The Department of Mathematics does not discriminate against applicants or students on the basis of race, color, national origin, ancestry or any other protected classification.
Preparing the Application The statement of purpose for graduate applications is carefully weighted by the admissions committee. The applicant’s statement should convince the committee that they are able to communicate effectively and with a deep understanding of mathematics. It is not intended to be a biographical sketch or a reflection on one’s decision to enter the field.
Three letters of recommendation are required. Letter writers should be faculty or others qualified to evaluate the applicant’s potential for graduate study in mathematics. The letters must be submitted online and by the application deadline.
Applicants should include any research papers, publications, and other original works they would like to have evaluated by the admissions committee.
The department requests that applicants submit GRE Mathematics Subject Test scores if practical. Applicants should check on the ETS website for test dates in their area to ensure the scores will be submitted before the application deadline. An official score report should be sent to Harvard Kenneth C. Griffin Graduate School of Arts and Sciences using code 3451.
While the admissions committee reviews all applications submitted before the deadline, missing math subject test scores provide one less data point available to evaluate the application. Depending on the strength of the application, the missing subject test scores may put the application at a disadvantage.
Applicants who are non-native English speakers and who do not hold an undergraduate degree from an institution at which English is the primary language of instruction must submit scores from the Internet Based Test (IBT) of the Test of English as a Foreign Language (TOEFL) or the International English Language Testing System (IELTS) Academic test.
Harvard Griffin GSAS requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.
Ph.D. Program in Pure Mathematics The department does not grant a terminal Master’s degree, but the Master’s can be obtained “on the way” to the Ph.D. by fulfilling certain course and language exam requirements.
In general, there is no transfer status application to the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences or to the Department of Mathematics. No formal credit is given for an MSc or MA earned elsewhere. All applicants are considered to be applying as first-year graduate students. The only difference Master’s study may make is to better prepare students for the Qualifying Exam.
All graduate students are admitted to begin their studies in the fall term. The department plans on an entering class of about twelve students. Since the admissions committee receives a few hundred applications, the competition is keen.
Funding Graduate Study Applicants are urged to apply for all funding available to them. If no outside funding is available to the applicant, financial aid in the form of scholarships, research assistantships, and teaching fellowships is available. In general, students who do not have outside support will get scholarship support in their first year, but students are required to act as a teaching fellow for one-half course (i.e. for a one-term course) in their second through fifth years.
The department strongly recommends applicants to seek out and apply for all sources of financing available to them for graduate study. Recommended sources for funding US graduate students are NSF Graduate Fellowships and NDSEG Fellowships . Applicants from the UK are urged to also apply for the Kennedy fellowships and applicants from UK, New Zealand, Canada and Australia for Knox fellowships . International students may apply for the Fullbright IIE or any home country fellowships available for study abroad.
Harvard John A. Paulson School of Engineering and Applied Sciences The Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) offers programs for both the Master’s degree and the Ph.D. degree in Applied Mathematics. Please visit the SEAS website for more information on degrees in applied mathematics at www.seas.harvard.edu
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:
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:
What you do day-to-day will largely depend on your specific research topic. However, you’ll likely:
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.
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 ).
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.
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.
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.
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 .
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.
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:
As mentioned above, there’s a high demand for skilled mathematicians and statisticians across a broad range of sectors. Some typical employers are:
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.
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
Actuary or Finance
Aerospace or Mechanical Engineering
Data Analyst
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.
The below chart provides useful insight into the destination of Math PostDocs after completing their PhD. The most popular career paths from other of highest to lowest is education, information and communication, finance and scientific research, manufacturing and government.
Note: The above chart is based on ‘UK Higher Education Leavers’ data [2] between 2012/13 and 2016/17 and contains a data size of 200 PostDocs. The data was obtained from the Higher Education Statistics Agency ( HESA ).
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 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 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.
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.
[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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The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.
The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .
Admissions information can be found on the BU Arts and Sciences PhD Admissions website .
Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.
Please reach out to us directly at [email protected] if you have further questions.
Description.
The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of interests of the faculty . The department has outstanding groups in the areas of algebra, algebraic geometry, analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of applied mathematics , computer science , operations research , and statistics .
A normal course load for a beginning graduate student is three courses per term.
There are no qualifying exams, but the program requires that all students pass four courses to be selected from the six core courses. First-year students are allowed to place out of some (possibly, all) of the core courses. In order to place out of a course, students should contact the faculty member who is teaching the course during the current academic year, and that faculty member will make a decision. The minimum passing grade for the core courses is B-; no grade is assigned for placing out of a core course.
At least two core courses should be taken (or placed out) by the end of the first year. At least four core courses should be taken (or placed out) by the end of the second year (cumulative). These time requirements can be waived for students with health problems or other significant non-academic problems. They can be also waived for students who take time-consuming courses in another area (for example, CS) and who have strong support from a faculty; requests from such students should be made before the beginning of the spring semester.
The core courses are distributed among three main areas: analysis, algebra and topology/geometry. A student must pass at least one course from each group. All entering graduate students are encouraged to eventually take all six core courses with the option of an S/U grade for two of them.
MATH 6110, Real Analysis
MATH 6120, Complex Analysis
MATH 6310, Algebra 1
MATH 6320, Algebra 2
MATH 6510, Introductory Algebraic Topology
MATH 6520, Differentiable Manifolds.
Students who are not ready to take some of the core courses may take MATH 4130-4140, Introduction to Analysis, and/or MATH 4330-4340, Introduction to Algebra, which are the honors versions of our core undergraduate courses.
The "What Is...?" Seminar is a series of talks given by faculty in the graduate field of Mathematics. Speakers are selected by an organizing committee of graduate students. The goal of the seminar is to aid students in finding advisors.
Schedule for the "What Is...?" seminar
The Cornell Graduate School requires that every student selects a special committee (in particular, a thesis adviser, who is the chair or the committee) by the end of the third semester.
The emphasis in the Graduate School at Cornell is on individualized instruction and training for independent investigation. There are very few formal requirements and each student develops a program in conjunction with his or her special committee, which consists of three faculty members, some of which may be chosen from outside the field of mathematics.
Entering students are not assigned special committees. Such students may contact any of the members on the Advising Committee if they have questions or need advice.
Analysis / Probability / Dynamical Systems / Logic: Lionel Levine Geometry / Topology / Combinatorics: Kathryn Mann Probability / Statistics: Philippe Sosoe Applied Mathematics Liaison: Richard Rand
To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.
The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and his/her special committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the core graduate courses.
To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the special committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes five to six years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.
The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the special committee. By the time of the oral admission to candidacy examination, the candidate should have selected as chairperson of the committee the faculty member who will supervise the research. When the thesis is completed, the student presents his/her results at the thesis defense or B Exam. All doctoral students take a Final Examination (the B Exam, which is the oral defense of the dissertation) upon completion of all requirements for the degree, no earlier than one month before completion of the minimum registration requirement.
Ph.D. students in the field of mathematics may earn a Special Master's of Science in Computer Science. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for this degree, the student must have a member representing the minor field on the special committee and pass the A-exam in the major field. The rules and the specific requirements for each master's program are explained on the referenced page.
Cornell will award at most one master's degree to any student. In particular, a student awarded a master's degree in a minor field will not be eligible for a master's degree in the major field.
Funding commitments made at the time of admission to the Ph.D. program are typically for a period of five years. Support in the sixth year is available by application, as needed. Support in the seventh year is only available by request from an advisor, and dependent on the availability of teaching lines. Following a policy from the Cornell Graduate School, students who require more than seven years to complete their degree shall not be funded as teaching assistants after the 14th semester.
Students who have special requests should first discuss them with their Ph.D. advisor (or with a field member with whom they work, if they don't have an advisor yet). If the advisor (or field faculty) supports the request, then it should be sent to the Director of Graduate Studies.
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The Department of Mathematics at the University of Chicago. 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.
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.
The PhD Program The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics.
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.
Degree Requirements. A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements.. NYU Shanghai Ph.D. Track. The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai.
News. Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences. Learn more about Harvard's Math community and our statement on diversity and inclusion.. The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.
For specific information on the Applied Mathematics PhD program, see the navigation links to the right. What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the Graduate Policies pages.
To apply for admissions and financial aid, or for additional information on admissions requirements for the Ph.D. program in pure mathematics, please go to the appropriate Harvard Kenneth C. Griffin Graduate School of Arts and Sciences website listed below.
Note: The above tuition fees are based on 12 UK Universities [1] for 2020/21 Mathematic PhD positions. The typical fee has been taken as the median value. In addition to the above, it's not unheard of for research students to be charged a bench fee.
The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin.. Courses: The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here.Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above.
The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete.
website creator . Program of Study. The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy. The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government.
Ranked in 2023, part of Best Science Schools. A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to discrete mathematics and ...
Course Requirements Mathematics PhD candidates must show satisfactory work in Algebra (110.601-602), Real Variables (110.605), Complex Variables (110.607), and one additional non-seminar mathematics graduate course in their first year. The first-year algebra and analysis requirement can be satisfied by passing the corresponding written qualifying exam in September of the first year; these ...
Overview of Graduation Requirements To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements: Course Credits: 45 cred ...
The Department of Mathematics of the University of Pennsylvania offers a full Graduate Program in Mathematics, conferring the degrees of Master of Arts (A.M.), Master of Philosophy (M.Phil.), and Doctor of Philosophy (Ph.D.).
Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at Doctoral Programs.The requirements for all these programs consist of three components: coursework, examinations, and dissertation in accordance to the guidelines described in the GT Catalogue.
The goal of our PhD program is to train graduate students to become research mathematicians. Each year, an average of five students complete their theses and go on to exciting careers in mathematics both inside and outside of academia.. Faculty research interests in the Johns Hopkins University Department of Mathematics are concentrated in several areas of pure mathematics, including analysis ...
Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research.
Students seeking a Ph.D. in Mathematical Sciences are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all ...
Thinking of applying to graduate school in mathematics? Penn was ranked 8th among all US universities in a leading national study, and our mathematics graduate program was recently highest in a study of graduate programs in arts and sciences at Penn.We have a very active and involved mathematics faculty, diverse course offerings and a broad seminar schedule, with a variety of research projects ...
The goal of our PhD program is to train graduate students to become research mathematicians. Our students go on to exciting careers in mathematics both inside and outside of academia. Faculty research interests in the Johns Hopkins University Department of Mathematics are concentrated in several areas of pure mathematics, including algebraic geometry, algebraic topology, category theory ...
The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense.
The Robert Noyce Master Teaching Fellowship program is empowering this cohort of teachers through evidence-based approaches to mathematics education and mentorship of fellow educators.