics is financed. National Fellowships A few students are able to win national fellowships. The national fellowships are awarded by
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.
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 ...
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 ...
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 ...
Harvard Mathematics Department Graduate Information
The pure math PhD admissions application is open. The application submission deadline is December 15, 2024. For information on admissions and financial support, please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.. Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. . Applicants can determine eligibility for ...
Graduate
Graduate. Graduate Students 2018-2019. The department offers programs covering a broad range of topics leading to the Doctor of Philosophy and the Doctor of Science degrees (the student chooses which to receive; they are functionally equivalent). Candidates are admitted to either the Pure or Applied Mathematics programs but are free to pursue ...
Department of Mathematics at Columbia University
Office of Student Affairs. 107 Low Library, MC 4304. New York, NY 10027. 212-854-6729. [email protected]. For information on the department and program: Michael Harris. Director of Graduate Studies. Department of Mathematics.
PhD in Applied Mathematics
PhD in Applied Mathematics Degree. Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities.
A Guide to Postgraduate Maths
Mathematics is a highly popular subject for postgraduate study, as it has a lot of scope for development and offers to build knowledge that will be relevant to a wide variety of sectors for decades to come. Alongside the mathematical intelligence that the course will develop, you'll strengthen a host of other skills during a mathematics degree.
Doctor of Philosophy in Mathematics (PhD)
Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics. The PhD program trains students to operate as research mathematicians. The focus of the program is on substantial mathematical research leading to the PhD dissertation ...
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;
Best PhDs 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.
Ph.D. (Mathematics)
The Indian market is quite welcoming for the Mathematicians, the median salary of a Doctorate holder in India is 8.14 Lacs. Median Package means that half of the Ph.D. holders have get more than 8.14 lacs and another half have get less than 8.14 lacs. The least 10 percent have got average package of 3.5 LPA and Highest 10 percent have got 30 LPA.
Graduate programs
Major: Mathematics. Charles E. Schmidt College of Science Degree: Doctor of Philosophy (Ph.D.) Research Areas: Pure and Applied Mathematics. Important information about applying to Graduate School: Official Transcripts: Official Transcripts and/or Official Foreign Credential Evaluations must be received from each college or university attended.
Introducing OpenAI o1
In our tests, the next model update performs similarly to PhD students on challenging benchmark tasks in physics, chemistry, and biology. We also found that it excels in math and coding. In a qualifying exam for the International Mathematics Olympiad (IMO), GPT-4o correctly solved only 13% of problems, while the reasoning model scored 83%.