open university maths phd

• My Account |
• StudentHome |
• TutorHome |
• IntranetHome |
• Contact the OU Contact the OU Contact the OU |
• Accessibility Accessibility

Postgraduate

• International
• News & media
• Business & apprenticeships

School of Mathematics and Statistics

Dynamic Forecasting in Dam Safety

Hard Disk Technology

Pharmacoepidemiology

Symbolic Dynamics and Aperiodic Order

New Horizons: Novel Aperiodic Materials

Algebraic Invariants in Symbolic Dynamics

Statistical Genetics

Complex Dynamics

Safety of Vaccines

Superoscillatory Imaging

Spectral Theory of Aperiodic Structures

Welcome to the school of mathematics and statistics.

• Study with us

• External Engagement

We are experts in distance learning, complemented by world-leading research in the mathematical sciences.

World-leading research

• Applied Mathematics and Theoretical Physics
• Combinatorics and Algebra
• Dynamical Systems
• History of Mathematics
• Mathematics Education
• Scholarship of Teaching and Learning

World-leading teaching

• Undergraduate study
• Postgraduate study
• Full- & part-time PhDs
• Graduate stories

Equality, Diversity and Inclusion

The School of Mathematics and Statistics is committed to ensuring equality, diversity and inclusion in all aspects of its work. We celebrate diversity in our students and staff, and we are active in challenging injustice and promoting equitable treatment for those from marginalised or under-represented groups. We constantly review and take action on issues surrounding fair access and representation. This includes, but is not restricted to, issues surrounding gender, ethnicity, LGBT+, neurodiversity, disability and accessibility, and socioeconomic status. In everything we do, we strive to achieve the Open University's vision of a fair and just society where:

• people are treated with dignity and respect
• inequalities are challenged
• we anticipate, and respond positively to, different needs and circumstances.

people picture source: https://unsplash.com/photos/nF8xhLMmg0c Red tiles picture source: https://unsplash.com/photos/mslrSX69KvQ Hard disk picture source: https://unsplash.com/photos/1iVKwElWrPA Safety vaccines picture source: https://unsplash.com/photos/FmrZ9-z4eVQ External engagement image source: https://unsplash.com/photos/J-Jb1niw1j0 Research image source: https://unsplash.com/photos/5fNmWej4tAA

The Open University

• Supported distance learning
• Funding your studies
• International students
• Global reputation
• Apprenticeships
• Develop your workforce
• Contact the OU

Undergraduate

• Arts and Humanities
• Art History
• Business and Management
• Combined Studies
• Computing and IT
• Counselling
• Creative Writing
• Criminology
• Early Years
• Electronic Engineering
• Engineering
• Environment
• Film and Media
• Health and Social Care
• Health and Wellbeing
• Health Sciences
• International Studies
• Mathematics
• Mental Health
• Nursing and Healthcare
• Religious Studies
• Social Sciences
• Social Work
• Software Engineering
• Sport and Fitness
• Research degrees
• Masters in Art History (MA)
• Masters in Computing (MSc)
• Masters in Creative Writing (MA)
• Masters degree in Education
• Masters in Engineering (MSc)
• Masters in English Literature (MA)
• Masters in History (MA)
• Master of Laws (LLM)
• Masters in Mathematics (MSc)
• Masters in Psychology (MSc)
• A to Z of Masters degrees
• Accessibility statement
• Conditions of use
• Privacy policy
• Cookie policy
• Manage cookie preferences
• Modern slavery act (pdf 149kb)

Follow us on Social media

• Student Policies and Regulations
• Student Charter
• System Status
• Contact the OU Contact the OU
• Modern Slavery Act (pdf 149kb)

© . . .

Our cookies

We use cookies for three reasons: to give you the best experience on PGS, to make sure the PGS ads you see on other sites are relevant , and to measure website usage. Some of these cookies are necessary to help the site work properly and can’t be switched off. Cookies also support us to provide our services for free, and by click on “Accept” below, you are agreeing to our use of cookies .You can manage your preferences now or at any time.

Privacy overview

We use cookies, which are small text files placed on your computer, to allow the site to work for you, improve your user experience, to provide us with information about how our site is used, and to deliver personalised ads which help fund our work and deliver our service to you for free.

The information does not usually directly identify you, but it can give you a more personalised web experience.

You can accept all, or else manage cookies individually. However, blocking some types of cookies may affect your experience of the site and the services we are able to offer.

You can change your cookies preference at any time by visiting our Cookies Notice page. Please remember to clear your browsing data and cookies when you change your cookies preferences. This will remove all cookies previously placed on your browser.

For more detailed information about the cookies we use, or how to clear your browser cookies data see our Cookies Notice

Manage consent preferences

Strictly necessary cookies

These cookies are necessary for the website to function and cannot be switched off in our systems.

They are essential for you to browse the website and use its features.

You can set your browser to block or alert you about these cookies, but some parts of the site will not then work. We can’t identify you from these cookies.

Functional cookies

These help us personalise our sites for you by remembering your preferences and settings. They may be set by us or by third party providers, whose services we have added to our pages. If you do not allow these cookies, then these services may not function properly.

Performance cookies

These cookies allow us to count visits and see where our traffic comes from, so we can measure and improve the performance of our site. They help us to know which pages are popular and see how visitors move around the site. The cookies cannot directly identify any individual users.

If you do not allow these cookies we will not know when you have visited our site and will not be able to improve its performance for you.

Marketing cookies

These cookies may be set through our site by social media services or our advertising partners. Social media cookies enable you to share our content with your friends and networks. They can track your browser across other sites and build up a profile of your interests. If you do not allow these cookies you may not be able to see or use the content sharing tools.

Advertising cookies may be used to build a profile of your interests and show you relevant adverts on other sites. They do not store directly personal information, but work by uniquely identifying your browser and internet device. If you do not allow these cookies, you will still see ads, but they won’t be tailored to your interests.

MSc in Mathematics

Open university, different course options.

• Key information

Course Summary

Tuition fees, entry requirements, similar courses at different universities.

Distance without attendance

Key information DATA SOURCE : IDP Connect

Qualification type.

MSc - Master of Science

Subject areas

Mathematics (General)

Course type

Advance your career with a high-level qualification. Delve deep into the aspects of pure and applied mathematics that interest you, choosing from areas such as fractal geometry, coding theory and calculus of variations. Choose from a wide range of modules. There are topics for not only mathematicians but mathematically inclined engineers and scientists. To conclude, you’ll complete an independent study, exploring a topic in detail and submitting a dissertation. Mathematics postgraduates can be found throughout industry, business and commerce, in the public and private sectors. Employers value the intellectual rigour and reasoning skills that mathematics students can acquire, their familiarity with numerical and symbolic thinking and the analytic approach to problem-solving which is their hallmark. There are a variety of reasons for studying mathematics at postgraduate level. You may want a postgraduate qualification in order to distinguish yourself from an increasingly large graduate population. You may find that your undergraduate mathematical knowledge is becoming insufficient for your career requirements, especially if you are hoping to specialise in one of the more mathematical areas, which are becoming more sought after by employers. Or you may want to move on to a PhD in Mathematics. The extent of opportunities is vast and mathematics postgraduates are equipped with skills and knowledge required for jobs in fields such as finance, education, engineering, science and business, as well as mathematics and mathematical science research.

UK fees Course fees for UK students

For this course (per year)

International fees Course fees for EU and international students

You should normally have a minimum of either: a 2:2 honours degree in mathematics or a 2:1 honours degree in a subject with a high mathematical content.

PGCE Primary with Maths

University of east london, phd/ mphil/ mres mathematics & statistics, university of strathclyde, mphil/phd in mathematics, manchester metropolitan university.

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. 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.

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.  

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

• Admission Policies
• Financial Support
• Ph.D. in Atmosphere Ocean Science
• M.S. at Graduate School of Arts & Science
• M.S. at Tandon School of Engineering
• Current Students

Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements .

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the  NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.

• My Account |
• StudentHome |
• TutorHome |
• IntranetHome |
• Contact the OU Contact the OU Contact the OU |
• Accessibility Accessibility

Postgraduate

• International
• News & media
• Business & apprenticeships
• Contact Contact Contact
• A to Z of courses
• Course types
• Masters degrees
• Postgraduate diplomas
• Postgraduate certificates
• Microcredentials
• Postgraduate modules
• Postgraduate distance learning
• Postgraduate qualifications
• Postgraduate entry requirements
• How will I study?
• Tutors and assessment
• Support, networking and community
• Disability support
• Fees and funding
• Postgraduate loan
• Credit or debit card
• Employer sponsorship
• Mixed payments

Credit transfer

• OU bursaries
• Grant funding
• Study costs funding
• Carers' Bursary
• Care Experienced Bursary
• Disability financial assistance
• STEMM bursary
• Over 60s bursary
• Creative Writing Scholarship
• Hayes Postgraduate Scholarship
• Disabled Veterans' Scholarships
• How to apply
• Research degrees
• Research areas
• Degrees we offer
• Fees and studentships
• Application process
• Being an OU research student
• Student views

• Credits measure the student workload required for the successful completion of a module or qualification.
• One credit represents about 10 hours of study over the duration of the course.
• You are awarded credits after you have successfully completed a module.
• For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
• Postgraduate Certificate in Mathematics

This certificate comprises two 30-credit modules from a wide choice. Tailor your study to areas that suit you. Develop problem-solving and decision-making skills relevant in business, commerce and industry. It’s also the first stage of our postgraduate mathematics programme – you can progress to the postgraduate diploma and MSc in Mathematics.

• Develops your problem-solving and decision-making capabilities
• A wide choice of modules enables you to tailor the course to your needs
• Helps you stand out in a crowded jobs market

This postgraduate certificate is the same as the first half of our Postgraduate Diploma in Mathematics (E23) and the first third of our MSc in Mathematics (F04)

How to register

Select the module you will study first, read the full description, and follow the instructions to register.

To gain this qualification, you need 60 credits as follows:

0–60 1  credits from:

You should note that the University’s unique study rule applies to this qualification. This means that you must include at least 20 credits from OU modules that have not been counted in any other OU qualification that has previously been awarded to you.

Learning outcomes, teaching and assessment

The learning outcomes of this qualification are described in four areas:

• Knowledge and understanding
• Cognitive skills
• Practical and professional skills

For this qualification, we do not allow you to count credit for study you have already done elsewhere.

On completion

On successfully completing this course, we’ll award you our Postgraduate Certificate in Mathematics. You’ll be entitled to use the letters PG Cert Maths (Open) after your name.

Regulations

As a student of The Open University, you should be aware of the content of the qualification-specific regulations below and the academic regulations that are available on our Student Policies and Regulations  website. 

We regularly review our curriculum; therefore, the qualification described on this page – including its availability, its structure, and available modules – may change over time. If we make changes to this qualification, we’ll update this page as soon as possible. Once you’ve registered or are studying this qualification, where practicable, we’ll inform you in good time of any upcoming changes. If you’d like to know more about the circumstances in which the University might make changes to the curriculum, see our Academic Regulations or contact us . This description was last updated on 19 March 2024.

You should normally have a minimum of either:

• a 2:2 honours degree in mathematics or
• a 2:1 honours degree in a subject with a high mathematical content.

If you don’t have such a qualification, your application will still be considered, but you may be asked to complete an entry test. Non-graduates will not normally be admitted.

Whatever your background, you should assess your suitability by completing our diagnostic quiz .

If you’re new to postgraduate study in mathematics, start with a single module: either the applied mathematics module Calculus of variations and advanced calculus (M820) or the pure mathematics module Analytic number theory I (M823) .

How long it takes

• Most students complete this qualification in two years, at the rate of one module per year.
• The minimum time you may complete this qualification in is one year.
• There’s no time limit for completing this qualification, but we can’t guarantee the same selection of modules will continue to be available.
• Some modules start only once every two years.

Career relevance

Mathematics is at the heart of advances in science, engineering and technology, as well as being an indispensable problem-solving and decision-making tool in many other areas of life. It is no surprise therefore that mathematics postgraduates can be found throughout industry, business and commerce, in the public and private sectors. Employers value the intellectual rigour and reasoning skills that mathematics students can acquire, their familiarity with numerical and symbolic thinking and the analytic approach to problem-solving which is their hallmark.

There are a variety of reasons for studying mathematics at postgraduate level. You may want a postgraduate qualification in order to distinguish yourself from an increasingly large graduate population. You may find that your undergraduate mathematical knowledge is becoming insufficient for your career requirements, especially if you are hoping to specialise in one of the more mathematical areas, which are becoming more sought after by employers. Or you may want to move on to a PhD in Mathematics. The extent of opportunities is vast and mathematics postgraduates are equipped with skills and knowledge required for jobs in fields such as finance, education, engineering, science and business, as well as mathematics and mathematical science research.

Careers and Employability Services have more information on how OU study can improve your employability.

Request your prospectus

Our prospectuses help you choose your course, understand what it's like to be an OU student and register for study.

Request prospectus

The Open University

• Study with us
• Supported distance learning
• Funding your studies
• International students
• Global reputation
• Apprenticeships
• Develop your workforce
• Contact the OU

Undergraduate

• Arts and Humanities
• Art History
• Business and Management
• Combined Studies
• Computing and IT
• Counselling
• Creative Writing
• Criminology
• Early Years
• Electronic Engineering
• Engineering
• Environment
• Film and Media
• Health and Social Care
• Health and Wellbeing
• Health Sciences
• International Studies
• Mathematics
• Mental Health
• Nursing and Healthcare
• Religious Studies
• Social Sciences
• Social Work
• Software Engineering
• Sport and Fitness
• Postgraduate study
• Masters in Art History (MA)
• Masters in Computing (MSc)
• Masters in Creative Writing (MA)
• Masters degree in Education
• Masters in Engineering (MSc)
• Masters in English Literature (MA)
• Masters in History (MA)
• Master of Laws (LLM)
• Masters in Mathematics (MSc)
• Masters in Psychology (MSc)
• A to Z of Masters degrees
• Accessibility statement
• Conditions of use
• Privacy policy
• Cookie policy
• Manage cookie preferences
• Modern slavery act (pdf 149kb)

Follow us on Social media

• Student Policies and Regulations
• Student Charter
• System Status
• Contact the OU Contact the OU
• Modern Slavery Act (pdf 149kb)

© . . .

PhD Program

During their first year in the program, students typically engage in coursework and seminars which prepare them for the  Qualifying Examinations .  Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis. Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics.

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

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

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry

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

Course Requirements for students starting in Autumn 2023 and later: 

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

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

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

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

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

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

© Stanford University . Stanford , California 94305 .

• The Open University
• Guest user / Sign out
• Study with The Open University

My OpenLearn Profile

Personalise your OpenLearn profile, save your favourite content and get recognition for your learning

Numbers, units and arithmetic

Course description

Course content, course reviews.

Do fractions and decimals make you apprehensive about maths? Do you lack confidence in dealing with numbers? If so, then this free course, Numbers, units and arithmetic, is for you. The course will explain the basics of working with positive and negative numbers and how to multiply and divide with fractions and decimals.

Course learning outcomes

After studying this course, you should be able to:

• write whole numbers and decimals in place-value columns and compare their sizes
• multiply and divide whole numbers and decimals by 10, 100, 1000 and so on
• indicate given fractions on a diagram and find equivalent fractions for a given fraction
• mark numbers on a number line
• choose appropriate units for a given purpose.

First Published: 21/12/2012

Updated: 10/05/2019

Rate and Review

Rate this course, review this course.

Log into OpenLearn to leave reviews and join in the conversation.

Create an account to get more

Track your progress.

Review and track your learning through your OpenLearn Profile.

Statement of Participation

On completion of a course you will earn a Statement of Participation.

Access all course activities

Take course quizzes and access all learning.

Review the course

When you have finished a course leave a review and tell others what you think.

For further information, take a look at our frequently asked questions which may give you the support you need.

About this free course

Become an ou student, download this course, share this free course.

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• CORRESPONDENCE
• 02 April 2024

How can we make PhD training fit for the modern world? Broaden its philosophical foundations

• Ganesh Alagarasan 0

Indian Institute of Science Education and Research, Tirupati, India.

You can also search for this author in PubMed   Google Scholar

You have highlighted how PhD training assessment has stagnated, despite evolving educational methodologies (see Nature 613 , 414 (2023) and Nature 627 , 244; 2024 ). In particular, you note the mismatch between the current PhD journey and the multifaceted demands of modern research and societal challenges.

Access options

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

24,99 € / 30 days

cancel any time

Subscribe to this journal

Receive 51 print issues and online access

185,98 € per year

only 3,65 € per issue

Rent or buy this article

Prices vary by article type

Prices may be subject to local taxes which are calculated during checkout

Nature 628 , 36 (2024)

doi: https://doi.org/10.1038/d41586-024-00969-x

Competing Interests

The author declares no competing interests.

Related Articles

See more letters to the editor

• Research management
• Scientific community

Ready or not, AI is coming to science education — and students have opinions

Career Feature 08 APR 24

After the genocide: what scientists are learning from Rwanda

News Feature 05 APR 24

The neuroscientist formerly known as Prince’s audio engineer

Career Feature 14 MAR 24

Female academics need more support — in China as elsewhere

Correspondence 16 APR 24

Citizenship privilege harms science

Comment 15 APR 24

Brazil’s postgraduate funding model is about rectifying past inequalities

Correspondence 09 APR 24

How we landed job interviews for professorships straight out of our PhD programmes

Career Column 08 APR 24

How two PhD students overcame the odds to snag tenure-track jobs

Adopt universal standards for study adaptation to boost health, education and social-science research

Correspondence 02 APR 24

Computational Postdoctoral Fellow with a Strong Background in Bioinformatics

Houston, Texas (US)

The University of Texas MD Anderson Cancer Center

Locum Associate or Senior Editor (Immunology), Nature Communications

The Editor in Immunology at Nature Communications will handle original research papers and work on all aspects of the editorial process.

London, Beijing or Shanghai - Hybrid working model

Springer Nature Ltd

Assistant Professor - Cell Physiology & Molecular Biophysics

Opportunity in the Department of Cell Physiology and Molecular Biophysics (CPMB) at Texas Tech University Health Sciences Center (TTUHSC)

Lubbock, Texas

Texas Tech University Health Sciences Center, School of Medicine

Postdoctoral Associate- Curing Brain Tumors

Baylor College of Medicine (BCM)

Energy AI / Grid Modernization / Hydrogen Energy / Power Semiconductor Concentration / KENTECH College

21, Kentech-gil, Naju-si, Jeollanam-do, Republic of Korea(KR)

Korea Institute of Energy Technology

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

US News & World Report Releases 2024 Rankings Of America’s Best Grad Schools

Texas A&M University is one of the nation’s leaders in graduate education, according to the latest rankings from U.S. News & World Report.

The university has 33 programs in the Top 50 spanning across agriculture, business, computer science, education, health, law, political science, public affairs, psychology, science, and veterinary medicine. U.S. News announced this week that the release of rankings for engineering, medical and clinical psychology will be delayed.

In its Best Graduate Schools ranking, the publication placed 10 of Texas A&M’s graduate programs in the Top 20; among those, six are Top 10:

College of Arts and Sciences

• Industrial and organizational psychology, No. 7 (No. 6 public)
• Inorganic chemistry, No. 5 (No. 2 public, No. 1 in Texas)
• Nuclear physics, No. 7 (No. 6 public, No. 1 in Texas)

School of Law, overall No. 26

• Dispute resolution, No. 5 (No. 3 public, No. 1 in Texas)
• Intellectual property, No. 6 (No. 2 public, No. 1 in Texas)

School of Veterinary Medicine and Biomedical Sciences, overall No. 10 (No. 9 public, No. 1 in Texas)

According to U.S. News , the rankings are based on expert opinion on program excellence and statistical indicators that measure the quality of a school’s faculty, research and students. Texas A&M currently enrolls 16,762 graduate and professional students (fall 2023), in more than 170 master’s, 94 doctoral and five professional degree programs.

“I’m so proud of our graduate students, the world-class faculty who mentor them and the outstanding programs that set them on a path to success in their chosen fields,” said Gen. (Ret.) Mark A. Welsh III, president of Texas A&M University. “Post-graduate education at Texas A&M contributes immeasurably to our research enterprise and our teaching and service missions. Congratulations to the students, faculty and staff whose work is reflected not just in rankings, but each and every day on our campuses and in the world at large.”

Texas A&M School of Law in Fort Worth, which has seen a remarkable rise in the U.S. News rankings, this year rose three spots overall, an increase of 57 spots in five years.

The Bush School of Government and Public Service, which ranks No. 26 overall in public affairs, has seen gains this round in non-profit management, up six places to No. 21. “The Bush School continues to make strides as a world-class Public Affairs school,” said Frank B. Ashley III, interim dean. “Employers know that graduates of our Public Service and Administration program are career-ready leaders with a passion for public service.”

Other notable rankings include:

• Analytical chemistry, No. 11 (No. 10 public)
• Applied mathematics, No. 13 (No. 6 public)
• Legal writing, No. 11 (No. 7 public, No. 1 in Texas)
• Marketing, No. 29 (No. 9 public)
• Management, No. 27 (No. 11 public)
• Statistics, No. 13 (No. 7 public, No. 1 in Texas)

View the full rankings for Texas A&M here and review the U.S. News methodology here .

Related Stories

Texas A&M Announces 2024-25 Parents Of The Year

Jacqueline and Kristopher Knoop are pillars of the Aggieland community.

Fund Started For Campus Ski Slope, Out Of Commission Due To Storm Damage

For decades on the otherwise flat lands of College Station, Mt. Aggie rose above to offer ski classes, until it was destroyed by a windstorm.

Texas A&M Names Head Yell Leader 

Jake Carter, a junior management student, will guide the 2024-25 Yell Leaders. 

Recent Stories

Texas A&M Facility To Enhance Advanced Manufacturing Workforce

Gov. Greg Abbott joined leaders from the Texas A&M System and the Rio Grande Valley area for a groundbreaking ceremony.

Texas A&M Names Josh Brewton ’27 As Newest Handler For Reveille X

Cadet from Cedar Park, Texas, will serve as the primary caretaker for the university’s official mascot.

Subscribe to the Texas A&M Today newsletter for the latest news and stories every week.