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Doctor of Philosophy in Mathematics

Department of Mathematics

Note: Students in this program can choose to receive the Doctor of Philosophy or the Doctor of Science in Mathematics. Students receiving veterans benefits must select the degree they wish to receive prior to program certification with the Veterans Administration. 

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Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

• The firm deadline for applications for Autumn 2025, is December 5, 2024.
• The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

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.

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.

• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

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

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

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

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

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

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

Browse PhD Opportunities in Mathematics

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

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

Additional Learning Modules

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

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

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

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

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

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

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

Tips to Consider when Making Your Application

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

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

How Much Does a Maths PhD Typically Cost?

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

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

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

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

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

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

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

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

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

What Jobs Can You Get with A Maths PhD?

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

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

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

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

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

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

How Much Can You Earn with A PhD in Maths?

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

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

Academic Lecturer

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

Actuary or Finance

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

Aerospace or Mechanical Engineering

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

Data Analyst

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

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

Facts and Statistics About Maths PhD Holders

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

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

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

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

Ruth Lawrence

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

Emmy Noether

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

Other Useful Resources

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

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

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

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

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

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

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

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

Browse PhDs Now

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Join thousands of other students and stay up to date with the latest PhD programmes, funding opportunities and advice.

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

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• Secondary Field
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School of Science

Mathematical sciences, ph.d in mathematics.

Exploring New Theories at the Forefront of Mathematics and its Applications

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

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

Program of Study

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

Requirements

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

The student’s program of study must include:

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

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

The program catalog can be found here .

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

Program Outcome

Students who successfully complete this program will be able to:

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

Financial Aid

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

Fellowships

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

Teaching Assistantship

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

Research Assistantship

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

Academic Opportunities

Graduate Academic Awards

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

SIAM Student Chapter at RPI

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

Amos Eaton 301

110 8th Street

Troy, NY 12180

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PhD in Mathematics

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

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

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

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

In addition to the above, PhD students often:

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

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.

Study Postgraduate

Content blocks, explore our phd in mathematics.

3 to 4 years full-time

3 October 2022

Mathematics Institute

University of Warwick

The PhD in Mathematics offers an intellectually stimulating and dynamic atmosphere research in both pure and applied mathematics. Study at the University of Warwick's Mathematics Institute, ranked 3rd in the UK in REF 2014, an international centre of research excellence.

Mathematics at Warwick covers a full range of both pure and applied areas. The Mathematics Postgraduate Degrees are appropriate for students with a strong and broad mathematical background who wish to continue to focus on primarily mathematical questions in their postgraduate work.

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

Teaching and Learning

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

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

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

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

First Class integrated MA, MMath or MSc degree in Mathematics or a science degree with high mathematical content.

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

There are no additional entry requirements for this course.

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

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Advice and Resources for Mathematics Graduate Students

Advice for beginning Math PhD Students

• Familiarize yourself with the requirements for the Math PhD program by clicking around our math department website. For now, focus on the “Stage I” requirements . Most students are in Stage I for one to two years.
• Your main goal as a Stage I student is to master the material in the three core areas: topology, algebra, and analysis. The “alpha courses” are designed to help you meet this goal. These are Math 591, 592 (topology), Math 593, 594 (algebra) and Math 596, 597 (analysis) . [If you are inclined toward applied math, there is an option to substitute Applied Analysis (Math 556, 572) for  topology or algebra.]
• Make a plan now for achieving this goal. Remember that every student is different! Your office mate with a Master’s degree may pass some QR exam immediately upon arrival. However, another may choose to take alpha courses in topology and analysis this year and save algebra for year two. Both are reasonable plans likely to lead to timely completion of Stage I.
• Our department publishes a list of graduate courses offered each semester. Read and admire these courses, but do not let them entice you away from the goal of Stage I: to master the material of the three core areas.
• You will be assigned a doctoral committee advisor, whom you will meet in August. Come prepared to that meeting with your tentative plan for and/or questions about completing Stage I. Your advisor will help you choose courses and refine your plan.
• Usually, the only good reason to skip an alpha course is that you have passed the QR Exam in the corresponding subject. In some cases, a student might substitute certain “beta” courses (600 level). For example, a student who has solved many hard problems in a graduate course on the same topics as Math 593 might substitute Math 614 for Math 593 and plan to take Math 594 in the winter.
• Be ambitious, but reasonable and flexible. If you are tempted to take all three QR exams upon arrival in August, go for it! Adjust your plan after getting the results.
• First year students should generally avoid “topics courses” ( most 700 and some 600 level courses ), intended primarily for PhD candidates. These courses are more specialized and may not prepare you as well for writing your PhD . Take courses where you will turn in regular assignments, bond with your peers over difficult problems, and allow your professors to get to know you mathematically.
• Remember that you are also adjusting to teaching! Taking two intense courses of your own, with problem sets and exams, may be enough. Four demanding courses plus teaching is not recommended.
• Revisit and revise your plans and goals regularly. It is wise to take QR exams as soon as you think you have a chance of passing. There is no penalty for failing, as long as you pass by the deadline.
• Looking ahead, the main goal of a Stage II student is to find a dissertation advisor. We will help you! Although you should not worry about this yet, it is never too early to get to know professors and older students, both mathematically and personally. Similarly, it is never too early to keep an eye on the  Seminar Offerings   or get involved once you feel adjusted and ready.  Start  by attending Junior Colloquium , at the very least.

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• Opportunities to teach in LSA’s Program for Computing in the Arts and Sciences (PCAS) April 23, 2024
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How challenging experiences led me to pursue a PhD in Mathematics by Shanise Walker

As a student graduating high school, I was convinced of one thing: I was going to be a high school mathematics teacher. Everything I had done in high school and the inspiration and encouragement I received from teachers, family, and friends helped me feel reassured that my decision was the right one. As a high school student, I excelled in every subject, but doing mathematics was a passion. My love for mathematics led me to tutoring both middle school and high school students in mathematics, participating in mathematics competitions, and learning about other areas of mathematics outside of the curriculum. I had even earned the highest achievement award every year for mathematics in my grade level, so being a high school mathematics teacher seemed like the perfect choice for me.

As an undergraduate student, I immediately declared that I wanted to be a mathematics education major. Although I would have to be accepted into the program, I was sure of my choice in major. Completing the requirements to get into the program were easy because I was eager to be a math teacher. For the first few years of undergrad, things were going well. I added the mathematics major to my degree program and became a double major in mathematics and mathematics education. I was accepted into the mathematics education program and was set on my goals; everything was going well.

Fast forward to the spring semester of junior year, something changed. While taking a math education course focused on technology in the classroom, I found myself in a situation that I could not explain and one that could not be explained to me at the time. One of the first assignments in the course was to write an argumentative essay on technology in the classroom and its benefits or hindrances. When I wrote my essay, I focused my attention on the hindrances and how too much technology could lead students to rely heavily on devices and not enough on understanding the concepts. In the end, I received a low score on this assignment and when I inquired about the low score, the teaching assistant responded, “It’s just wrong.” This was just the beginning of a long battle of receiving low grades because “it’s just wrong.” Those words haunted me, so I stopped inquiring and just accepted the grades. I received lower grades than my peers, even on assignments where we had the same answers. I really disliked going to that class, but I knew I needed to finish the course because it was a requirement for my mathematics education degree. The real test came during the group final project. The project consisted of a group paper and a class demonstration on teaching a math topic to students. For the group paper, my group scored near perfect, but on the class demonstration, I scored significantly lower than my classmates. My group members and I did not understand it since I had written over half of the group paper and the project idea was one that I had brought to the group. I spent countless hours working on this project only to get near perfect or perfect grades on the group graded portion of the project but a low grade on my individual portion.

After receiving the group project grade, I had had enough. I decided to meet with the instructor of the course about my grades and my displeasure with the course. During our meeting, I asked the instructor to explain to me why my grades were much lower than classmates, especially on assignments where we had the same answers. It was then that I learned that this was not about my work, but about who I am. The professor outright admitted that the teaching assistant had given me lower scores because I was Black. The professor was already aware of the situation and had been for semesters before I became a student in his course. It had happened to other Black students who had taken the course before me. I was given assurance that while my grades were low, my final grade would not be. When I left that meeting, I cried. I was angry. While I knew that the particular teaching assistant would not be a grader for any other courses I would take in the major, I felt that I no longer had a place of belonging in that major. Despite feeling like I didn’t belong, I still had a passion for teaching high school mathematics, so I was determined to complete the degree.

The determination to continue with my mathematics education degree would change while I was a participant in an 8-week summer REU mathematics program. When I arrived at the REU program, I had no knowledge of how to conduct mathematics research and I was also unsure of what exactly I would be researching. However, with good mentorship from my research mentor and a postdoctoral student (now a tenured faculty member), I found myself interested in mathematics beyond teaching it. I was interested in solving math problems and I found that sense of community during the REU program that was lacking in my home department. Within the first few weeks of the REU program, I had decided that I wanted to get a PhD in mathematics–a thought I had not had before. My research mentor gave me advice on preparing and applying to graduate school. I took the advice and applied for PhD mathematics programs.

When I returned to my university the fall after the REU program, I was still pursuing a double major in mathematics and mathematics education. I knew that I had only one semester of coursework before I would be student teaching, but there was some unrest in me in continuing my mathematics education degree. I had just come from spending an entire summer doing math research, and I had this motivation in me to pursue a PhD. A week before classes started, I dropped my remaining mathematics education courses. After dropping the courses, I found myself in the position of being able to graduate at the end of the semester since I needed only one mathematics course and one elective course in a certain area to graduate. However, I decided I wanted to stay the entire senior year, so I enrolled in two mathematics courses and other electives.

While I dropped my mathematics education courses, I did not immediately drop my mathematics education major because I was still a bit torn about the idea of perhaps not being able to teach high school mathematics. However, before the fall semester ended, I went for it. I dropped the major and pursued my newfound interest of getting a PhD in mathematics. I started on a research project with a faculty member in the mathematics department and began submitting applications for graduate school. I submitted a number of applications for PhD in mathematics programs before the Thanksgiving break, so everything was going well.

In the spring of my senior year, I had another incident that solidified my pursuit of a mathematics PhD. I attended a graduate school fair at my institution to learn about other graduate programs at other institutions. While doing so, I stumbled upon a master’s program in mathematics education and thought to myself: “Well, maybe I could get my teaching certification while in this program because after all, I still had a passion to teach high school mathematics.” The program was at an institution close to my hometown, so that also meant that I would be able to spend more time with my family. The deadline to apply to the master’s program had not yet passed, so I thought to myself I would give it a shot. I spoke with the program’s representative, and we discussed the program and my GRE scores. She told me that I would likely get into the program with probationary status due to my GRE composite score. When I told her I had already been accepted into PhD programs in mathematics, there was a bit of shock on her face (and I am sure on mine as well). What I knew to be true was that my GRE Verbal Reasoning score was not as high, but I had done well on the GRE Mathematics portion. The composite score missed the mark for their institution to be granted full admission, so with this information in mind, I did not apply to the program. I continued with my plan to get a PhD in mathematics and finally decided that teaching high school mathematics was not the best fit for me. The following fall, I went off to graduate school, pursuing a mathematics PhD program at the same institution I had done the REU. Six years later, I completed the program and earned a PhD in mathematics.

Now, as I write about this experience almost ten years later, for the first time I ask myself, “How can eight weeks change the whole course of your life?” This is exactly what the REU program did for me. It changed the course of my life. It gave me a mathematical experience that I had not encountered before. It provided me with the mentorship I needed to succeed and gave me a sense of belonging in the mathematics community that I had not felt before. It also provided me with motivation to pursue something different–a doctoral degree. For this, I am grateful.

Two years ago, I had an opportunity to fulfill my passion of teaching high school mathematics. I taught calculus to a group of underrepresented minority students at a STEM summer program for high school students. This experience was just as joyful as I thought it would be, and I will always cherish it.

1 Response to How challenging experiences led me to pursue a PhD in Mathematics by Shanise Walker

Hi, I’m really inspired by your passion ,persistence and clarity to stick on to take up mathematics at research level. Currently I’m doing my ph. D program in management in India. But having graduated in bachelor’s degree in maths, I now have ardent desire to continue my masters and then proceed to do ph. d in maths. Though it’s 30 years since I lost touch, your life story is still furthering my passion. Thanks and a nice flow of narrative. Regards, Soundra

Comments are closed.

Opinions expressed on these pages were the views of the writers and did not necessarily reflect the views and opinions of the American Mathematical Society.

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If you want to do a PhD in mathematics, how important is it to start immediately after finishing undergraduate studies?

I'm about to finish my undergraduates studies; I majored in mathematics and minored in physics, and I always intended on going to grad school to pursue a PhD in mathematics, but I've been having doubts recently. I did well in all my courses (3.92 GPA), but I'm trying to seriously consider if my background is strong enough now and if I'd truly have the motivation to stick it out. I've also been thinking even if I decided to give it a shot, it might be nice to take some time off for rest and to improve on some of my weaker areas. But I've been told by a few people that if you want to do a PhD in mathematics, you have to go pretty much right after undergrad , mainly because recent letters of recommendation are so important, and professors forget you after a time. So I wanted to know if this is true , and also thought I'd ask for advice if anyone has been in a similar situation.

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• 12 Why do you want a phd? What career do you want to have? If you're questioning your resolve it probably is not a good idea. –  David Peterson Commented Dec 17, 2014 at 23:57
• 4 If you're questioning your resolve it probably is not a good idea. Lots of people who question whether a PhD is right for them (or their careers later) do very well in academia. –  Kimball Commented Dec 18, 2014 at 2:44
• 13 Lots of people who question whether a PhD is right for them (or their careers later) do very well in academia after they find an answer . –  JeffE Commented Dec 18, 2014 at 6:03
• "time off ... to improve on some of my weaker areas". Natural impulse, but I've seen this described several times as a fallacy. Generally speaking the best place to work on your weaker areas is in a university , not on a year out. The logic of taking time to rest follows (although IIRC some institutions including Cambridge still think it's not wise, and advise strongly against it for mathematicians). But the logic of taking time off from studying mathematics to get better at mathematics (normally) doesn't! –  Steve Jessop Commented Dec 18, 2014 at 10:21

5 Answers 5

The other answers don't really address the issue of recommendations, so let me, at least briefly. I've been on our math PhD admission committee several times and we get many applications from people who've gotten their undergrad some time ago.

First, yes there is some truth to it being easier to get in right after your undergrad degree. The letters of recommendation are important. If your professors know you quite well, and the department is relatively small, they should still be able to write you decent letters after a year or two hiatus, but if it gets to 5-10 years, they may not, and with that kind of time lapse, their letters won't count for as much anyway.

My advice would be to consider what else you want to do. Is there something else you really want to do for awhile (peace corps, travel, interesting job opportunity)? If so, it won't kill your chances for grad school, but you may have to apply to more backup schools. If you're out for longer, it might be best to do a masters first before getting into a PhD program.

If you don't have any definite ideas, why don't you try applying to a few masters programs (Vladhagan's suggestion of trying a masters first is a good idea to give you a sense of what you want to do and give yourself a better background) and a few PhD programs that seem interesting to you? At the same time, maybe go to a career fair and send out a few job applications in the spring? The PhD programs that accept you (at least if you're in the US) at least should give you an opportunity to visit, so even if you're undecided about a PhD in the spring, visiting these schools (and similarly any job interview impressions) may help you make a decision.

• Wait, do I understand correctly that in the US you can start your PHD straight after your bachelor/undergraduate program? –  David Mulder Commented Dec 18, 2014 at 12:41
• 3 @DavidMulder: Yes, that's correct (at least in math and most fields I know), but typically graduate level masters work is built-in to the PhD program, so it usually takes 5-6 years in math. –  Kimball Commented Dec 18, 2014 at 13:01

But I've been told by a few people that if you want to do a PhD in mathematics, you have to go pretty much right after undergrad, mainly because recent letters of recommendation are so important, and professors forget you after a time.

You do not have to start a PhD program "pretty much right after undergrad". It is most common to do so, but there is a substantial minority of students who are older and/or spent several years out of school. In (American, at least) academia, your age counts for nothing; the ticking clock in the sky keeps track of the number of years since your PhD. I know several people who spent years off from undergrad in the sense of leaving school but clearly kept up with their mathematical reading and learning -- while in the Israeli army, culinary school, creative writing programs... -- and started grad school with skills at least at good as those around them and a maturity that most 22 year-olds lack. I've looked through hundreds verging on thousands of job applicants' CVs, and I am struck by how often the stronger candidates were in their 30's rather than their 20's when they got their PhD.

Of course the biggest risk in taking time off between undergrad and grad is that you will get distracted by the rest of the world and not come back for graduate study. But that's only a risk in the context of your original plan: if you found something else that you like better than being a graduate student, good for you. It is also relatively common that after a fairly small time away -- one or two years -- people realize that they really do prefer an academic career. (For some reason this seems to be most common among high school teachers. Isn't that a bit sad?) If you're not totally committed to a PhD program, taking time off and seeing whether your desire waxes or wanes is a pretty smart idea.

Of all things in your decision, I don't think that going straight to a PhD program because you're worried that your professors will forget about you is a good strategy. Professors don't forget about students that quickly, but after a few years, they may. To combat this, I would say: if you are not sure whether you want to do a PhD right away, why not apply right away to PhD programs? Certainly knowing where you can get in and seeing the programs that admitted you are all factors in your decision. If you apply right away, professors will write letters for you, and if you go away even for a long time, those letters should still be equally usable afterwards: your past undergraduate performance is not a function of time.

• 4 +1 for "apply right away". First find out what your options are, and then make a decision, not the other way around. –  JeffE Commented Dec 18, 2014 at 6:05

At least in my area of the world (Western US) and among the professors from the institution where I did grad work, almost everyone did a master's degree first. There are exceptions to this of course. How I see it is if you are a genius, go on to the PhD directly. Otherwise, a MS can give you some good background without drinking from a fire hose. This is how I improved my weaker areas. I was weak in analysis before grad school. I was able to take 4 analysis classes (graduate level!) for my MS and it was a significant boost.

When I applied to PhD programs, I got my letters from professors I had taken graduate classes from (and my thesis advisor). This allowed them to comment not just on how well they thought I would do in grad school, but how well I actually had done. This also allowed for them to comment on my research. I think it made me a stronger PhD candidate.

I will back up that you will need to be (somewhat) confident that you can become very strong in a specific niche. But that is why you go to grad school; its purpose is to make you strong in your field. And your strengths may change. I entered grad school as a group theorist and left as a probabilist.

• 1 I heard the opposite at my undergrad, that you should just jump in for the PhD, and possibly drop out with the MS if you don't want to stick it out. It varies a lot from person to person. –  Ian Commented Dec 18, 2014 at 1:29
• ^Applying to a PhD program and possibly dropping out with a MS might be better if you need funding (this of course depends on the program). –  JimmyK4542 Commented Dec 18, 2014 at 1:49
• 1 almost everyone did a master's degree first — That doesn't say much. I also got an MS first, but it was an administrative hurdle in the middle of a PhD program; the department didn't have an MS program that one could be admitted into separately. –  JeffE Commented Dec 18, 2014 at 6:07
• @JeffE You also are a CS professor, which is a different discipline than pure maths. I would hazard to say (and it is very true at the university where I currently teach) that in CS, those who do a PhD commonly skip the MS. –  Vladhagen Commented Dec 19, 2014 at 1:31
• Theoretical computer science isn't that different from math. I have former PhD students who picked up math MS degrees on the way, and former MS students who got math PhDs. And most of the math PhDs I know don't have MS degrees. –  JeffE Commented Dec 20, 2014 at 4:14

I doubled in math and physics at MIT, and went on to get a PhD. in physics. Although I had a successful career, first as a supergravity theorist and then as a computational physicist, I have always wished I had gone into math, which was my stronger love and better talent.

You don't have to be uniformly strong in all areas to do wel in a math PhD program. (Although many nice ideas stem from creative ideas in unrelated parts of math.) You do have to be pretty sure you can become insanely strong in one area, and you do need to be confident that you will love what you are doing.

• 1 Your answer seems a little strange. I also do not have an advanced degree in Mathematics. But that fact makes me feel less not more qualified to answer the question. –  emory Commented Dec 19, 2014 at 0:20

Entering a PhD program is a major commitment that you should not enter into if you're not completely ready. Your question shows that you're very unsure about what you want to do. Thus I would not recommend entering a PhD program at this point in time.

It is certainly possible to work for a while and then go back to graduate school.

My own personal experience is that when I got my BS degree (in Computer Science), many friends urged me to go on to graduate school immediately. Instead, I went to work as a software developer for the next three years. It became clear that I would need at least an MS degree in order to advance within the company that employed me so I went back to graduate school for an MS in applied mathematics. During my first semester as a full time graduate student I became very interested in a new area (interior point methods for LP), and applied to switch into the PhD program so that I could really immerse myself in that topic. I wouldn't recommend this approach to everyone, but at the same time, I'm quite certain that it helped me to have worked for a while before going back to graduate school.

• You touch on one of the (IMHO, anyway) best reasons for taking some time between BS and PhD: work in industry for a decade or so, and with care and a bit of luck, you won't have to worry about student loans or financial aid. –  jamesqf Commented Dec 18, 2014 at 18:57
• Going back to graduate school I had a relatively new car paid off and some IRA money that I cashed out towards the end of my PhD to help pay expenses. That money certainly helped. On the other hand, I had to dramatically expenses to survive on my TA stipend. –  Brian Borchers Commented Dec 18, 2014 at 19:49

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By April 15th of a PhD student's second year, a written summary of work accomplished towards finding a research advisor and research area shall be submitted to the Graduate Program Advisor, to serve as the PhD candidate's Year Two milestone and annual evaluation. Although candidates are not beholden to any research advisor or area of study until the end of their third year, this summary shall primarily detail efforts made towards the advancement of the individual's research path. Students should mention guidance sought from potential advisors concerning what out-of-department courses and advanced APPM courses are best matched to their research interests. The document must also include an indication of how students will use their APPM summer fellowship to enhance their research training. For acceptable research training activities for Year Two, please see the first paragraph of the, "Dissertation Advisor, Faculty Mentor, and Research Plan," section of the Supplement. The summary should be signed by an APPM core faculty member relevant to the student's activities. Questions can be directed to [email protected] or the Graduate Program Chair.

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Claire Bowen (ACMS PhD'18) elected American Statistical Association (ASA) Fellow

Published: August 14, 2024

Author: Kathy Phillips

Claire Bowen, ACMS (PhD'18) was elected as an American Statistical Association (ASA) Fellow in 2024 "For her significant contributions in the field of statistical data privacy, leadership activities in support of the profession, and commitment to mentoring the next generation of statisticians and data scientists."

Bowen is the first alumni from ACMS to be elected as an ASA fellow, a prestigious recognition and the fellow designation limited to one-third of 1% of membership each year. At Notre Dame, Bowen worked with Professor Fang Liu on her doctoral thesis titled "Data Privacy via Integration of Differential Privacy and Data Synthesis"

Bowen is currently a senior fellow and leads the Data Governance and Privacy Practice Area at the Urban Institute. Her research focuses on developing technical and policy solutions that aim to safely expand access to confidential data for advancing evidence-based policy-making. She also has interests in improving science communication and integrating data equity into the data privacy process. Further, she is a member of the Census Scientific Advisory Committee and several other data governance and data privacy committees as well as an adjunct professor at Stonehill College.

Raygun becomes viral sensation during breaking performance at 2024 Paris Olympics: Social media reacts

Breaking , more commonly known as breakdancing, made its debut as an Olympic sport this week at the 2024 Paris Games , with 17 B-girls and 16 B-boys making their way to France with the hopes of securing a gold medal.

On the first day of competition, viewers from across the world were treated to a different kind of introduction — not to the sport itself, but one of its athletes.

Though she was a long way from winning a gold medal, likely no breaker Friday captured the imagination of the international audience more than Rachael Gunn, an Australian breaker who competes under the name “Raygun.”

REQUIRED READING: Follow USA TODAY's coverage of the 2024 Paris Olympics

Raygun went 0-3 in her head-to-head competitions Friday — falling to Logistx of the United States, Syssy of France and eventual silver medalist Nicka of Lithuania by a combined score of 54-0 — and failed to record a point across those three matches, but for what she lacked in smoothly executed moves, she made up for in the hearts she won over with her demeanor.

Raygun’s short-lived Olympic experience made her a celebrity, one who people became even more enamored with once they learned more about her.

The 36-year-old Gunn, who was one of the oldest qualifiers in the breaking competition, has a PhD in cultural studies and is a college professor at Macquarie University in Sydney. Her research focuses primarily on breaking, street dance and hip-hop culture while her work draws on “cultural theory, dance studies, popular music studies, media, and ethnography.”

“In 2023, many of my students didn’t believe me when I told them I was training to qualify for the Olympics, and were shocked when they checked Google and saw that I qualified,” Gunn said to CNBC earlier this month .

Unlike much of her competition in Paris, Gunn took up break dancing later in life. She didn’t enter her first battle until 2012.

On Friday, a person who began the day as a little-known academic ended it as a viral worldwide sensation.

Here’s a sampling of the reaction to Raygun and her performance:

2024 PARIS OLYMPICS: Meet the members of Team USA competing at the 2024 Paris Olympics

Social media reacts to Raygun’s breaking performance at 2024 Paris Olympics

I could live all my life and never come up with anything as funny as Raygun, the 36-year-old Australian Olympic breakdancer pic.twitter.com/1uPYBxIlh8 — mariah (@mariahkreutter) August 9, 2024

Give Raygun the gold right now #breakdancing pic.twitter.com/bMtAWEh3xo — n★ (@nichstarr) August 9, 2024

my five year old niece after she says “watch this!” : pic.twitter.com/KBAMSkgltj — alex (@alex_abads) August 9, 2024

I'd like to personally thank Raygun for making millions of people worldwide think "huh, maybe I can make the Olympics too" pic.twitter.com/p5QlUbkL2w — Bradford Pearson (@BradfordPearson) August 9, 2024

The Aussie B-Girl Raygun dressed as a school PE teach complete with cap while everyone else is dressed in funky breaking outfits has sent me. It looks like she’s giving her detention for inappropriate dress at school 🤣 #Olympics pic.twitter.com/lWVU3myu6C — Georgie Heath🎙️ (@GeorgieHeath27) August 9, 2024

There has not been an Olympic performance this dominant since Usain Bolt’s 100m sprint at Beijing in 2008. Honestly, the moment Raygun broke out her Kangaroo move this competition was over! Give her the #breakdancing gold 🥇 pic.twitter.com/6q8qAft1BX — Trapper Haskins (@TrapperHaskins) August 9, 2024

my dog on the lawn 30 seconds after i've finished bathing him pic.twitter.com/A5aqxIbV3H — David Mack (@davidmackau) August 9, 2024

My wife at 3AM: I think I heard one of the kids Me: No way, they are asleep *looks at baby monitor* pic.twitter.com/Ubhi6kY4w4 — Wes Blankenship (@Wes_nship) August 9, 2024

me tryna get the duvet off when i’m too hot at night #olympics pic.twitter.com/NM4Fb2MEmX — robyn (@robynjournalist) August 9, 2024

Raygun really hit them with the "Tyrannosaurus." pic.twitter.com/ZGCMjhzth9 — Mike Beauvais (@MikeBeauvais) August 9, 2024

Raygun (AUS) https://t.co/w2lxLRaW2x — Peter Nygaard (@RetepAdam) August 9, 2024

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The University of Wisconsin-Eau Claire's master of science in data science is a fully online degree program intended for students with a bachelor’s degree in math, statistics, analytics, computer science, or marketing; or three to five years of professional experience as a business intelligence analyst, data analyst, financial analyst, information technology analyst, database administrator, computer programmer, statistician, or other related position.

The rigorous program is the first online master's degree in data science offered in the UW System and is helping fill a critical need for data scientists. Using analytics, statistics, programming, business and storytelling, data scientists have the unique and important job of transforming big data into actionable insights. The field is already growing at an incredible pace, and as today's world continues to generate more and more data, employers across the country are in consistent need of professionals who know how to understand and interpret data.

Designed with input from industry leaders, the data science program offers a comprehensive, multidisciplinary curriculum grounded in computer science, math and statistics, management and communication. Coursework throughout the degree will show you how to clean, organize, analyze and interpret data using current industry tools and analytical methods. Since data scientists must also understand privacy and security policies, part of the curriculum throughout the program focuses on how to appropriately handle data found in financial records, medical records, consumer patterns, internet searches and other real-world situations — knowledge that is needed in countless industries and organizations.

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The master of science in data science is a 12-course, 36-credit online master's degree that prepares students for complex and fast-paced careers in data science and analytics. 

Featuring a multidisciplinary curriculum that draws primarily from computer science, mathematics and statistics, management and communication, the program teaches students how to derive insights from real-world data sets — both structured and unstructured. Using the latest data science tools, analytical methods and sophisticated visualization techniques, graduates learn to communicate their data discoveries and recommendations clearly. A focus on building leadership and communication skills rounds out the degree.

Here are a few courses in Master of Science in Data Science at UW-Eau Claire.

Foundations of Data Science

Introduction to data science and its importance in business decision making.

Visualization and Unstructured Data Analysis

Covers various aspects of data analytics including visualization and analysis of unstructured data such as social networks.

Ethics of Data Science

Ethical issues related to data science, including privacy, intellectual property, security, and the moral integrity of inferences based on data.

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As Opioid Deaths Plague Baltimore, the City’s Strategy Is Silence

The city has declined to divulge its plans or hold hearings on one of the worst public health crises in the United States, saying it does not want to jeopardize its lawsuit against drugmakers.

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By Adam Willis and Alissa Zhu

Adam Willis and Alissa Zhu are reporters for The Baltimore Banner. They have examined the city’s response to its overdose crisis as part of The Times’s Local Investigations Fellowship.

For years, Baltimore’s leaders gave overdoses little public attention, even as the death rate swelled to unprecedented levels. But for a few weeks this summer, it seemed that the city would respond to its drug epidemic with new urgency.

The City Council was about to hold four hearings — planned after The New York Times and The Baltimore Banner reported that the overdose rate here was far higher than in any other major American city. And Mayor Brandon Scott had just announced a $45 million legal settlement with a drug manufacturer, raising the possibility of well-funded new public health efforts to combat the epidemic, which had claimed nearly 6,000 lives here in the past six years.

But hours before the first hearing, as demonstrators prepared to rally outside City Hall, the council president abruptly canceled the session, at the request of Mr. Scott’s administration.

The administration said that holding any of the public meetings would jeopardize a lawsuit the city had filed accusing numerous opioid makers and distributors of causing the crisis by flooding Baltimore with pills. City leaders believe the case could result in a transformative amount of money for its overdose response — far more than the $45 million it collected in a settlement with a single company that shipped relatively few drugs to Baltimore.

The decision to cancel the hearings was in keeping with the city’s reluctance in recent months to divulge nearly any details of its overdose prevention efforts, citing the lawsuit, which is scheduled for trial in September. Almost every council member was unwilling to comment on the hearings or on overdoses in the city, including several who had discussed overdoses earlier in the year.

It is not uncommon for governments to limit public statements during litigation, and some lawyers and public health experts said it was understandable to avoid hearings on the eve of a trial. But others said the decision raised questions about Baltimore’s response plan — and how it was addressing shortcomings in the city and state’s efforts to curb the epidemic. Residents have been mostly left in the dark.

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Tuesday, August 13, 2024 | By jtitone

Doctoral thesis defence in Physics

Alicia Martin, a Doctor of Philosophy candidate in the Department of Physics, will defend her thesis titled “Monte Carlo Validation of Dose, Quality Assurance Protocols and Shielding in Radiation Therapy” on Wednesday, Aug. 21 at 1 p.m., in Plaza building room 600F.

The examination committee includes Brian Roy, Chair; Thad Harroun, Supervisor; Kevin Ross Diamond, External Examiner (McMaster University); Shahryar Rahnamayan, Internal External Examiner, and Kirill Samokhin and Edward Sternin, Committee Members.

Tags: FMS , Physics , Thesis defence Categories: Events

FMS News and Events

• Aug 19 – Master of Science Project Presentation – Samiha Tasmin
• Aug 2 – Master of Science Thesis Defence – Fardad Pirri
• July 23 – PhD Thesis Defence – Gregory Foran
• July 15 – Master of Science thesis defence – Abhishek Kumar
• May 31 – Master of Science Thesis Defence – Pierre Simiganoschi
• May 29 – Master of Science Thesis Defence – Quanjian Li
• May 21 – Doctor of Philosophy Thesis Defence – Frank Betancourt
• May 16 – Master of Science Thesis Defence – Georgina Louise Gardner

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If you get a PhD, are you pretty much saying "I want to do research in academia"? Also, if I wanted to work in industry is a masters degree sufficient or would I benefit from spending the extra money to get a phd?j

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