how to get phd in maths

• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

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

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

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

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

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

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

Browse PhD Opportunities in Mathematics

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

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

Additional Learning Modules

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

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

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

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

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

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

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

Tips to Consider when Making Your Application

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

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

How Much Does a Maths PhD Typically Cost?

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

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

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

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

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

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

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

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

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

What Jobs Can You Get with A Maths PhD?

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

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

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

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

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

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

How Much Can You Earn with A PhD in Maths?

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

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

Academic Lecturer

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

Actuary or Finance

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

Aerospace or Mechanical Engineering

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

Data Analyst

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

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

Facts and Statistics About Maths PhD Holders

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

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

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

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

Ruth Lawrence

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

Emmy Noether

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

Other Useful Resources

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

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

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

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

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

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

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

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

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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.

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.

PhD in Mathematics

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

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

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

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

In addition to the above, PhD students often:

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

Ph.D. Degree Programs

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

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

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

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

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

Ph.D. in Mathematics

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

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

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

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

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

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

Written Qualifying Examinations

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

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

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

• 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:  

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.  

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.

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Guide to Graduate Studies

The PhD Program The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one’s own way. For this reason, a Ph.D. dissertation involving some original research is a fundamental part of the program. The stages in this program may be described as follows:

• Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
• Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
• Making a first original contribution to mathematics within this chosen special area.

Students are expected to take the initiative in pacing themselves through the Ph.D. program. In theory, a future research mathematician should be able to go through all three stages with the help of only a good library. In practice, many of the more subtle aspects of mathematics, such as a sense of taste or relative importance and feeling for a particular subject, are primarily communicated by personal contact. In addition, it is not at all trivial to find one’s way through the ever-burgeoning literature of mathematics, and one can go through the stages outlined above with much less lost motion if one has some access to a group of older and more experienced mathematicians who can guide one’s reading, supplement it with seminars and courses, and evaluate one’s first attempts at research. The presence of other graduate students of comparable ability and level of enthusiasm is also very helpful.

University Requirements

The University requires a minimum of two years of academic residence (16 half-courses) for the Ph.D. degree. On the other hand, five years in residence is the maximum usually allowed by the department. Most students complete the Ph.D. in four or five years. Please review the program requirements timeline .

There is no prescribed set of course requirements, but students are required to register and enroll in four courses each term to maintain full-time status with the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Qualifying Exam

The department gives the qualifying examination at the beginning of the fall and spring terms. The qualifying examination covers algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. Students are required to take the exam at the beginning of the first term. More details about the qualifying exams can be found here .

Students are expected to pass the qualifying exam before the end of their second year. After passing the qualifying exam students are expected to find a Ph.D. dissertation advisor.

Minor Thesis

The minor thesis is complementary to the qualifying exam. In the course of mathematical research, students will inevitably encounter areas in which they have gaps in knowledge. The minor thesis is an exercise in confronting those gaps to learn what is necessary to understand a specific area of math. Students choose a topic outside their area of expertise and, working independently, learns it well and produces a written exposition of the subject.

The topic is selected in consultation with a faculty member, other than the student’s Ph.D. dissertation advisor, chosen by the student. The topic should not be in the area of the student’s Ph.D. dissertation. For example, students working in number theory might do a minor thesis in analysis or geometry. At the end of three weeks time (four if teaching), students submit to the faculty member a written account of the subject and are prepared to answer questions on the topic.

The minor thesis must be completed before the start of the third year in residence.

Language Exam

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. Almost all important work is published in one of these four languages. Accordingly, students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination. Students are asked to translate one page of mathematics into English with the help of a dictionary. Students may request to substitute the Italian language exam if it is relevant to their area of mathematics. The language requirement should be fulfilled by the end of the second year. For more information on the graduate program requirements, a timeline can be viewed at here .

Non-native English speakers who have received a Bachelor’s degree in mathematics from an institution where classes are taught in a language other than English may request to waive the language requirement.

Upon completion of the language exam and eight upper-level math courses, students can apply for a continuing Master’s Degree.

Teaching Requirement

Most research mathematicians are also university teachers. In preparation for this role, all students are required to participate in the department’s teaching apprenticeship program and to complete two semesters of classroom teaching experience, usually as a teaching fellow. During the teaching apprenticeship, students are paired with a member of the department’s teaching staff. Students attend some of the advisor’s classes and then prepare (with help) and present their own class, which will be videotaped. Apprentices will receive feedback both from the advisor and from members of the class.

Teaching fellows are responsible for teaching calculus to a class of about 25 undergraduates. They meet with their class three hours a week. They have a course assistant (an advanced undergraduate) to grade homework and to take a weekly problem session. Usually, there are several classes following the same syllabus and with common exams. A course head (a member of the department teaching staff) coordinates the various classes following the same syllabus and is available to advise teaching fellows. Other teaching options are available: graduate course assistantships for advanced math courses and tutorials for advanced undergraduate math concentrators.

Final Stages

How students proceed through the second and third stages of the program varies considerably among individuals. While preparing for the qualifying examination or immediately after, students should begin taking more advanced courses to help with choosing a field of specialization. Unless prepared to work independently, students should choose a field that falls within the interests of a member of the faculty who is willing to serve as dissertation advisor. Members of the faculty vary in the way that they go about dissertation supervision; some faculty members expect more initiative and independence than others and some variation in how busy they are with current advisees. Students should consider their own advising needs as well as the faculty member’s field when choosing an advisor. Students must take the initiative to ask a professor if she or he will act as a dissertation advisor. Students having difficulty deciding under whom to work, may want to spend a term reading under the direction of two or more faculty members simultaneously. The sooner students choose an advisor, the sooner they can begin research. Students should have a provisional advisor by the second year.

It is important to keep in mind that there is no technique for teaching students to have ideas. All that faculty can do is to provide an ambiance in which one’s nascent abilities and insights can blossom. Ph.D. dissertations vary enormously in quality, from hard exercises to highly original advances. Many good research mathematicians begin very slowly, and their dissertations and first few papers could be of minor interest. The ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren’t known; and (2) a somewhat fatalistic attitude concerning “creative ability” and recognition that hard work is, in the end, much more important.

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.

Overview of the Application Procedure

Welcome to the MIT Mathematics Graduate Admissions page. This page explains the application process in general. For complete details, go to the on-line application which is available mid-September to December. These instructions are repeated there.

MIT admits students starting in the Fall term of each year only. Admission is to the PhD program only; there is no Masters program. There is no separate application for financial support; all admitted students are offered support.

Submitting GRE scores is entirely optional: We will accept scores if submitted (and are most interested in the Math Subject test result, if any) but it will not hurt your application if not included.

To apply, follow these steps:

Fill out the on-line application by 23:59, EST, December 15.

You will be submitting:

• Field(s) of interest
• Personal information/addresses
• International student data
• Three or more names and e-mail addresses of letter writers
• Educational and work history, including IELTS/TOEFL scores (preferably from this year), and honors
• Grades in math/science/engineering courses and overall
• Statement of objectives
• Outside financial support and potential outside support
• Credit/debit card payment of $75
• The Math department requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Arrange for submission of (official reports only)

• Letters of recommendation
• For international students, IELTS (or TOEFL iBT)

We recommend that before November 15 you notify your letter writers that you will be needing evaluations from them, so that they have time to prepare them and submit them by December 15. Once you have submitted your on-line application, instructions to your letter writers will be generated for you. You are responsible for making sure that your letter writers have copies of these instructions.

You self-reported your grades in step 1, but we require an official transcript for all admitted students. If/when we request this, arrange for an official copy of your college transcript to be sent to:

Academic Services, Room 2-110 Dept of Mathematics, MIT 77 Massachusetts Ave. Cambridge MA 02139-4307 USA

TOEFL reporting codes Institution code: MIT = 3514 Mathematics Department code: 72

International Students

IELTS is the English language proficiency test we prefer, but we also accept the TOEFL iBT . (On the other hand, we generally do not accept the TOEFL PBT.) To have IELTS results reported, indicate "Mathematics Department, Massachusetts Institute of Technology (MIT)" on your IELTS test application; no code or address is needed. To have TOEFL iBT results reported, use the codes above (3514 for MIT, and 72 for Mathematics).

If you are an international student, you should take the IELTS (or TOEFL iBT) by December 31. If you will receive an undergraduate degree from an English-language university in an English-speaking country after attending it for at least three years, then the Math Department will waive the English language proficiency test requirement.

Please address questions about the application process to [email protected] . You can find more information about MIT graduate admissions in general at the MIT Graduate Admissions site .

Computational Science and Engineering

Students with primary interest in Computational Science may also consider applying to the interdisciplinary Computational Science and Engineering (CSE) program, with which the Mathematics Department is affiliated. For more information, see https://oge.mit.edu/programs/computational-science-and-engineering-phd/ .

Department of Mathematics

Phd requirements.

• Prospective Graduate Student FAQ
• Graduate Board Oral Exam
• Graduate Courses

Qualifying Exams

• Recent PhD Theses
• Graduate Awards

Course Requirements

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

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

Teaching Seminar

Candidates must take, attend, participate in, and pass the course 110.771 (GTA Teaching Seminar). The seminar is an important part of the preparation for classroom teaching, and thus an essential part of mathematics graduate education. The seminar is generally required in a student’s first year at JHU. A student supported by an external fellowship may delay taking the seminar until the spring before they are required to TA (but may not postpone the seminar entirely).

Candidates must pass written qualifying exams by the beginning of their second year in Analysis (Real & Complex) and in Algebra. Exams are scheduled for September and May of each academic year, and the dates are announced well in advance. More information as well as old exams and syllabi can be found on the Qualifying Exams page .

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

PhD Dissertation

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

Our PhD program does not have a foreign language requirement.

The MA Degree

Although the Department of Mathematics does not admit students seeking a terminal MA degree, students in the PhD program may earn an MA degree.

MA candidates must complete:

• Four graduate courses given by the Hopkins Department of Mathematics
• Two additional courses at the graduate or 400 level, other than 110.401, 110.405 and 110.415, given by the Hopkins Department of Mathematics, or with the permission of the graduate program director, graduate mathematics courses given by other departments or universities.

All courses used to satisfy the requirements must be completed with a grade of B- or better. (Advanced graduate courses completed with a grade of P can also be used to satisfy the requirements.)

Graduate Programs

Mathematics.

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

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

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

Additional Resources

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

Application Information

Application requirements, gre subject:.

Not required

GRE General:

Dates/deadlines, application deadline, completion requirements.

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

Alumni Careers

Contact and Location

Department of mathematics, mailing address.

• Program Faculty
• Program Handbook
• Graduate School Handbook

Ph.D. Program Overview

Description.

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

Core Courses

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

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

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

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

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

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

"What is...?" Seminar

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

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

Special Committee

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

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

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

Current Advising Committee

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

Admission to Candidacy

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

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

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

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

Masters Degree in the Minor Field

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

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

Graduate Student Funding

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

Special Requests

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

School of Science

Mathematical sciences, ph.d in mathematics.

Exploring New Theories at the Forefront of Mathematics and its Applications

Doctoral studies form our core graduate program.  The faculty in the department excel in numerous areas of applied mathematics and are well versed in many related disciplinary fields, thus they are highly qualified to train graduate students and mentor them in producing high-quality research and dissertations at the intersection of mathematics and the sciences or engineering.  Our Ph.D. training opens doors to research careers in academia, government laboratories, and industry and our department has a strong record of placing Ph.D. students in prestigious postdoctoral positions at top-tier universities and labs, and in industrial positions.

Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office of Graduate Education .

Program of Study

The Ph.D. degree results from following a program of study in mathematics or in applied mathematics.

Requirements

Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office or Graduate Education .

The student’s program of study must include:

• At least six, 4-credit (nonthesis) graduate mathematics courses (i.e., those with numbers MATH 6XXX or MATP 6XXX).
• At least one 3- or 4-credit course at the graduate (6000) level outside the department (i.e., not coded MATH or MATP and not cross-listed with any department course), selected in consultation with the math adviser.
• All doctoral students must pass a written preliminary exam as well as an oral qualifying examination and complete an oral candidacy presentation.

In addition, the course MATH 6591 Research in Mathematics is strongly suggested. Any deviations from these requirements must have the approval of the Department’s Graduate Committee.

The program catalog can be found here .

Resources frequently used by graduate students in Mathematics can be found here .

Program Outcome

Students who successfully complete this program will be able to:

• Demonstrate mastery of graduate-level courses covering a range of topics, including mathematical analysis, mathematical methods and modeling, computational mathematics, and operations research.
• Demonstrate mastery of graduate-level courses in at least one area outside of mathematics.
• Conduct high-quality original research on a topic in mathematics or applied mathematics with results suitable for journal publications and technical presentations.
• Read and interpret research level articles in mathematics and develop new mathematical concepts.
• Develop mathematical formulation and solution of scientific problems from a range of disciplines.
• Communicate sophisticated mathematical ideas and concepts concisely and effectively in both oral and written form.

Financial Aid

There are several potential ways that a Math Sciences graduate student can get financial support while enrolled at RPI. The most common methods are:

Fellowships

There are many opportunities for students to obtain fellowships to support their graduate studies.  These fellowships can come from inside or outside the department or the Institute.  For example, recent fellowships have been available from the Department of Education, and there are competitive fellowships available from the National Science Foundation. The specifics of fellowships vary from year to year, and the  Graduate Student Coordinator has information on available fellowships and application procedures.  Your academic advisor in the department is another good source of information about fellowships. You should be sure to consider that the Math Sciences Department has guidelines for continuation of support for doctoral students. Graduate students who receive full support from the Department should plan to complete their doctoral programs within four or five years. Students can expect that their support will continue through this period, provided that they continue to make satisfactory progress toward their degree and they continue to perform well in their teaching assignments. "Satisfactory progress" means completing courses, required examinations (preliminary, qualifying, and candidacy), selecting a research area, and making progress toward completing a thesis. If a student requires support beyond the fifth year, each situation will be considered individually.

Teaching Assistantship

Teaching Assistant (TA) assignments vary significantly throughout Rensselaer Polytechnic Institute. In the Department of Mathematical Sciences, TA-ships are typically one-year appointments that cannot be extended for more than two years. They tend to be of two types. TA-ships can take the form of independent classroom teaching (often called recitations), which may include small lectures, problem solving, computer labs, grading, office hours, etc. The TA works with a TA Supervisor, who is the faculty member teaching the course. The vast majority of TA-ships are of this form. A few teaching assistantships take the form of grading and office hours only. All TA’s are required to participate in RPI’s TA Training Program as well as the Department’s TA Orientation prior to their first semester of teaching. In addition, all TA’s must attend the TA Seminar before or during their first semester of teaching at RPI. A graduate student, the Math Sciences Department Master TA, typically teaches this one-credit course (graded as Satisfactory/Unsatisfactory). The topics of this course vary according to the needs of the participants. In the past they have included: Maple, Grading, Laptops, Composing Quizzes, Campus Resources, Academic Honesty, Proctoring Exams, Extra Help, Office Hours, Latex, Making a Syllabus, etc.  In addition, each TA has their class visited and feedback is provided.

Research Assistantship

Many faculty in the Math Sciences Department have research funding that can be used to support graduate students who are interested in doing research in their field. The Research Assistantships (RA’s) do not typically have any teaching component. This allows a graduate student to have more time to work on Master’s or Ph. D. research. This is a topic you may want to talk to your advisor about.

Academic Opportunities

Graduate Academic Awards

Academic awards for graduate students who demonstrated outstanding ability in his or her academic work.

SIAM Student Chapter at RPI

SIAM exists to ensure the strongest interactions between mathematics and other scientific and technological communities through membership activities, publication of journals and books, and conferences.

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How to get into a top mathematics PhD program?

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

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

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

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

2 Answers 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Disclaimer: not a mathematician

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

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Study Postgraduate

Phd in mathematics (2025 entry).

Course code

6 October 2025

3-4 years full-time

Qualification

Mathematics Institute

University of Warwick

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Find out more about our Mathematics PhD at Warwick

The PhD in Mathematics offers an intellectually stimulating and dynamic research course. Study at the University of Warwick's Mathematics Institute, an international centre of research excellence, ranked 3rd for research power and 3rd for the number of 4* research outputs in REF 2021 (amongst UK universities).

Course overview

Mathematics at Warwick covers the full spectrum of mathematics and its applications. The Mathematics Postgraduate Degrees are appropriate for students with a strong and broad mathematical background who wish to engage in advanced mathematical techniques and attack mathematical research problems in their postgraduate work.

All students are required to undergo training in Year One and are encouraged to make use of further training opportunities available in subsequent years. Training ranges from gaining a broader knowledge of mathematics through taught modules, seminars and workshops, to enhancing your professional and transferrable skills. Our PhD students undertake high quality original research and are being well-prepared for a career, either in academia or elsewhere.

Teaching and learning

Students are required to complete a series of modules in their first year (from a very wide selection of bespoke modules), with assessment including an oral examination component. Upon the successful completion of these modules, students are required to complete a research project before being formally upgraded to a PhD at the end of the first year.

Training will be supplemented with attendance to seminars, cohort building activities, and additional transferable skills training.

General entry requirements

Minimum requirements.

First Class Honours undergraduate integrated Master's (4-year) degree from a UK university in Mathematics or a science degree with high mathematical content, or the equivalent qualification and grade from a non-UK university.

Alternatively, applicants who have a Bachelor's degree AND a Distinction in a postgraduate Master's degree would be considered.

English language requirements

You can find out more about our English language requirements Link opens in a new window . This course requires the following:

• IELTS overall score of 6.5, minimum component scores not below 6.0

International qualifications

We welcome applications from students with other internationally recognised qualifications.

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Additional requirements

There are no additional entry requirements for this course.

Our research

The mathematics department covers a wide range of research areas in mathematics and its applications.

You may also wish to explore the research interest of current Warwick academics .

Find a supervisor

The 'Find A Supervisor' link below will allow you to explore the research interests of academics within the department. Please include in your application the names of potential supervisors, with interests aligned with yours, or people you would like to work with.

The mathematics department, unlike some other departments, does not require students to make any arrangements with any potential supervisors before applying, though of course you are welcome to contact them directly and discuss your interests and any potential projects they may offer.

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Research proposals

Warwick academics can supervise thesis research in a wide range of topics in mathematics and its applications. In addition, all PhD projects are expected to be co-supervised by an external partner, bringing knowledge, data and experience to the modelling of real-world problems.

The mathematics department covers a wide range of research areas Link opens in a new window in mathematics and its applications.

Research proposal guidance

In many cases, applicants have not settled on a specific area or project and have rather broad interests. If that is the case, this document can be used to describe your interests, your background on those areas, and what attracts you to those topics for example. This will help in assessing your application and help us determine potential supervisors and projects that you might be interested in.

Find out more about writing a research proposal.

Tuition fees

Tuition fees are payable for each year of your course at the start of the academic year, or at the start of your course, if later. Academic fees cover the cost of tuition, examinations and registration and some student amenities.

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Fee Status Guidance

We carry out an initial fee status assessment based on the information you provide in your application. Students will be classified as Home or Overseas fee status. Your fee status determines tuition fees, and what financial support and scholarships may be available. If you receive an offer, your fee status will be clearly stated alongside the tuition fee information.

Do you need your fee classification to be reviewed?

If you believe that your fee status has been classified incorrectly, you can complete a fee status assessment questionnaire. Please follow the instructions in your offer information and provide the documents needed to reassess your status.

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Additional course costs

As well as tuition fees and living expenses, some courses may require you to cover the cost of field trips or costs associated with travel abroad.

For departmental specific costs, please see the Modules tab on the course web page for the list of core and optional core modules with hyperlinks to our  Module Catalogue  (please visit the Department’s website if the Module Catalogue hyperlinks are not provided).

Associated costs can be found on the Study tab for each module listed in the Module Catalogue (please note most of the module content applies to 2022/23 year of study). Information about module department specific costs should be considered in conjunction with the more general costs below:

• Core text books
• Printer credits
• Dissertation binding
• Robe hire for your degree ceremony

Scholarships and bursaries

Scholarships and financial support.

Find out about the different funding routes available, including; postgraduate loans, scholarships, fee awards and academic department bursaries.

Living costs

Find out more about the cost of living as a postgraduate student at the University of Warwick.

Mathematics Funding Opportunities

Find out more about the various funding opportunities that are available in our department.

Mathematics at Warwick

Our challenging Mathematics degrees will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.

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Our courses

• Mathematics (Diploma plus MSc)
• Mathematics (MSc)
• Mathematics (PhD)

How to apply

The application process for courses that start in September and October 2025 will open on 2 October 2024.

For research courses that start in September and October 2025 the application deadline for students who require a visa to study in the UK is 2 August 2025. This should allow sufficient time to complete the admissions process and to obtain a visa to study in the UK.

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We understand how important it is to visit and explore your future university before you apply. That's why we have put together a range of online and in-person options to help you discover more about your course, visit campus, and get a sense of postgraduate life at Warwick. Our events offer includes:

• Warwick hosted events
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Why Warwick

Discover why Warwick is one of the best universities in the UK and renowned globally.

9th in the UK

of the UK's best universities (The Guardian University Guide 2024, The Times and Sunday Times Good University Guide 2024.)

5th Most Targeted University

by the UK's top 100 graduate employers (The Graduate Market in 2023, High Fliers Research Ltd.)

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out of 1,500 institutions across 104 locations (QS World University Rankings 2024.)

10th in the UK

for our 'Graduate Prospects' score. (The Times and Sunday Times Good University Guide 2024.)

Gold Standard Teaching

Gold, the highest possible rating across all three categories (student experience, student outcomes, and overall) (Teaching Excellence Framework 2023)

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We may have revised the information on this page since publication. See the edits we have made and content history .

About the information on this page

This information is applicable for 2025 entry. Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.

Quick Links +

Applied ph.d. program requirements (fall 2024).

This plan requires a total of 60 units. Students will enroll for 12 units per quarter including research, academic, and seminar units. Before advancing to Candidacy for a doctoral degree, a student must have satisfied all requirements set by the graduate program, maintained a minimum GPA of 3.0 in all course work undertaken (except those courses graded S or U), passed the PhD Preliminary Examination, and passed the Qualifying Examination. A dissertation and an exit seminar are required.

Course Requirements

• Area A (12 units in one of the series) : (i) Analysis Series MAT 201AB/MAT 201C/MAT 205/MAT206 (Analysis) or (ii) Methods of Applied Mathematics MAT 207ABC.  
• Area B (8 units in one of the series): (i) Data Science series: Numerical Optimization (MAT 258A), Discrete and Mixed-Integer Optimization (MAT258B), Mathematics of Data Science (MAT 270); or (ii) Numerical Methods series: Numerical Methods: Fundamentals (MAT 226A), Numerical Methods: Large-Scale Matrix Computations (MAT 226B), Numerical Methods: Ordinary Differential Equations (MAT226C), Numerical Solutions of Differential Equations A, B and C (MAT 228ABC); or (iii) Probability series: Probability Theory A and B (MAT235AB), Mathematical Statistics III (STA231C); or (iv) Theoretical Computer Science series: Theoretical Computer Science (ECS220), Design and Analysis of Algorithms (ECS222).  
• Graduate Advanced Mathematics: 12 units of 200-level Mathematics courses whose course numbers are 279 or less. These include courses from areas A or B not selected as core courses. One mathematics-oriented graduate course outside of Mathematics, could be substituted but only with prior approval by GGAM Chair.  
• Field of Specialization (FOS): Minimum of 15 units in a field of specialization, such as, any courses in Area A or B not taken to satisfy the core requirements, optimization, and control, differential equations, probability and statistics, discrete mathematics, mathematical physics, mathematical biology, harmonic analysis and signal processing, etc. Out of this minimum of 15 units, at least one course of 3 or more units must be outside of Mathematics. Courses outside of the mathematics department have to be approved by the Chair of the graduate group. For a list of preapproved courses, see the GGAM webpage and consult with the potential thesis advisor. An updated list of courses can be found in https://appliedmath.ucdavis.edu/graduate/sample-depth-courses  
• Advanced Mathematics: Maximum of 12 units, in three 100 level (i.e.upper division) math courses.  
• GGAM miniconference: Attendance at the annual GGAM mini-conference, which takes place during winter quarter graduate welcome and consists of faculty talks and a student poster session showcasing the research being done at GGAM, is required in the first or second year, for which 1 unit of 290 will be given in order to document compliance.  
• MAT 290 seminars  
• MAT 390 and Teaching: Each student who accepts a TAship in the Department of Mathematics is required to complete MAT390, which is taught every Fall quarter. Most students take this in their first year, even if they are supported by a fellowship. MAT 390 does not count toward degree units (but does count for the 12-unit minimum required for registration each quarter). All PhD students are required to be teaching assistants for at least one quarter. Exceptions require approval of the GGAMEXEC. Students beyond their first year are encouraged to apply for positions as Associate-Instructors to develop and improve their lecturing skills.  
• Research Units: Students can register for research units but these units cannot substitute course requirements unless previously reviewed and approved by the chair of the graduate group.

Ph.D. Preliminary Examination

The Ph.D. Preliminary Examination is a written examination covering materials from the student’s chosen tracks Area A (MAT 201AB or MAT 207ABC) and Area B: Data Science: (MAT 168, MAT170); Numerical Methods (MAT128ABC); Probability (MAT 135AB); and Theoretical Computer Science (ECS220, ECS222). The exam is offered in June and September every year. PhD students are required to pass this examination before the end of their second year.  They may take the examination multiple times; what matters is when they pass, not how many attempts.

Qualifying Examination

Students must complete the course requirements before taking their Qualifying Examination (QE). The QE will consist of a written research proposal, a syllabus of materials relevant to the research proposal covered in the chosen tracks in Areas A and B, and oral examination. Approximately six weeks before the date of the proposed QE, the research proposal, along with the QE Application, is submitted to GGAMEXEC for approval. Once approved and required signatures obtained, the QE Application will be forwarded to the Office of Graduate Studies for final approval. The QE should be taken by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program. Passing the QE makes the student eligible for advancement to candidacy.

Dissertation

The doctoral dissertation is an essential part of the Ph.D. program. A topic will be selected by the student, under the guidance of the Dissertation Advisor. Students are encouraged to begin their research activity as early as possible. The dissertation must contain an original contribution of publishable quality to the knowledge of applied mathematics. Acceptance of the dissertation by the dissertation committee must follow Graduate Studies guidelines (Plan B). The program does not have any program-specific requirements, such as length or presentation format. Instructions on preparation of the dissertation and a schedule of dates for filing the thesis in final form are available from Graduate Studies; the dates are also printed in the UC Davis General Catalog.

Exit Seminar

Ph.D. students are required to give a 60-minute seminar presentation, open to the public, on their dissertation subject.

Optional Final Oral Examination (at the discretion of the Dissertation Committee)

After the exit seminar, the student’s dissertation committee may meet privately with the student to discuss the contents of the dissertation and ask additional questions. Satisfaction of this requirement must be verified by the Dissertation Committee Chair.

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Ph.D. Mathematics Course, Eligibility, Entrance Exams, Syllabus, Colleges, Jobs and Scope 2024

Satyam Purwar

Content Curator

Ph.D. (Mathematics) - Latest Notifications

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Ph.D. Mathematics is a Doctorate of Mathematics course . It is the study of structure, space, quantity, and change. It seeks out patterns and formulates new conjectures. On the completion of a doctorate, scholars should submit their ‘thesis’ and, then they deserve the respective degree they are pursuing. 

The duration of the program is a minimum of 3 years and a maximum of 5-6 years . The minimum qualifications and other eligibility criteria for admission are M.Sc. Degree in Mathematical or Physical Sciences/ B. Tech Candidates from any discipline can also apply/ Some Institutes also offer direct admission for Graduate students with excellent academic performance. Ph.D. Mathematics is a broad-based course involving a minimum course credit requirement and a research thesis.

After completion of this course, graduates may work in fields like Banks, Investment Firms, Commerce Industry, Business Industry, Colleges, Universities, Research and Development Firms, Indian Civil Services, Inventory Management, Insurance Agencies, Statistics, etc. These professionals may work in positions like Mathematician, Statistician, Loan Officer, Accountant, Economist, Demographer, etc. The average salary for these professionals ranges between INR 3 to 9 Lakhs as per their experience and expertise in this field.

Ph.D. Mathematics: Course Highlights

Ph.D. Mathematics: What is it about?

Ph.D. Mathematics is the program of choice for students who wish to pursue a career in a mathematical research field.

• The minimum duration of this course is 2-years , whereas you can complete this course in a maximum time span of 3-5 years .
• Ph.D. Mathematics is a full-time doctoral degree.
• In Ph.D. Mathematics, students study statistical concepts relating to inspection, engineering design, and quality assurance.
• Ph.D. in Mathematics course involves research that uses various methods of mathematical types associated with the graph theory, asymptotic analysis, scientific computation, bifurcation theory, probability and statistics, ordinary and partial differential equations, stability theory, singular perturbations, and stochastic processes.
• In this course, major topics studied by the students are correlation, normality, probability, sampling, regression, and confidence intervals in reliability. This course is designed to enrich the applications like algebra and trigonometry, systems of linear equations, algebraic fractions, literal equations, quadratic equations, right triangles, vectors, word problems, and their solutions.

Why study the Ph.D. Mathematics course?

Candidates who are inclined towards a research career, many positions are available in research institutions and universities for them. And who wish to pursue a teaching career, well-paying teaching positions are available in plenty in private engineering colleges. Many research labs of multinational companies, financial services companies, and others are massively recruiting Indian mathematicians.

Some of the popular reasons why Ph.D. Mathematics must be pursued is as follows:

• This program prepares someone to keep momentum with the expanding frontiers of knowledge and provides research training relevant to the present social and economic objectives of the country.
• It comprehends to write a good research report and acquires the skill of presenting data in graphical form.
• They can also go for accountancy and business services , banking, investment and insurance, government, and public administration.
• They can become teachers and lecturers in schools and colleges/universities respectively; for becoming a lecturer in colleges they should pass the NET exam and the UGC guidelines.

Ph.D. Mathematics: Admission Process

Most colleges and institutes offering Ph.D. Mathematics courses admit students based on the graduate degree level examination marks. Some institutes, however, do conduct entrance examinations to judge a candidate’s capability.

The following are the two major pathways through which Ph.D. Mathematics admissions takes place:

Merit-Based Admission:

Most private universities such as Lovely Professional, AMU, and others that offer Ph.D. (Mathematics) courses usually admit students based on the marks secured at the master’s/ graduate degree. Apart from this, these colleges may conduct a Personal Interview or a small Written Test to further know the candidate and his/her skills.

Entrance Exam Based:

Top Ph.D. Colleges like Chandigarh University, RKMVCC, Stella Maris College, etc. offer admission in the Ph.D. (Mathematics) program through entrance examinations that usually consist of MCQ based questions related to Algebra, Analysis, Discrete Mathematics, etc. helping the college to screen the deserving candidates for admission.

After the result declaration of these Entrance Exams, colleges may further conduct a Personal Interview Round of the qualified candidates to know their interest in the course, skills, and career and might go through their Art Portfolio as well.

Ph.D. Mathematics: Eligibility

The common Ph.D. (Mathematics) eligibility criteria to be successfully admitted into a college offering this course is as follows:

• M.Sc./ Master’s Degree in Mathematical or Physical Sciences
• B. Tech Candidates from any discipline can also apply, it may vary by Institutes.
• Some Institutes also offer direct admission for Graduate Students with excellent academics records.
• Each college also further has a set minimum aggregate marks. Overall, it should be 55% (50% for SC / ST).

The above-stated eligibility criteria are the basic eligibility criteria. Each college will have its criterion on which prospective candidates are judged.

Ph.D. Mathematics: Entrance Exams

Some colleges that offer Ph.D. (Mathematics) programs require their candidates to sit for an entrance examination. This paper carries a total of 100 marks where candidates need to conclude writing the exam within a period of 3 hours.

Listed below are some of the popular Ph.D. Mathematics entrance exams.

• CSIR-UGC NET for JRF Entrance Exam: CSIR UGC NET is a national-level exam conducted by the National Testing Agency (NTA) on behalf of Council of Scientific and Industrial Research (CSIR) to shortlist candidates for the award of Junior Research Fellowship (JRF) or lectureship in Indian universities and colleges.
• UGC NET Entrance Exam: The UGC NET for JRF, also known as National Eligibility Test (NET) or NTA-UGC-NET, is the test for determining the eligibility for the post of Junior Research Fellowship (JRF) or Asst. Professor award in Indian universities and colleges.
• NBHM Entrance Exam: National Board for Higher Mathematics is a board in India that conducts a national entrance exam intended to foster the development of higher mathematics, help in the establishment and development of mathematics centers, and give financial assistance to research projects and to doctoral and postdoctoral scholars.

There are few private colleges like Chandigarh University , LPU , etc. conducts their own entrance tests for this course.

How to Prepare for a Ph.D. Mathematics Entrance Exams?

The syllabus for Ph.D. Mathematics entrance exams will vary from institute to institute. However, most exams concentrate on mathematics-related subject knowledge and skills.

The paper shall have two different parts,

• Part I - Here 10 questions will be given. Out of these, 6 will have to be answered. This part will carry 40 marks.
• Part II - Here also 10 questions will be given, out of this 6 ought to be answered. This part will carry 60 marks.

The following sections are generally covered in Ph.D. Mathematics entrance exams syllabus:

• Abstract Algebra
• Complex Analysis
• Elements of Numerical Analysis
• Linear Algebra
• Ordinary Differential Equations
• Partial Differential Equations
• Real Analysis

Students should consider buying study material and practice material of Ph.D. Mathematics entrance exams so that they prepare well for the same. This paper carries a total of 100 marks where candidates will need to conclude writing the exam within a period of 3 hours.

How to get admission in a good Ph.D. Mathematics college?

To get admission in top Ph.D. Mathematics colleges, the following points must be kept in mind:

• The application process for most of the institutes starts in January every year and the classes begin in August.
• The Colleges shortlist candidates through respective entrance exams followed by an interview.
• The best way is to appear for CSIR-NET and UGC-NET exams to get a good college for Ph.D. and for some of the colleges’ GATE is also used as a prerequisite.
• For example, ISI Kolkata uses the GATE score for admission in its Ph.D. Mathematics program. Some institutes also take admission through the NBHM Screening test conducted for Ph.D. Scholarships.

Ph.D. Mathematics: Syllabus

Although the Ph.D. Mathematics course curriculum varies from college to college, it mostly consists of some common foundation courses that students can select based on his/her interests.

The table below shows common subjects that are included in the structured Ph.D. Mathematics syllabus and subjects included in it:

Ph.D. Mathematics: Books

Tabulated below are some of the Ph.D. Mathematics subject books that can help students to have a broader and better understanding of the course. The books mentioned below will also help the students in cracking various Ph.D. Mathematics exams.

Ph.D. Mathematics: Top Colleges

The table below shows the best Ph.D. Mathematics colleges and universities that offer the course in a full-time mode.

View More   Top Ph.D. Mathematics Colleges

College Comparison

The tabulation below shows the comparison made among the three top Ph.D. Mathematics colleges in India.

Source: Official Websites of Colleges and Universities

Course Comparison

Ph.D. Mathematics Vs Ph.D. Economics

Both Ph.D. Mathematics and Ph.D. Economics have a bright future in the field of research with several aspects. There are many colleges in India who prefer both of the courses in their academic structure. Check the table below for more comparative details:

Source: Official Surveys

The eligibility and admission criteria for both these degrees are the same. In terms of Career and Salary, both Ph.D. Mathematics and Ph.D. Economics almost have the same career prospects and job opportunities, and individuals can earn an average salary of around INR 2-9 Lakhs per annum or more in some cases depending upon candidate's skills, knowledge, and experience.

Ph.D. Mathematics: Job Prospects and Career Options

In India, Ph.D. Mathematics is one of the top career choices made by students. There are lots of job opportunities available in India as well as in foreign countries for Mathematical graduates.

• Ph.D. graduates may work in a wide range of mathematical areas like Numerical Analysis, Computational Complex Analysis Group, Biomathematics Group, Complexity and Networks, Dynamical Systems, Fluid Dynamics, Mathematical Physics, etc.
• Graduates who have the ability to handle customers and basic knowledge about the industry may also work in both private and government banks.
• They can also seek employment in various sectors such as in markets research, public accounting firms, government and private banks, government and private financial sectors, budget planning, consultancies, and corporations.
• Top companies that offer jobs for these professionals are Aquis, Airtel, ITC Infotech, IBM Global Services, ABC Consultants, NEXT Techno Enterprises, Brainfuse, etc.

The table below shows some of the most common Ph.D. Mathematics job profiles and career prospects after completing the course is as follows:

Source: Payscale

Ph.D. Mathematics: Future Scope

Students having a Ph.D. mathematics degree are importantly serving the education industry and due to the laws of UGC one position of Head of Department is always secured for Ph.D. holders only.

• Employment of mathematicians in India is expected to grow by 23% as the surging demand for knowledge and expertise in private sector analytics firms.
• The private sector offers better pay and opportunities. The package can also increase if they add advanced computing skills and statistical tools in their profile.

Ph.D. Mathematics: FAQs

Ques. What are the top colleges for Ph.D. Mathematics?

Ans. The top institutes and colleges for Ph.D. Mathematics are Banaras Hindu University, Aligarh Muslim University, Amity University Noida, Birla Institute of Technology Ranchi, Queen Mary’s College, among others.

Ques. What are the subjects in Ph.D. Mathematics?

Ans. Some of the subjects taught in Ph.D. Mathematics are Algebra, Calculus, Discrete Mathematics, Differential Equations, Computational Techniques, Differential Geometry, etc.

Ques. Which job profiles are available for a Ph.D. Mathematics?

Ans. Students of Ph.D. Mathematics can work as Mathematician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Demographer, Professor, etc.

Ques. What is the annual average tuition fee charged for a Ph.D. Mathematics program?

Ans. The annual average tuition fee at the top Ph.D. Mathematics colleges is between INR 2K to INR 3 Lakh.

Ques. What is the scope of the Ph.D. Mathematics course?

Ans. Students can choose for both private and public sector jobs in several sectors like the professor, loan counselor, Insurance Manager, etc.

Ques. What is the average salary in Ph.D. Mathematics?

Ans. The salary ranges from INR 3-9 Lakhs per annum as per the job profile.

Ques. What are the job positions in the Ph.D. Mathematics field?

Ans. Job positions like Mathematician, Statistician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Cryptographer, Demographer, Professor, etc. are available in the Ph.D. Mathematics field.

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12 Reviews found

research in MANIT

Campus life.

You can avail free internet, computer labs, library, e-library (all reputeted Journals like scopus, sci, scie, ugc, ieee etc) and most important support of yor guide. anuual function, conferences, workshop, tranning session which will help you for exploring the research and enhance your knowldge. also time to time sports activities, social activities are held and you can take part accordinly.

Loan/ Scholarship Provisions

@ the time of my admission tution fees is 26000 per year in two installment and 20000 thesis submission fees and no other fees included. If you are GATE/ NET qualified then eligible for stipends (25000/ month) which is a good amount. Otherwise no stipends for scholars. other stationary amount yo have to bear. after completion of PhD you can apply for projects and earn monthly.

Life of campus is good.It has students from various regions of India and also from countries like Africa ,Niziria etc. Most of students of the CUP are from Kerala and South .It has a good library wher you can stay upto midnight.

If you have any external funding then you can easily avail that fellowship.But if you don't have any fellowship then university provide a fellowship of 8000 per month to scholors which doesn't have any external funding.

Home of the traditional- SRC

Course curriculum overview.

Actually I like mathematics from my childhood itself. That's why I chose Mathematics in UG. And also I like teaching profession. So I would like to complete PhD. My guide help me lot for my research. And also other faculties of my department are also so supportive and motivating for my research.

Placement Experience

Usually at the final semester students get the opportunities for the placement. Lot of schools and companies around Trichy came here for the interview. Capgemini, SRV higher secondary school from samayapuram and AKT school from kallakurichi are the most visited schools for our campus.

Campus Life at NIT Rourkela

NIT Rourkela has nice research environment and many professsor are collaborating with some foreign unoversity professsor. The infrastructure and campus are the main attraction to many students and PhD scholars. NIT Rourkela has also actively working placement Cell. 3 students got 45 lakh package and 9 students got 43 lakh package during this pandemic year. The statistic for placement shows that its placement percentage is going to increase in upcoming days.

I have joined in this course because I want to do research in Optimization.Faculties are highly motivated towards research. Most of the Faculties have done their PhD in Top IITs and Teaching standard is upto the mark. There are two term. One is mid semi and another is End term. We have to solve the assignment regularly to perform well in the exam and exam paper are mostly moderate to difficult level.

The revolutionary mathematics research institute

Though I was doing my Master's in mathematics I had to focus more on the TIFR GS entrance exam to pursue my Ph.D. in Mathematics. Not only that, after I qualified the exam with good ranking, but only 1.5 % of top merit list students were being considered! It was such a critical situation, yet eventually, I was noticed and called for the interview that went quite well.

TIFR is financed by the Department of Atomic Energy of Government of India. A minimal (or no) fee is charged for the course, in fact, an effective amount as accommodation is given to the students depending on the course they choose.

Pursuing PhD mathematics

I want to take a doctoral degree in mathematics because I always have a huge interest in mathematics so that's the reason I opt that course. Chandigarh university provided a huge area of research so that reason i choose Chandigarh university. Firstly fill the registration forms for the entrance test then give entrance test.

College Events

Chandigarh university celebrates every festival of all religions and they organize various events eveRy month like DJ night, tech events, fresher party, farewell parties also hostels night. Bollywood and Hollywood celebrities are visiting the campus for promotion of their movies.

IIT Patna PhD in mathematics

After doing PhD we can apply for assistant professor. IIT Patna provide stipend and fellowship by mhrd, csir, ugc, dst, nbhm, pmrf e. t. c. I am a CSIR fellow whuch give fellowship very late but IIT Patna provide some help if we needed money which you can return after getting money.

PhD is higer degree and needed for to be a professor. We have to do 5 courses from elective including English literature. After that we have labs for research and computational work. We are free to choose our course paper so it reduces our complications for unwanted subjects.

My college experience

An annual book/contingency grant of Rs. 32,000 and support for research-related domestic and international travel is available to students. Junior Research Fellowships are awarded to all selected PhD students. These fellowships include a monthly stipend ranging from Rs. 25,000/- to Rs. 28,000/-, hostel accommodation (or a house rent allowance) and medical benefits.

They are various extra-cirricular activities provided by the college. They are various grounds provided for badminton, soccer and cricket. They are coaches too if you want to learn a sport and they are various events conducted. They are also labs provides for yoir research and they are well equipped.

Phd admission to Math dept

All students of the elite Indian Institutes of Technology, patna whose annual family income is less than ? 9 lakh will be eligible for interest-free education loans for a period of of five years.if you are admitted though external fellowship you give rs 31000 per month for initial three months which can be returned after start external fellowship. And if you admitted through gate you will get 31000 per month which credited first week of the month.

Research Scholars' Day (popularly known as RSD) is an annual event celebrated by the research scholars of IIT Patna. In this programme, the students are present there research paper and many of famous scientists are invited in this program.

My Doctoral College

'Anwesha', is IIT Patna’s annual 3-day techno-cultural festival organised by the student community. Indian Institute of technology Patna each year celebrates its Technical Fest, christened as ''CELESTA'. This is a great beginning, which strives to inculcate interest in young minds to pursue technology and make it their passion. It was started in 2008 and since then it has gained unmatched popularity. It is a cultural celebration held around 'Diwali'. Beautiful decoration through lights added with fantastic cultural performances makes IIT Patna really reverberate with joy during the ‘Reverberance’. The Students' Gymkhana Building, situated in the IIT Patna hostel compound, has a synthetic badminton court and a gymnasium. In addition, the students have access to a basketball court, a volleyball court, table tennis tables and a football-cum-cricket ground within the transit campus. State-of-the-art facilities for all sports are planned at IIT Patna’s main campus in Bihita. We have good gender ration in campus. There is no such problems.

All students of the Indian Institutes of Technology Patna (IITP) whose annual family income is less than Rs.9 lakh will be eligible for interest-free education loans for a period of five years, the human resource development ministry said on Thursday. Earlier, the interest subvention scheme was for students whose annual family income was Rs.4.5 lakh.

Wastage of time and life

Worst among all the IITs, characterless, rude, unethical, all the works to be performed by teaching assistants which are research scholars. Institute lacks faculty and research scholars have to perform all the academic tasks of guide as well as teaching supervisor.

Need to fulfill the required CGPI in a year and then a comprehensive examination will be held. After successful completion of comprehensive exam including written test and presentation of the work done in past, finally registered as a Ph D. student.

Jadavpur University is the great

Fee structure and facilities.

The fee structure is very low in this university so that any poor student can effort their expenses. In addition, there are few scholarships available in this university like Merit cum means fellowship.

Internships Opportunities

Engineering faculty of this university offers various internship in India as well as abroad also. During the internship, some stipend was offered by the various companies/institute.

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.

IIT Madras - Indian Institute of Technology - [IITM]

IIT Delhi - Indian Institute of Technology [IITD]

IIT Bombay - Indian Institute of Technology - [IITB]

IIT Kharagpur - Indian Institute of Technology - [IITKGP]

IIT Kanpur - Indian Institute of Technology - [IITK]

IIT Roorkee - Indian Institute of Technology - [IITR]

BITS Pilani (Pilani Campus)

IIT Guwahati - Indian Institute of Technology - [IITG]

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10 of Futurama's smartest science references and gags

Good news, everyone! With "Futurama" season 12 about to land, here are 10 of the best science and math-based jokes from the sci-fi comedy's 25-year history.

1. Number theory

2. get with the program, 3. light speed-plus, 5. a quantum finish, 6. the ultimate strip, 7. infinite screens and nothing on, 8. black hole fun, 9. raise the proof, 10. another day in paradox.

When "Futurama" first beamed onto planet Earth in 1999, it was no surprise that a TV series co-created by "The Simpsons" mastermind Matt Groening was packed with smart references to pop culture and current affairs. But beyond the conveyor belt of gags about " Star Trek " and the state of planet Earth, the show's team of writers — many of whom are science graduates — have also managed to squeeze in plenty of ingenious references to physics, mathematics and other branches of the sciences.

Below we've picked out √100 (okay, 10) of the best science references from "Futurama"'s quarter century on our screens — running the full gamut from simple sight gags, to jokes directed squarely at the finest mathematical minds in the galaxy. 

Oh, and because the numbering system for "Futurama" seasons hasn't always been as constant as ∏, we've stuck with the nomenclature currently used by Hulu (US) and Disney Plus (UK).

If there's a mathematical equivalent of the pun, then "Futurama" has turned the play on numbers into an artform. These have varied in complexity across the show's run, ranging from relatively simple sight gags (Route 66 rebranded as √66, 7-Eleven reinvented as 711) to jokes only mathematicians will understand. 

For example, when season two's horror pastiche "The Honking" whisked Bender away to a "Shining"-esque haunted house, the number he saw in the mirror was 1010011010 — fairly innocuous in base 10, but 666 (aka the number of the Beast) in binary.

You also have to look closely at the name of the nightclub in season six episode "Rebirth" to truly understand its relevance — Studio 122133 is just another way of expressing Studio 54, the legendary New York night spot.

While resident robot Bender has generally made an effort to talk like a human, "Futurama" has also referenced vintage computer languages. 

Bender used Olde FORTRAN Malt Liquor as a power-up in the PlayStation 2 "Futurama" game, and the brand's still going strong in 3023 when Professor Farnsworth takes a swig in season 11 episode "I Know What You Did Next Xmas".

BASIC also gets a look in. In a gag that will engage the nostalgia circuits in many a veteran programmer, the sign on the wall of Fry and Bender's apartment says:

30 GO TO 10

In season four's "Kif Gets Knocked Up A Notch", meanwhile, Kif creates a holodeck pony for his beloved Amy, programmed using "four million lines of BASIC" — an endeavour that must have taken considerable time and effort.

But perhaps we shouldn't be surprised that a show set in the 31st century is so fascinated by retro computing. Season one episode "Fry and the Slurm Factory" revealed that the 6502 processor used in the first Apple II computer — way back in 1977 — can also be found in Bender's head.

Albert Einstein 's theories of relativity have long been fundamental to our understanding of the universe, but the fact that nothing can travel faster than the speed of light is a massive inconvenience to writers of science fiction. Some storytellers get around the problem by warping or bending space (see "Star Trek" and "Dune"), while others send spacecraft into an alternative "hyperspace" dimension (see "Star Wars" and "Babylon 5") to condense epic journeys between stars into the runtime of a movie or TV episode. 

Few franchises have been as creative as "Futurama", however, where it turns out that scientists worked out how to increase the speed of light in 2208 — a cunning ruse that makes faster interstellar travel possible without violating the rules laid down by Einstein. The concept is nearly as ingenious as the afterburners on Professor Farnsworth's dark matter engines, which run at an impressive 200% efficiency.

From the 1138 that keeps cropping up in "Star Wars" to the A113 that's ubiquitous in Pixar movies, pop culture loves using numbers as in-jokes. While those two examples are, respectively, references to "THX-1138" (George Lucas's debut movie) and a classroom at CalArts (California Institute of the Arts), the 1729 that's a regular guest star in "Futurama" is a big deal in mathematics.

In the show, Bender is his mother's 1729th son; the serial number of the Nimbus, Zapp Brannigan's ship, is BP-1729; and one of the parallel realities in season four's "The Farnsworth Parabox" is Universe 1729.

Despite its seemingly non-descript nature, 1729 is the most famous "taxi cab" or Ramanujan-Hardy number , the smallest number that can be expressed as the sum of two positive integer cube numbers in more than one way — in this case, 13 + 123 and 93+103. 

1729 isn't the only taxi cab/Ramanujan-Hardy number to cameo in "Futurama", either, because 87,539,319 (which can be expressed as 1673 + 4363, 2283 + 4233 and 2553 + 4143) features on an actual taxi cab in 2007 movie "Bender's Big Score".

Whether they're using goal-line technology or cameras of mind-boggling sophistication, sports administrators are always looking for new ways to make impossibly tight margin calls. "Futurama" suggests this will still be the case a thousand years from now.

In season three episode "The Luck of the Fryish", electron microscopes are used to separate a dead heat in a horse race at Flushing Downs. Unfortunately, not even quantum levels of accuracy are enough to stop punters from disputing the result. "No fair!" moans Professor Farnsworth. "You changed the outcome by measuring it!".

It's a neat practical demonstration of the Observer Effect, as a phenomenon that had already doomed Erwin Schrödinger's infamous cat also ruined Farnsworth's chances of winning big at the bookmakers.

Any schoolkid can create a Möbius strip with a piece of paper and some glue, but the mathematics behind these single-sided loops is truly intriguing. 

In season 10 episode "2-D Blacktop", Leela and Professor Farnsworth race each other around a Möbius dragstrip, and the circuit's unconventional geometry proves rather confusing when the competitors reach the finish line — on the wrong side of the track. 

"[There's] two more laps," says a rival street racer. "You forgot on a Möbius strip two laps is one lap." 

"You kids and your topology," laughs Dr Zoidberg in a refrain that was probably echoed by mathematicians everywhere.

(It's worth noting that the science here is considerably more plausible than the ridiculous high-octane physics that powers the "Fast & Furious" series.)

It's an unfortunate fact of 21st century life that there are many more movies and TV shows than we'll ever have time to watch. Spare a thought, then, for the residents of 31st century New New York, who are faced with literally infinite choice every time they head to the flicks. 

The ℵ0 in the name of futuristic cinema chain Loew's ℵ0-Plex refers to aleph-null, which — in mathematics — is the smallest infinite cardinal number. So while the screen count is on the low side when it comes to infinities, even the most completist cinephiles will struggle to reach the end of a playlist that includes "It Came From Planet Earth", "Planet of the Clams" and "Quizblorg, Quizblorg".  

Like Bart's weekly words of blackboard wisdom in "The Simpsons", the caption in "Futurama"'s opening credits changes from episode to episode. 

"What happens in Cygnus X-1 stays in Cygnus X-1" (from season seven's "The Prisoner of Benda") may look like a simple sci-fi-themed riff on the famous Las Vegas catchphrase, but there's more to the destination than initially meets the eye.

When it was identified in 1971, X-ray source Cygnus X-1 was widely regarded as the first black hole ever discovered, and subsequently became the subject of a bet between physicists Stephen Hawking and Kip Thorne (famously the scientific consultant on " Interstellar "). Hawking bet against black holes existing in this particular region of space, explaining in " A Brief History of Time " that "[the bet] was a form of insurance policy for me. I have done a lot of work on black holes, and it would all be wasted if it turned out that black holes do not exist. But in that case, I would have the consolation of winning my bet." 

Hawking did eventually concede the wager, which won Thorne a year's subscription to "Penthouse" magazine. Had Hawking won, he'd have received four years of satirical British mag "Private Eye".

This is another entry from "The Prisoner of Benda", and a rare example of pop culture not just referencing mathematics but enhancing it, too.

As well as being responsible for many of "Futurama"'s most memorable episodes, regular writer Ken Keeler holds a PhD in applied mathematics from Harvard. He applied this knowledge to devise an actual mathematical theorem (based on group theory) to explain a key plotline of the episode — namely that however many mind swaps are made between two characters, it's possible to ensure that everyone's mind is eventually reunited with its original body. 

This scenario will almost certainly never come up in real life, of course, but it's comforting to know someone's considered the mathematics, just in case.

At times real-life mathematics can be even stranger than the ideas "Futurama"'s writers come up with on screen. 

In season eight episode "Benderama", Professor Farnsworth invents the Banach-Tarski Dupla-Shrinker, a machine capable of creating two smaller copies of an object. The professor's motivation is simple — he wants smaller sweaters and more of them because he's shrinking and getting colder — but Bender sees the machine as an opportunity to duplicate himself. These duplicates then duplicate themselves into more duplicates, who duplicate themselves (ad infinitum) until the Earth is overrun by millions of tiny nano-Benders. 

The actual mathematics of the Banach-Tarski paradox is even weirder — and counterintuitive — than its fictional counterpart. The theorem states that a solid, three-dimensional ball can be broken down into a finite number of discrete elements that can then be reassembled to create two identical copies of the original ball. Presumably the show's writers surmised that unleashing infinite Benders of the same dimensions was too weird, even for "Futurama"'s science-literate audience. 

Season 12 of "Futurama" debuts on July 29 on Hulu in the US and Disney Plus in the UK, where you can also watch all of the previous seasons.  

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Richard's love affair with outer space started when he saw the original "Star Wars" on TV aged four, and he spent much of the ’90s watching "Star Trek”, "Babylon 5” and “The X-Files" with his mum. After studying physics at university, he became a journalist, swapped science fact for science fiction, and hit the jackpot when he joined the team at SFX, the UK's biggest sci-fi and fantasy magazine. He liked it so much he stayed there for 12 years, four of them as editor. 

He's since gone freelance and passes his time writing about "Star Wars", "Star Trek" and superheroes for the likes of SFX, Total Film, TechRadar and GamesRadar+. He has met five Doctors, two Starfleet captains and one Luke Skywalker, and once sat in the cockpit of "Red Dwarf"'s Starbug.  

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