phd maths duration

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.

PhD Program

More information and a full list of requirements for the PhD program in Mathematics can be found in the University Bulletin .

During their first year in the program, students typically engage in coursework and seminars which prepare them for the  Qualifying Examinations .  Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis. 

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

• real analysis
• geometry and topology
• applied mathematics

Course Requirements for students starting prior to Autumn 2023

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

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

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

Course Requirements for students starting in Autumn 2023 and later

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

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

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

Years 4&5

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

Throughout the PhD Program

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

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

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.

• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

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

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

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

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

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

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

Browse PhD Opportunities in Mathematics

Application of artificial intelligence to multiphysics problems in materials design, study of the human-vehicle interactions by a high-end dynamic driving simulator, physical layer algorithm design in 6g non-terrestrial communications, machine learning for autonomous robot exploration, detecting subtle but clinically significant cognitive change in an ageing population, how long does it take to get a phd in maths.

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

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

Additional Learning Modules

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

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

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

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

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

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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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.

Overview of the PhD Program

For specific information on the Applied Mathematics PhD program, see the navigation links to the right. 

What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the  Graduate Policies  pages. 

General Ph.D. Requirements

• 10 semester-long graduate courses, including at least 8 disciplinary.   At least 5 of the 10 should be graduate-level SEAS "technical" courses (or FAS graduate-level technical courses taught by SEAS faculty), not including seminar/reading/project courses.  Undergraduate-level courses cannot be used.  For details on course requirements, see the school's overall PhD course requirements  and the individual program pages linked therein.
• Program Plan (i.e., the set of courses to be used towards the degree) approval by the  Committee on Higher Degrees  (CHD).
• Minimum full-time academic residency of two years .
• Serve as a Teaching Fellow (TF) in one semester of the second year.
• Oral Qualifying Examination Preparation in the major field is evaluated in an oral examination by a qualifying committee. The examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in a chosen field and of assessing the student's ability to synthesize knowledge already acquired. For details on arranging your Qualifying Exam, see the exam policies and the individual program pages linked therein.
• Committee Meetings : PhD students' research committees meet according to the guidelines in each area's "Committee Meetings" listing.  For details see the "G3+ Committee Meetings" section of the Policies of the CHD  and the individual program pages linked therein.
• Final Oral Examination (Defense) This public examination devoted to the field of the dissertation is conducted by the student's research committee. It includes, but is not restricted to, a defense of the dissertation itself.  For details of arranging your final oral exam see the  Ph.D. Timeline  page.
• Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee, meet the standards of significant and original research.

Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

• a Secondary Field (which is similar to a "minor" subject area).  SEAS offers PhD Secondary Field programs in  Data Science and in  Computational Science and Engineering .   GSAS  lists  secondary fields offered by other programs.
• a Master of Science (S.M.) degree conferred  en route to the Ph.D in one of several of SEAS's subject areas.  For details see here .
• a Teaching Certificate awarded by the Derek Bok Center for Teaching and Learning .

SEAS PhD students may apply to participate in the  Health Sciences and Technology graduate program  with Harvard Medical School and MIT.  Please check with the HST program for details on eligibility (e.g., only students in their G1 year may apply) and the application process.

In Applied Mathematics

• First-Year Exploration
• Areas of Application
• AM & Economics
• How to Declare
• Who are my Advisors?
• Secondary Field
• Senior Thesis
• Research for Course Credit (AM 91R & AM 99R)
• AB/SM Information
• Peer Concentration Advisors (PCA) Program
• Student Organizations
• How to Apply
• PhD Timeline
• PhD Model Program (Course Guidelines)
• Oral Qualifying Examination
• Committee Meetings
• Committee on Higher Degrees
• Research Interest Comparison
• Collaborations
• Cross-Harvard Engagement
• Clubs & Organizations
• Centers & Initiatives
• Alumni Stories

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.  

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.

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PhD in Mathematics

The doctoral program in the Department of Mathematics offers the personalized attention of a small department while also providing a wide range of faculty who offer expertise to support dissertation research. The  graduate student environment  in the department is collaborative and rigorous, with many opportunities for mentorship, peer interaction and interdisciplinary opportunities across and outside the university.

PhD graduates go on to work as policy makers, consultants, data analysts, professors, researchers at internationally renowned institutions and much more. 

Prospective Students

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Teaching Assistantships and Funding

Full-time PhD students in mathematics are supported primarily through teaching assistantship (TA) positions. Students making acceptable progress in the PhD program are normally funded for at least five (and sometimes six) years.

While teaching assistant (TA) positions are usually offered to PhD students, master’s and part-time students are also invited to apply through the  Office of Graduate Student Assistantships and Fellowships website .

• A stipend in the form of a GW fellowship
• Tuition credits (up to nine credit hours per semester)
• A salary in exchange for teaching work

PhD students apply for teaching assistantships as part of the general GW application process. Applications to the doctoral program completed before February 1 will receive full consideration for TA positions.

The duties of TAs may include teaching a course, conducting recitations, assisting in a computer lab, holding office hours, grading homework and proctoring and grading exams. Such duties typically take about 15 hours per week. 

The graduate committee, in consultation with students' advisors, makes recommendations to CCAS for renewal of support; these recommendations are subject to the approval of the CCAS Associate Dean for Graduate Studies. Students making good progress toward earning a PhD and performing their teaching duties well usually receive at least five years of support. Requests for a sixth year of funding can be made when there is good evidence that the student is likely to complete the degree in the sixth year.

Several activities for new graduate students are held the week before the fall semester begins: 

• a  Graduate Teaching Assistant Program  (GTAP) orientation organized by the  GW Office of Graduate Student Assistantships and Fellowships ;
• an English test and interview for international students; and
• an orientation for mathematics graduate students, organized by the Department of Mathematics.

At the GTAP orientation, each new TA gives a five-minute sample presentation to a small group of peers and is evaluated for effective communication. All students, especially international students, are encouraged to discuss their presentation in advance with their academic advisor.

"I owe my success to my beginning days in the U.S. — to all the wonderful professors at GW. If not for their constant support, I would not have completed my PhD and all this would be moot!"

Sita Ramamurti PhD '95, 2020 Leo Schubert Teaching Award

Course Requirements

The following requirements must be fulfilled:

The general requirements stated under  Columbian College of Arts and Sciences, Graduate Programs .

The requirements for the  Doctor of Philosophy Program .

Pre-candidacy

Pre-candidacy requirements include satisfactory completion of 48 credits of coursework and achievement of a passing grade in the general examination.

After completing 36 credits of coursework, students may petition the graduate committee for approval to take MATH 6995 , but students may take no more than 12 credits in any combination of MATH 6995 and MATH 8999 in a single academic year.

Students wishing to take courses outside the department must petition and obtain the approval of the graduate committee.  The committee may limit the number of such courses that students take.

Subject to the approval of the graduate committee (requested via petition), students may take up to 12 credits of courses  offered by other institutions  in  the  Consortium of Universities of the Washington Metropolitan Area .   Students wishing to take such courses must petition and obtain the approval of the graduate committee.

Subject to the approval of the graduate committee (requested via petition) and the agreement of the instructor, students may take up to 12 credits from the following upper-level undergraduate courses for graduate credit, provided that additional graduate-level coursework is completed in these classes.

General examination

The general examination consists of two preliminary examinations. One examination is in two to four subjects selected from algebra, analysis, topology, and applied math, and the other is a specialty examination in a research area approved by the department.

Post-candidacy requirements

Post-candidacy requirements include the successful completion of an additional 24 credits of graduate coursework, including at least 6 credits of MATH 8999 ; the completion of the dissertation; and the successful defense of the dissertation in a final oral examination.

No more than 15 credits in any combination of MATH 6995 and MATH 8999 may be among the student's final 18 credits of required coursework.

Once a student successfully completes 24 post-candidacy credits, they must register for 1 credit of CCAS 0940  each subsequent fall and spring semester until they have successfully defended their dissertation, thereby completing the degree program.

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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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.

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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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.

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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.

Mathematics Education PhD

Doctor of philosophy.

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Admissions Information

Displaying requirements for the Spring 2025, Summer 2025, and Fall 2025 terms.

• Points/Credits: 75
• Entry Terms: Spring, Summer, Fall

Application Deadlines

Select programs remain open beyond our standard application deadlines , such as those with an extended deadline or those that are rolling (open until June or July). If your program is rolling or has an extended deadline indicated above, applications are reviewed as they are received and on a space-available basis. We recommend you complete your application as soon as possible as these programs can close earlier if full capacity has been met.

Application Requirements

Requirements from the TC Catalog (AY 2023-2024)

Displaying catalog information for the Fall 2023, Spring 2024 and Summer 2024 terms.

View Full Catalog Listing

Doctoral Degrees

All candidates for the Ed.D., Ed.D.C.T., or Ph.D. degrees are expected to demonstrate both mathematics and mathematics education competencies through a series of certification examinations taken upon the completion of 60 graduate points. Certification examinations test the student’s knowledge of current research and theory in mathematics education and mathematics content. Examinations are offered once in the fall, spring, and summer terms. Courses recommended as preparation for the examinations in mathematics education include MSTM 6037,  MSTM 4019, and other mathematics education courses; Courses recommended as preparation for the examinations in mathematics are 6000- level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Alternatively, they may register for advanced content courses and, with permission of the program, sit for the content area certification examination upon completion of the course. Incoming doctoral candidates should register for MSTM 6037 Professional Seminar in Mathematics during the first year of doctoral studies.

Doctoral students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Doctor of Philosophy in Mathematics Education

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree program requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Candidates are encouraged to develop an association with a faculty member early in their studies to identify a problem area of mutual interest to plan a course of studies that leads to the competencies needed to complete dissertation research and prepare for a professional role. Further details are available in the brochures on doctoral studies and in the general descriptions of doctoral programs available from the Office of Doctoral Studies (ODS).

A program of study for the Doctor of Philosophy degree must include at least 45 points taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 60 points in mathematics, mathematics education, statistics, and computing. At least 35 points should be in advanced courses – including research courses (MSTM 6500 or 6501 and MSTM 7500). (Any Teachers College course at the 6000 level or above, any Columbia University Graduate School of Arts and Sciences course with a “G” prefix, any “W” course numbered above 4000, or any transferred course with a graduate-level prerequisite will be considered an advanced course.) Further, 15 points in the philosophical, psychological, and curricular foundations of education must be included in every Ph.D. degree program. Students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Candidates for the Ph.D. degree are required to demonstrate competency in two languages chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the program to request one substitution. Students in mathematics may not use computer languages or statistics to satisfy the language requirement.

The Ph.D. dissertation is a scholarly study contributing new theoretical knowledge to the field and should be planned early in the program when sufficient advanced courses have been completed to permit the candidate to enroll in relevant research courses. Ph.D. dissertations in mathematics education should be (1) experimental studies in learning, (2) analytical studies in policy theory in mathematics education, or (3) other scholarly investigations of problems and issues of broad significance in the field.

The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.

• View Other Degrees

Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

Phone: (212) 678-3381 Fax: (212) 678-8319

Email: tcmath@tc.edu

Mathematics Education, PHD

On this page:, at a glance: program details.

• Location: Tempe campus
• Second Language Requirement: No

Program Description

Degree Awarded: PHD Mathematics Education

This transdisciplinary PhD program in mathematics education accommodates students from a variety of academic backgrounds. It provides students with a solid foundation in graduate-level mathematics as well as research skills and perspectives that enable them to incorporate mathematics into such core educational areas as:

Conducting individual and collaborative research in the learning and teaching of mathematics is an integral part of the program.

Degree Requirements

Curriculum plan options.

• 84 credit hours, a written comprehensive exam, an oral comprehensive exam, a prospectus and a dissertation

Required Core (12 credit hours) MTE 501 Research in Undergraduate Mathematics Education I (3) MTE 502 Research in Undergraduate Mathematics Education II (3) MTE 503 Research in Undergraduate Mathematics Education Ill (3) MTE 504 Research in Undergraduate Mathematics Education IV (3)

Electives (42 credit hours)

Area Courses (12 credit hours)

Research (6 credit hours) MTE 792 Research (6)

Culminating Experience (12 credit hours) MTE 799 Dissertation (12)

Additional Curriculum Information Four to five graduate-level (500 and above) elective courses from mathematics, cognitive science, psychology, educational technology, philosophy or research should be taken as approved by the advisor.

For the area courses, students are required to take four graduate-level courses from the following areas of interest: mathematics, applied mathematics or statistics. Students should see the academic unit for the approved course list.

Students should see the school's website for information about qualifier and comprehensive examinations based on math coursework.

The doctoral dissertation culminating experience consists of a dissertation prospectus, oral dissertation defense and the submission of a final revised, formatted dissertation document to the Graduate College. Dissertations are composed under chair- and committee-supervised research, including literature review, research, data collection and analysis, and writing.

When approved by the student's supervisory committee and the Graduate College, up to 30 credit hours from a previously awarded master's degree may be used for this program. If students do not have a previously awarded master's degree, the remaining coursework is made up of electives and research.

Admission Requirements

Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences.

Applicants are eligible to apply to the program if they have earned a bachelor's or master's degree in mathematics or a closely related area, with exceptionally high grades in advanced coursework in mathematics, from a regionally accredited institution.

Applicants must have a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in the last 60 hours of their first bachelor's degree program or a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in an applicable master's degree program.

All applicants must submit:

• graduate admission application and application fee
• official transcripts
• statement of education and career goals
• writing sample
• three letters of recommendation
• proof of English proficiency

Additional Application Information An applicant whose native language is not English must provide proof of English proficiency regardless of their current residency.

At least two of the letters of recommendation must be from faculty.

Next Steps to attend ASU

Learn about our programs, apply to a program, visit our campus, application deadlines, learning outcomes.

• Able to complete original research in applied mathematics.
• Able to incorporate mathematical concepts into novel teaching methods.
• Address an original research question in mathematics education.

Career Opportunities

Graduates of the doctoral program in mathematics education have opportunities in Arizona, the U.S. and internationally. Opportunities are typically at research universities and liberal arts colleges, community colleges, and education consulting firms and in roles such as:

• faculty-track academic
• education consultant or analyst
• mathematics professor, instructor or researcher

Program Contact Information

If you have questions related to admission, please click here to request information and an admission specialist will reach out to you directly. For questions regarding faculty or courses, please use the contact information below.

• [email protected]
• 480/965-3951

Alternatively, use our A–Z index

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Discover more about postgraduate research

PhD Pure Mathematics / Overview

Year of entry: 2024

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The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Other combinations of qualifications and research or work experience may also be considered. Please contact the admissions team to check.

Full entry requirements

Apply online

In your application you’ll need to include:

• The name of this programme
• Your research project title (i.e. the advertised project name or proposed project name) or area of research
• Your proposed supervisor’s name
• If you already have funding or you wish to be considered for any of the available funding
• A supporting statement (see 'Advice to Applicants for what to include)
• Details of your previous university level study
• Names and contact details of your two referees.

Programme options

Programme description

The The Department of Mathematics has an outstanding research reputation. The research facilities include one of the finest libraries in the country, the John Rylands University Library. This library has recently made a very large commitment of resources to providing comprehensive online facilities for the free use of the University's research community. Postgraduate students in the Department benefit from direct access to all the Library electronic resources from their offices.

Many research seminars are held in the Department on a weekly basis and allow staff and research students to stay in touch with the latest developments in their fields. The Department is one of the lead partners in the MAGIC project and research students can attend any of the postgraduate courses offered by the MAGIC consortium.

For entry in the academic year beginning September 2024, the tuition fees are as follows:

• PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500 International, including EU, students (per annum): Band A £28,000; Band B £30,000; Band C £35,500; Band D £43,000; Band E £57,000
• PhD (part-time) UK students (per annum): Band A £2393; Band B £3,500; Band C £5,000; Band D £7,250; Band E 12,250 International, including EU, students (per annum): Band A £14,000; Band B £15,000; Band C £17,750; Band D £21,500; Band E £28,500

Further information for EU students can be found on our dedicated EU page.

The programme fee will vary depending on the cost of running the project. Fees quoted are fully inclusive and, therefore, you will not be required to pay any additional bench fees or administration costs.

All fees for entry will be subject to yearly review and incremental rises per annum are also likely over the duration of the course for Home students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit the postgraduate fees page .

Always contact the Admissions team if you are unsure which fees apply to your project.

Scholarships/sponsorships

There are a range of scholarships, studentships and awards at university, faculty and department level to support both UK and overseas postgraduate researchers.

To be considered for many of our scholarships, you’ll need to be nominated by your proposed supervisor. Therefore, we’d highly recommend you discuss potential sources of funding with your supervisor first, so they can advise on your suitability and make sure you meet nomination deadlines.

For more information about our scholarships, visit our funding page or use our funding database to search for scholarships, studentships and awards you may be eligible for.

Contact details

Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality.  Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .

Programmes in related subject areas

Use the links below to view lists of programmes in related subject areas.

• Mathematics

Regulated by the Office for Students

The University of Manchester is regulated by the Office for Students (OfS). The OfS aims to help students succeed in Higher Education by ensuring they receive excellent information and guidance, get high quality education that prepares them for the future and by protecting their interests. More information can be found at the OfS website .

You can find regulations and policies relating to student life at The University of Manchester, including our Degree Regulations and Complaints Procedure, on our regulations website .

• Mathematics Education

Doctor of Philosophy (PhD)

Advance Your Career

The Ph.D. program emphasizes research and requires a written dissertation for completion. The program is individualized to meet the needs of graduate students. The student must develop, with the guidance from the major professor and committee, a program that is applicable to their background and interest. The average Ph.D. program requires 4-6 years beyond a master’s degree. The program is comprised of coursework in four major areas.

• Mathematics or a related area
• Cognate Area
• Research Core

This residential program has rolling admission . Applications must be fully complete and submitted (including all required materials) and all application fees paid prior to the deadline in order for applications to be considered and reviewed. For a list of all required materials for this program application, please see the “ Admissions ” tab.

July 1 is the deadline for Fall applications.

November 15 is the deadline for Spring applications.

March 15 is the deadline for Summer applications.

*Those applicants interested in being considered for any available PhD funding should submit completed applications by December 1 for the following Fall semester.

Program at a Glance

• Major/Department: Curriculum and Instruction
• Research Area: Mathematics Education
• Degree Objective: Doctor of Philosophy (PhD)
• Program Delivery: Residential
• Does this program lead to licensure? * No , this is a non-licensure program
• Application Deadlines: July 1 (Fall), November 15 (Spring), March 15 (Summer)

Start Your Giant Leap with One Small Step

Request Information

Mathematics Education Courses

15-18 credit hours

In mathematics education, students engage in courses that cover topics in the cognitive and cultural theories of learning and teaching mathematics, and the role of curriculum in mathematics education.

A three (3) course sequence is required that consists of:

• EDCI 63500 – Goals and Content in Mathematics Education
• EDCI 63600 – The Learning of Mathematics: Insights and Issues
• EDCI 63700 – The Teaching of Mathematics: Insights and Issues

In addition, students are encouraged to take (6 – 9) hours of EDCI 620: Developing as a Mathematics Education Researcher

Related Course Work

Minimum of 6 credit hours

All students should have appropriate course work in mathematics, statistics, educational technology, or a related field. Students without a master’s level background in mathematics may be required to take more courses in mathematics. This will be determined by the student’s major professor and advisory committee.

9 credit hours

Students will take three graduate courses in a self-selected cognate area. Cognate area selection should be discussed with the student’s major professor and advisory committee. Possible cognate areas include: mathematics, psychology, philosophy, sociology, technology.

Research Core Courses

15 credit hours

All doctoral students in the Department of Curriculum and Instruction must complete five (5) courses from areas in research methodology and analysis before beginning their dissertation:

• EDPS 53300 – Introduction to Research in Education
• EDCI 61500 – Qualitative Research Methods in Education
• STAT 51100 – Statistical Methods OR EDPS 55600 – Introduction to Quantitative Data Analysis
• EDPS 63000 – Research Procedures in Education
• Advance electives in either quantitative or qualitative methods

In addition to a submitted application (and any applicable application fees paid), the following materials are required for admission consideration, and all completed materials must be submitted by the application deadline in order for an application to be considered complete and forwarded on to faculty and the Purdue Graduate School for review.

A completed master’s degree is required prior to admission.

Application Requirements

Here are the materials required for this application

• Transcripts (from all universities attended)
• Minimum undergraduate GPA of 3.0 on a 4.0 scale
• 3 Recommendations
• Academic Statement of Purpose
• Personal History Statement
• Writing Sample
• International Applicants must meet English Proficiency Requirements set by the Purdue Graduate School

We encourage prospective students to submit an application early, even if not all required materials are uploaded. Applications are not forwarded on for faculty review until all required materials are uploaded.

How to Apply

When submitting your application for this program, please select the following options:

• Select a Campus: Purdue West Lafayette (PWL)
• Select your proposed graduate major: Curriculum and Instruction
• Please select an Area of Interest: Mathematics Education
• Please select a Degree Objective: Doctor of Philosophy (PhD)
• Primary Course Delivery: Residential

This program does not lead to licensure in the state of Indiana or elsewhere. Contact the College of Education Office of Teacher Education and Licensure (OTEL) at [email protected] before continuing with program application if you have questions regarding licensure or contact your state Department of Education about how this program may translate to licensure in your state of residence.

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Laura Bofferding

Amber brown, signe kastberg, rachael kenney, jill newton, questions contact the office of graduate studies at [email protected] ..

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Mathematics Education PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Mathematics Education

Discovery Day

Join us online on 21st August to learn more about postgraduate study at Edinburgh.

Find out more and register

Research profile

By joining the School of Mathematics, you will have opportunities to interact with educational research groups in Mathematics as well as cognate disciplines such as the Edinburgh Physics Education Group, and the interdisciplinary Centre for Research in Digital Education. As a research student you will be part of a vibrant and dynamic community of educators, with expertise in educational research and opportunities to develop and pursue your research goals. You can be certain of a rich academic setting with opportunities available for students to gain a breadth of knowledge from leading experts.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

• Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

Career opportunities

Graduates are expected to find employment in positions at public universities, private schools, community colleges, and vocational institutions to teach students at associates, bachelors, masters, or even doctoral level.

Due to their area of expertise, many graduates with a PhD in Mathematical Education will focus on training the next generation of teachers and educational support staff for secondary schools. 


There are many other potential career paths for holders of a PhD in mathematics, including finance and IT.

Entry requirements

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country
• English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

• Academic Technology Approval Scheme

If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees.

Scholarships and funding

Featured funding.

• School of Mathematics funding opportunities
• Research scholarships for international students

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

• your programme
• the duration of your studies
• your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

• UK government and other external funding

Other funding opportunities

Search for scholarships and funding opportunities:

• Search for funding

Further information

• Graduate School Administrator
• Phone: +44 (0)131 650 5085
• Contact: [email protected]
• Programme Director, Professor Chris Sangwin
• Phone: +44 (0)131 650 5966
• Contact: [email protected]
• School of Mathematics
• James Clerk Maxwell Building
• Peter Guthrie Tait Road
• The King's Buildings Campus
• Programme: Mathematics Education
• School: Mathematics
• College: Science & Engineering

Select your programme and preferred start date to begin your application.

PhD Mathematics Education - 3 Years (Full-time)

Phd mathematics education - 6 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 22 January 2024 will receive full consideration for funding. Later applications will be considered until all positions are filled.

• How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes:

IIT Bombay Department of Mathematics

The m.sc mathematics programme, ph.d admissions.

• You are here:

Admission to Ph.D programme in Mathematics and Statistics

2016 ). With state-of-the art infrastructural facilities and a sound research base, IITB Mathematics offers a Ph.D. programme in a wide variety of areas. The program leading to the Ph.D. degree involves a course credit requirement and a research project leading to thesis submission. All that you need to know about admissions to our PhD program can be found in the information brochure for PhD admissions, which can be found at the following link. ----- A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers a Ph.D. program in a wide variety of areas. To know more about the research interests of faculty members, please visit the page here . The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers Ph.D. program in the areas of Mathematics and Statistics. Admission to the PhD program is based on a written test and interview. There are separate written tests and interviews for students in Mathematics and Statistics. The syllabus is given below. Students are required to choose one option specifying either Mathematics or Statistics.

To know more about the research interests of faculty members, please visit the page here . The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

Syllabus for Entrance exam can be found here Past question papers can be found here

Syllabus for Mathematics Entrance Exam

Syllabus for Statistics Entrance Exam

Past Question Papers

PhD Admissions

Choose Colour

Chennai Mathematical Institute

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Teaching Tip: Giving Students Extra Time for Tests

Mathematics faculty members at Moorpark College piloted an intervention to increase allotted time for all students to complete math tests—and saw more students pass.

By  Ashley Mowreader

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Test anxiety can harm students’ academic success, but a new initiative at Moorpark College found that learners who have more time to take math tests perform better than their peers.

malerapaso/E+/ Getty Images 

Many college students struggle with math anxiety or test taking, which can make entry-level math courses even more challenging.

Administrators at Moorpark College in California were interested in understanding the relationship between students’ testing experience and how they performed in the class over all, so they piloted a testing intervention this past spring, asking professors to reduce test content or extend testing time.

The program saw more students pass the classes, with greater gains among historically disadvantaged students in math, including women and Black students. Survey data also highlighted students’ decreased anxiety around testing, the added ability to review mistakes and increased confidence making educated guesses.

The background: Early childhood education research points to the value of timed testing for math skills , such as multiplication tables, to build students’ skills and overall learning, but time pressure doesn’t benefit learners later on in higher education, explains Oleg Bespalov, dean of institutional effectiveness at Moorpark, part of the Ventura County Community College District.

One of the misconceptions around testing is that reduced content or extended time decreases the academic integrity or rigor of the assessment. Moorpark faculty members consider the initiative to be centered on a growth mindset, instead allowing students to grow from their mistakes and show full mastery of the content without unnecessary stress.

Further, while some careers do demand students to meet high-pressure deadlines, few of them require complex mathematics to be completed in under an hour, meaning the experience isn’t setting students up for future success, either.

To test this theory, Moorpark used grant funding to incentivize faculty to reimagine their assessments, by increasing testing time, decreasing the length of the test or both.

How Flexible Should Faculty Be?

Flexibility is a key desire among today’s college students, with recent survey results from Inside Higher Ed ’s Student Voice study finding 31 percent of learners want faculty members to be more flexible with deadlines and 25 percent want professors to use alternative grading practices.

The argument against flexibility, in addition to prioritizing faculty member’s time and workload, is that deadlines and structure promote student achievement and dropping them is a detriment to learning.

A recent study from Cornell University found flexible deadline policies that allowed students to submit assignments for no penalty around one to two weeks after the deadline gave students more agency with their schedule and helped them be less stressed.

How it works: The college put out a call to mathematics faculty members to join a community of practice. Professors were eligible to participate if they had taught the course before (allowing data collection both before and after) and received $1,250 per course they chose to revise. Eight faculty members opted in to the experiment in spring 2023.

Rena Weiss, a mathematics professor at Moorpark, was granted faculty release time to monitor innovations at projects in math courses at the college and oversaw the experiment, among others.

Funding Change

State law has reduced the availability of remedial courses at California public institutions , but not all students are academically prepared to enter college-level courses , requiring new and innovative kinds of interventions to promote student success in these classes.

The California Community College system allocated $64 million in one-time funding to support developmental education reform policies in the 2022 budget, which was allocated to colleges across the state to improve successful completion of transfer-level math and English courses. Moorpark College received $829,920.33 in funding, which covers this experiment and future iterations of it.

Faculty met monthly in their community of practice to share ideas, problems and data. There was no formal requirement for how testing had to change, other than it must reduce the amount of time pressure on students through shortening the test or lengthening time to complete it.

“We wanted this open-ended within your own teaching style—do what you think will provide more time per question for the student,” Weiss says.

To accommodate the extra time needed, many professors chose to partner with the testing center to deliver tests, allowing learners to complete their exam during one of two time slots that given week. This decision also freed up scheduled class time for additional teaching or test prep, Weiss says.

Claudia Gutierrez taught Math M10, Mathematics for Elementary Teachers, and opted to double students’ testing time from the usual 75-minute class period to 2.5 hours. Students completed their exams in the campus testing center, proctored by center staff. Gutierrez also taught a precalculus course that had both shorter exams and lengthened time for testing.

Faculty members made sure to maintain the rigor of their assessments, just making testing less lengthy.

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The impact: Across the 44 sections and 963 students in the experiment, students earned an A, B or C grade 4.4 percentage points more (56 percent), compared to their peers in traditionally taught courses and the same course taught the year prior. Women had a 9.1-percentage-point higher rate of passing the class, as well.

Moorpark’s data also pointed to a 26.9-percentage-point increase among Black students, but the experiment population was too small for the data to be statistically valid, says Oleg Bespalov.

In surveys, Gutierrez’s students said the additional time provided more time to review their test for mistakes, plus they were less rushed, had less testing anxiety and felt more confident in making educated guesses on multiple-choice questions.

This could be due to the extra time only, but Gutierrez also made sure to remind students that they had extra time to check their work and that there wasn’t pressure to be the first one done, helping make the environment more comfortable. The testing center option also allowed students with other responsibilities (such as work or caregiving priorities) to choose when to take their exam in a way that fit their schedules.

Looking ahead: Moorpark leaders plan to include additional math faculty members in a second phase of the experiment, providing similar stipends for first-time participants and smaller funds for returning professors.

While shortening the test did help students with their testing anxiety, Gutierrez says it created a downstream effect where there was more material she wanted to cover in later tests, so she’s looking to deliver tests more frequently to ensure all course content is assessed.

Leaders are also bracing to see if having more professors participate in the experiment creates a greater demand for the testing center, which in turn could lessen availability of that space.

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Career Prep Tip: Provide Resources for Undocumented Learners

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Math Department Announces 2024 Pólya and Osserman Awards

Clockwise from top left: Pranav Nuti, Haoya Li, Andrew Lin, and Nikhil Pandit

Stanford Mathematics is pleased to announce the 2024 recipients of the Pólya Teaching Fellow Award (Haoya Li and Pranav Nuti) and the Robert Osserman Teaching Award (Andrew Lin, Nikhil Pandit and Hannah Prausnitz-Weinbaum).

The Pólya Teaching Fellow Award is named in honor of George Pólya, Professor of Mathematics at Stanford from 1940 to 1953. This award honors at least one graduating PhD student each year for their outstanding teaching during their time in the program. 

The Robert Osserman Teaching Award is named in honor of Robert Osserman, Professor of Mathematics at Stanford from 1955 to 1990, and honors PhD students for outstanding contributions as a TA. 

The Pólya Teaching Fellow and Robert Osserman Teaching Awards consists of a $500 prize and certificate presented at the Mathematics Commencement ceremony, on Sunday, June 18, 2024.

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Inflation math is changing America's dinner plans

Alina Selyukh

KD Deshmukh says he recently celebrated his spouse's birthday with a salmon dinner at home. He also buys in bulk, clips coupons and has switched to more store brands to save money at the grocery store. Steven Pruitt hide caption

Higher prices have Americans reconsidering their dinner and coffee.

For the first time in years, people's grocery hauls are getting bigger. And many are choosing to splurge a bit at the supermarket over going out to eat, prompting fast-food and other chains to step up deals and meal combos.

This week, McDonald's reported its first decline in sales since the COVID-19 pandemic shutdowns of 2020. Sales at Denny's dipped 0.6% , and profit at Wendy's declined in the latest quarter. Starbucks sales fell 2% in the U.S. as people came in less often.

"When [restaurant inflation is] still ahead of where grocery inflation is," Denny's CEO Kelli Valade told investors this week, "we definitely feel like people are probably still saying, 'I should just cook at home a little bit more often.'"

Chipotle is 're-emphasizing generous portions' after social-media complaints

In the past year, grocery prices increased 1.1%, federal data shows , while the cost of restaurant meals grew 4.1%.

Choosing a grocery splurge over dinner out

Those price increases are much lower than in recent years. Yet they are layered on top of many past price hikes, which companies tend to blame on higher costs from wages, ingredients, packaging and transportation. Since mid-2020 , the cost of groceries has grown 19%, while restaurant prices have jumped almost 24%.

This has more shoppers recalibrating where they are willing to put extra dollars.

Take KD Deshmukh, an engineer in Tulsa, Okla., who has tightened his budget by buying more in bulk or with coupons and often switching from brand names to store brands. When deciding how to celebrate his spouse's birthday recently, the couple chose a trip to a higher-end seafood market for a homemade dinner over an outing.

Sticker shock: How the supermarket has become a potent symbol of inflation in America

"Instead of going to a restaurant," he says, "we were like, 'We are pretty good cooks — let's go splurge on a better piece of salmon that we know came in fresh.' And it's a bit of premium but definitely worth it."

Market research firm Circana has tracked this shift for months: While many shoppers are reaching for cheaper store labels, a growing number of them are also upgrading to premium brands.

"Because at least it's a little treat," says Circana's Sally Lyons Wyatt. "It's a little reward of — all right, I'm cutting back in these places, but at least I can have something that I perceive to be better quality, better taste, better experience" at home.

Prices at supermarkets are rising much slower than those at restaurants, and some prices are actually declining. Elijah Nouvelage/AFP via Getty Images hide caption

In fact, after years of shoppers getting less, even when spending more money at the grocery store, they are now leaving the supermarket with more items, Circana finds. At the same time, food purchases at cafes and other eateries have declined since the start of the year.

Some chains win — some chains lose

The impact on restaurants varies. Sit-down restaurants saw more diners in May and June compared with those months last year but came out flat in July, according to OpenTable's tracking of online reservations.

KFC, Arby's and Buffalo Wild Wings saw fewer visitors in July compared with last year, according to Placer.ai, which tracks foot traffic. Visits to Burger King, Wendy’s and Taco Bell increased.

Fast-casual chains — think Chipotle, Shake Shack, Panera — have benefited the most from the dinner reshuffle, as more people choose those chains' burritos, burgers and sandwiches over a pricier sit-down meal.

Inflation is pinching Americans — but they are still splurging on their pets

A similar trade-down is no longer helping McDonald's, which is losing business from inflation-wary lower-income families.

"They're dropping out of the market, eating at home and finding other ways to economize, cutting down on trips," McDonald's CEO Chris Kempczinski told investors . The chain still gets more higher-income customers, but "it's just not enough to offset the pressure that we're seeing on that low-income consumer."

McDonald's is extending its $5 meal deal through the summer, saying the offer is helping to draw more customers. Mario Tama/Getty Images hide caption

More deals to coax diners

McDonald's is now extending the run of its new $5 value meal through the summer and is doubling down on promotions like free fries for purchases through its app. Speaking to investors, executives didn't talk about lowering regular menu prices but called out the chain's own inflationary costs as reaching 20% to 40% around the world over recent years.

As restaurant chains present their financial reports, a focus on deals and value meals is a big theme. Starbucks has been offering discounts and meal combos more frequently.

Companies' quarterly earnings reports hint at possible relief from high prices

One priority for Starbucks is to "demonstrate our value by making sure customers believe that Starbucks experience is worth it every time," CEO Laxman Narasimhan told investors.

That's tricky now that more people are watching their going-out budgets. At the grocery store, the most common items people are upgrading on include wine, pasta sauce and pizza dough.

"The Italian night is still huge, especially the premium Italian night," says Circana's Lyons Wyatt. "That night, I don't think, will go away anytime soon."

NPR's Scott Horsley contributed to this report.

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Neeraj Chopra at Paris 2024 Olympics: Javelin throw schedule and event times for India

Picture by Getty Images

India’s Neeraj Chopra qualified for the men’s javelin throw final at the Paris 2024 Olympics with a season-best 89.34m throw at the Stade de France on Tuesday. He will now look to defend his title on Thursday.

The Indian javelin throw ace is the reigning Olympic and world champion in the event. At Tokyo 2020, the 26-year-old won the gold medal in men’s javelin throw and became the first Indian to ever medal in an athletics event at the Olympics.

Neeraj Chopra’s Olympic javelin throw event will be available to watch on live streaming and telecast in India.

At Paris 2024, javelin throw events, like all field events, is being conducted over two phases - the qualification round and the final medal round.

In the qualifying round, the field of 32 athletes was divided into two groups: A and B. Nine athletes secured direct entry to the final by meeting the pre-approved entry standard of 84m. The remaining three spots for the 12-man final were filled by the next-best performers.

Men’s javelin throw qualification groups at Paris 2024 Olympics

• Group A : Julius Yego (Kenya), Oliver Helander (Finland), Leandro Ramos (Portugal), Keshorn Walcott (Trinidad and Tobago), Kishore Jena (India), Teura'itera'i Tupaia (France), Julian Weber (Germany), Roderick Genki Dean (Japan), Alexandru Mihaita Novac (Romania), Dawid Wegner (Poland), Toni Keranen (Finland), Ihab Abdelrahman (Egypt), Curtis Thompson (USA), Patriks Gailums (Latvia), Pedro Henrique Rodrigues (Brazil), Jakub Vadlejch (Czechia)
• Group B : Neeraj Chopra (India), Gatis Cakss (Latvia), Max Dehning (Germany), Cameron McEntyre (Australia), Arshad Nadeem (Pakistan), Marcin Krukowski (Poland), Lassi Etelatalo (Finland), Nnamdi Chinecherem (Nigeria), Luiz Mauricio da Silva (Brazil), Moustafa Mahmoud (Egypt), Artur Felfner (Ukraine), Timothy Herman (Belgium), Anderson Peters (Grenada), Andrian Mardare (Moldova), Edis Matusevicius (Lithuania), Cyprian Mrzyglod (Poland)

Neeraj Chopra comfortably qualified for the javelin throw final with an 89.34m throw on his first attempt.

Neeraj Chopra at Paris 2024 Olympics: men’s javelin throw schedule

As per Indian Standard Time (IST)

Paris 2024 Olympics javelin throw final - order

• Jakub Vadlejch (CZE)
• Anderson Peters (GRN)
• Keshorn Walcott (TTO)
• Arshad Nadeem (PAK)
• Julian Weber (GER)
• Julius Yego (KEN)
• Lassi Etelatalo (FIN)
• Neeraj Chopra (IND)
• Andrian Mardare (MDA)
• Oliver Helander (FIN)
• Luiz Mauricio da Silva (BRA)
• Toni Keranen (FIN)

Neeraj Chopra came into the Paris 2024 Olympics having won the Federation Cup back home in India in May and the Paavo Nurmi Games in Turku in June. He came second at the Doha Diamond League, his first outing of 2024, with a then-season best of 88.36m.

While the Indian javelin star, who holds the national record of 89.94m, hasn’t been at his best, Neeraj has the habit of peaking on the big stage, just like he did at Tokyo 2020 and the 2023 World Championships in Budapest.

The biggest threat to Neeraj’s title defence, meanwhile, will stem from a familiar face - Czechia’s Jakub Vadlejch , the Tokyo 2020 silver medallist.

The 33-year-old, recently crowned the European champion, has been in Neeraj’s coattails in big-ticket events for the past few years, finishing behind the Indian at Tokyo 2020 as well as the 2022 and 2023 world championships.

However, he seems to have turned a corner since, having beaten Neeraj at the 2023 Zurich Diamond League before besting his Indian rival again in the Eugene finals to lift the trophy.

Vadlejch has also beaten Neeraj once this year, having finished above the Indian at the Doha Diamond League. Essentially, the Czech has had Neeraj’s number in their last three meetings.

Neeraj’s good friend and Pakistani rival Arshad Nadeem will also look to throw in a challenge for the grand title. He finished behind Neeraj to take silver from Budapest 23 but has proven himself a worthy threat.

Nadeem recently returned from injury and threw 84.21m at the Paris Diamond League but is a 90m thrower at his best, a mark Neeraj is yet to breach.

Julian Weber, the reigning European Games champion from Germany and world No. 3, has demonstrated remarkable consistency this year, delivering throws exceeding 85m in each event. He will be another top contender for the medal.

Two-time world champion Anderson Peters of Grenada has also been rediscovering his form slowly after injuries sustained during a mugging on a boat two years back. He failed to qualify for the finals at Tokyo but will hope to make amends in Paris.

Trinidad and Tobago’s Keshorn Walcott, the London 2012 Olympic champion and Rio 2016 bronze medallist, Kenya’s Julius Yego, silver medal winner from Rio 2016 and former world champion and European bronze medallist Oliver Helander of Finland will also be competing.

Fellow Indian Kishore Jena, who gave Neeraj a tough time at the Asian Games last year before settling for silver, was unable to qualify for the javelin throw final.

Where to watch Neeraj Chopra at Paris 2024 Olympics live in India

Live streaming of Neeraj Chopra’s Paris 2024 Olympics men’s javelin throw athletics events will be available on JioCinema. Neeraj Chopra’s Olympic match will be telecast live on the Network 18 TV channel in India.

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