math phd timeline

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Upon arrival, new students may take the preliminary exams . Students who pass the exams can by-pass the 600-level sequences and take the beginning Ph.D. 700-level courses as outlined in The Second Year .

In addition to the general requirements for a Ph.D. mandated by the Graduate School, a minimum of 36 700-level (or above) mathematics credits must be earned. All four basic sequences 733-734 , 735-736 , 741-742 , and 761-762 are required.

The First Year

To be in good standing every student must pass either two Master's level exams on the year-long 600-level courses: algebra ( MTH 661 / 662 ), topology ( MTH 631 / 632 ), and analysis ( MTH 633 / 634 ) or pass one qualifying exam on one of the four core year-long 700-level courses (mentioned above) before the start of their second year. The exams are given once in June and once in August. No exam may be taken more than twice.

The Second Year

Students normally take three 700-level courses during their second year. Two of the three courses will concern material for their qualifying exams. To be in good standing every student must pass an additional qualifying exam before the start of their third year. No exam may be taken more than twice.

The Third Year

Students must complete any remaining core year-long 700-level courses. A specialty is chosen and coursework will begin concentrating in this area. To be in good standing every student must complete the qualifying exam requirement by June and are required to find a dissertation advisor also by June.

The Fourth Year

Research and coursework in your area of research.

The Fifth Year

Research continues and the dissertation is written. For students who wish to continue in academics, applications are sent out in the fall.

The Sixth Year

Only in exceptional cases will support be extended to a sixth year.

Department of Mathematics

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These are the general steps to obtain your PhD in Applied Mathematics at CU Boulder.

• 18 credit hours must be from APPM at 5000+ level.
• The 18 hours of APPM credits must include 5600 & 5610 (numerics I & II), 5440 & 5450 (analysis I & II), and one more approved \sequence" (see supplement for a list of approved sequences).
•  6 credit hours must be a two-course out-of-department sequence. This sequence needs approval (pre-approval recommended!) from graduate chair. Must be at 5000+ level, and not duplicate material taught by APPM.
• Two 1 credit seminar courses are required. Must be taken after the rst year.
• You must maintain a GPA of 3.0 or better, and earn at least a B- in each class.
• Doctoral students must take and pass two preliminary exams by August at the end of their first year.
• In January, first-year PhD students can choose to take either PDEs or Statistics.
• In May, first-year PhD students can choose to take either Applied Analysis or Numerical Analysis.
• Make-up exams are offered in August.
• You may take any one exam no more than two times. 

The goal of this document is for students to provide a summary of all the work they have done so far to advance along their research path here including obtaining research training, identifying a research area of interest, and interacting with potential research advisor(s). Students should mention guidance received on advanced course to be taken. The document must also include an indication of how students will use their APPM summer fellowship to enhance their research training. See the "Dissertation Advisor, Faculty Mentor, and Research Plan," section of the Supplement for guidance on activities of interest to discuss. The summary must be signed by an APPM core faculty member relevant to the student's activities and is due April 15th of a PhD student's second year. Questions can be directed to [email protected] or the Graduate Program Chair.

The Graduate Chair will be the advisor for all incoming students.  Once the student has selected an area of specialization and found an Advisor who will take them on, they will inform the Graduate Chair and the Graduate Coordiator.  This usually happens after the students passes their Preliminary Exams and start to focus of their dissertation.

If you are planning on using transfer credits from another accreditied University.  Please review this form below and submit the appropriate paperwork.

​ Request for Transfer of Credit

The purpose of the comprehensive exam is to ensure that the student has a sufficient grasp of the fundamentals of the chosen thesis area to begin research, the ability to exchange ideas and information with the members of the examining board (thesis committee), and a broad base of knowledge in applied mathematics. 

Before the comprehensive exam, the Ph.D. student must submit a 5-10 page thesis proposal, complete with motivation for the topic and references to key papers, to each member of the thesis committee.  This proposal should be written in consultation with the chair of the thesis committee.

The exam will consist of a presentation by the student on his/her research proposal for a maximum of one hour in length, followed by a questioning period of up to one additional hour.  The presentation portion is open to all faculty and students in the program. 

Students will need to be registered in classes for the semester they are going to complete their examination for it to count towards that semester. This includes the summer semester.

• Select Committee (see rules on Exam Report) 
• Schedule Comprehensive date and location with committee members. For help reserving rooms, please visit ems.colorado.edu or email [email protected] .
• Inform Graduate Coordinator ( [email protected] ) of your date, location, and member names, and the Graduate Coordinator will help you procure Graduate Faculty Appointments for any out-of-department members when you submit an up-to-date CV to amagradco. ( at least 2 weeks prior to Comp date)
• Complete Doctoral Exam Report  for committee approval (at least 2 weeks prior to Comp date)
• Submit Title and Abstract to [email protected]  to post in department (at least 2 weeks prior to Comp date) See example  or .tex file
• Complete Candidacy application  for an Advanced Degree

The exam will consist of a presentation by the student on his/her research proposal, followed by a questioning period of up to one additional hour.  The presentation portion is open to all faculty and students in the program. 

• Select Committee (see rules on Exam Report)
• Submit Title of Thesis to Graduate School – see doctoral deadlines  for dates
• Get Graduate Chair signature/approval
• Make copy for Graduate Coordinator
• Submit original to Graduate School
• Print a copy of Thesis Signature page, get original signatures and submit the form directly to the Graduate School. 
• Have Committee Chair pick up Exam Report from Graduate Coordinator prior to Thesis Defense. (Graduate Coordinator will have it ready at least 48 hrs. prior to Exam time)
• Submit Thesis to Graduate School electronically - see doctoral deadlines  for dates and instructions.
• One copy must be printed single sided, on 8.5 x 11 watermarked paper of at least 25 % cotton and 20# weight.
• The other two copies can be printed double sided, on 8.5 x 11 watermarked paper of at least 25 % cotton and 20# weight. 
• Submit Thesis to CU Electronic Scholars Depository - see instructions .
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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.

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Degree Timeline

Ph.d. timeline.

The following time line is meant to provide general guidance - individual cases may vary.

• Attend Research seminars
• Take part in Professional Development activities
• Be aware of Funding sources to enhance your activities
• Take part in activities of Graduate math organizations
• Be aware of policies/opportunities for concurrent Masters and Certificate programs
• Build depth from advanced courses
• Meet with your Academic Mentor regularly
• Complete the Qualifying Requirements
• The Teacher Training Program
• Select your research direction
• Choose your PhD Research Advisor from the Math graduate primary/secondary faculty
• Prepare for the Preliminary Exam
• Year 3: Complete Preliminary Exam and begin thesis work
• Year 4: Thesis work
• Fall: Write thesis and apply for jobs
• Spring: Follow deadlines required to graduate , defend thesis, and interview for jobs

Ph.D. Degree Requirements

• Complete the  Qualifying Requirement
• Pass the  Preliminary Examination
• Write and defend the  Dissertation
• Six semesters (Fall/Spring) of full-time enrollment Note: Enrollment in CTN 1-01 is necessary for a PhD student to maintain active/full-time status.
• Graduate School Responsible Conduct of Research (RCR) training requirements

The Graduate School requires that you complete paper work for both the Preliminary Exam and the Thesis Defense at least ONE MONTH BEFORE the scheduled date.  Read the information above carefully, and let the DGSA ( [email protected] ) know as soon as you are ready to schedule the exam and defense.

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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.

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Meet with DGS, and select coursework.  Students with strong preparation in Mathematical Analysis, Linear Algebra, or Mathematical Statistics may opt to take the written part of the doctoral preliminary exam in August prior to the start of classes.

Focus on coursework and preparing for written part of doctoral preliminary exam.  Attend colloquia and research seminars.  Talk to faculty, and narrow down research area.  Work with DGS to choose advisory committee by the end of February.  Submit initial doctoral plan of study.

Take the two area exams comprising the written part of the doctoral preliminary exam in May.  Retake in August, if necessary.  Work with advisor and committee.

Continue coursework.  Retake remaining written area exams in January.  Choose a dissertation advisor and committee, and revise doctoral plan of study.  Students without an MA in Mathematics should speak with DGS to be awarded the MA.

Work with dissertation advisor and committee.

Continue to attend colloquia and research seminars.  Coursework transitions to include more specialized research courses such as

• Graduate Seminar in Computational Mathematics (MAT 701), Seminar in Computational Statistics (STA 701)
• Topics in Computational Mathematics (MAT 709), Topics in Computational Statistics (STA 709)
• Directed Doctoral Research (MAT 790)

Complete oral part of the doctoral preliminary exam.  Prepare written dissertation outline.  Prepare and defend dissertation topic proposal.

Work with advisor and committee.

Continue to attend colloquia and research seminars.  Continue specialized research coursework and begin completing dissertation hours. Apply for admission to candidacy and submit final doctoral plan of study.

Continue to attend colloquia and research seminars.  Apply for jobs.  Finish dissertation research and defense.   Apply to graduate , and complete exit forms.

Mathematics

PhD Timeline

The majority of a MPhil/PhD student's time is taken up with research. However, there are certain other requirements that you need to complete at various points before you can submit your PhD thesis.

The following is intended to highlight what these are and when you should do them. 

Throughout your studies: 

• Meet regularly with your supervisor and conduct research.
• Attend relevant seminars, in particular the Postgraduate seminar. 
• Keep your Research Log up to date.  
• Log all courses and training activity via the Skills Development page. 
• Attend 4 LTCC courses. (These are graduate level mathematics courses intended to broaden your mathematical education.) 
• Give a short talk at the postgraduate seminar on your research (in month 13 or 14 of your studies). 
• Write an upgrade dissertation. 
• Arrange an "upgrade viva" with your supervisor in order to upgrade from MPhil to PhD status. (This should happen between 12 and 18 months after starting at UCL.) 

Years 3 & 4

• Submit exam entry form at least 4 months before you intend to submit your thesis. 
• Ensure that your supervisor submits the examiner nomination form for which you will need to provide a "Thesis Template" (i.e. an abstract). 

All students are expected to obtain 20 skills points (equivalent to 2 weeks training) per year. Please note the link to "Departmental Training" when you log into the Skills Development Programme. You can obtain skills points for attendance at seminars, LTCC courses, teaching, marking, presentations, writing papers, attending Graduate School courses. 

Useful links

• UCL Research Log
• LTCC Courses
• UCL Doctoral Skills Development

Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The application deadline for fall 2024 admission has passed. Applications for fall 2025 admission will open in September 2024.

For information on admissions and financial support, please visit the Harvard Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

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Ph.D. Admissions

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• M.S. Admissions

The application window for Fall 2024 is closed.

The Mathematics Department offers two programs to obtain a Ph.D. Applicants can pursue a Ph.D. in  Applied & Interdisciplinary Mathematics or Mathematics.  Please use the "Programs" link at the left to explore our offerings.

• Three Letters of Recommendation  (May submit up to 5 letters, but only 3 are required.)
• Curriculum Vitae or Resume
• Academic Statement of Purpose (concise - no limit)
• Personal Statement (500 word limit)
• TOEFL iBT Special Home Edition and IELTS Indicator online test are accepted.
• Exemption rules:   https://rackham.umich.edu/admissions/applying/tests/
• List of  International English Exclusive Institutions  approved by Rackham

GRE General Test scores are no longer included in the admission process in accordance with a  policy of the Rackham Graduate School .

GRE Mathematics Subject Test scores are strictly optional. However, if an applicant chooses so, they may submit them as a combined pdf file with their transcript or personal statement.

Application Timeline

The Mathematics Department's graduate programs only accept applications for Fall semesters. 

General Requirements for Admission

A student must have completed a bachelor's degree at an accredited college or university by the time of entry in order to be considered for admission.

Applied & Interdisciplinary Mathematics (AIM) Ph.D. Admissions Requirements

Successful AIM Ph.D. applicants will demonstrate an interest in an interdisciplinary area of applied mathematics in addition to substantial mathematical ability. Two types of students are generally considered for admission to the AIM Ph.D. program:

• Mathematics majors with excellent grades in mathematics courses and excellent letters of recommendation. The admissions committee will also take into account other scholarly activities such as summer research experience, published papers, or courses in other fields.
• Non-mathematics majors from the physical, life, or engineering sciences, or from other appropriate areas of study. Such students are expected to have completed at least two upper division mathematics courses, and/or have substantial exposure to mathematics in other courses, and may submit a GRE mathematics subject test score. Other experience in working with mathematics (for instance, summer research positions) will also be taken into account, as well as grade point average and letters of recommendation.

Mathematics Ph.D.  Admission Requirements The undergraduate major need not be mathematics, but a student should have mastered material roughly equivalent to the undergraduate mathematics major at The University of Michigan including:

• three semesters of calculus
• one or two semesters of differential equations
• one semester courses in modern algebra, linear algebra, geometry or topology
• advanced calculus of one and several variables

In addition, a student should have completed at least three additional mathematics courses and at least two courses in related fields such as statistics, computer science, or the physical sciences. Students with strong records in less comprehensive programs will be considered for admission but if admitted should expect to spend the first one or two semesters in graduate school completing their undergraduate preparation in mathematics. Based on historical data, we expect that successful applicants to the Ph.D. program will have an overall GPA of at least 3.3 on a 4.0 scale.

Application Requirement Details

GRE, TOEFL, and IELTS Tests

• GRE General test scores are not required. 
• GRE Mathematics Subject Test scores may be submitted as a combined pdf file with your transcript or personal statement. (Optional)
• TOEFL or IELTS exam is required for students whose native language is not English
• TOEFL and IELTS exams should not be older than two years as of the Admission Deadline.
• Minimum TOEFL and IELTS scores must meet Rackham's requirements here .
• TOEFL or IELTS Exemptions are only given per Rackham's rules here .
• ETS school code for the University of Michigan Rackham Graduate School is 1839

Letters of Recommendation

Letters of recommendation play an especially crucial role in the admission process. At least three letters are required, and up to five may be submitted. Applicants should choose as recommenders people who know their strengths and weaknesses relevant to graduate study in mathematics. The most useful letters are those which list in some detail the accomplishments of the student and make direct comparisons with other students who have succeeded at major U.S. graduate schools. International students already in the U.S. should submit letters from their U.S. institution, whenever possible.  Please register your recommenders for the electronic Letters of Recommendation when using the Online Application.  Letters received after the application deadline will be accepted, but should be received within 1 week of that deadline.

Those students who will have completed a Master's degree in Mathematics by the time they begin studies at the University of Michigan must apply to the Ph.D. program. Others may apply to either program. 

Academic Statement of Purpose

Focus your academic statement on your mathematical interests, research experience, published papers, math camps, teaching & tutoring experience etc. Be sure to mention any specific faculty with whom you wish to work.

Personal Statement:

Focus your personal statement on what makes you unique, any struggles you have experienced and overcome, and why you feel U-M Math is the right place for you.  Be sure to include any hardships you have experiencedand how you overcame them. These could be financial, familial, or personal.

Transcript Submission:

The Mathematics Admissions Committee will review uploaded transcripts with university logos during the application process.  While these are considered "unofficial" transcripts because they have been opened from their original sealed envelopes, they are acceptable.  If an applicant receives an offer of admission, an official transcript in a sealed envelope will need to be mailed from the institution directly to the Rackham Graduate School.

Please submit your most current transcript with your online application by the due date.  If you would like the Admissions Committee to see your Fall term scores, you may email them to [email protected] after the due date, and they will be included with your application.

Additonal Application Materials: If you have additional materials you would like to submit with your application, you may email them to [email protected].  Be sure to include your name and umid number in the email and attach files in pdf format.

Note:  All credentials submitted for admission consideration become the property of the University of Michigan and will not be returned in original or copy form.

Additional Information:  Please visit the admissions page of the Rackham Graduate School for additional information regarding admission including: minimum graduate school requirements, residency, and application fees.    Unfortunately, application fee waivers are not available for international students.

Financial Support for Ph.D. Students

Ph.D. Programs

Most students enrolled in the Ph.D. program in Mathematics are granted full financial support including an annual stipend, tuition waiver, and health insurance for a period of five years, subject to satisfactory progress. The Department offers aid in the form of Graduate Student Instructorships, Research Assistantships, and Fellowships.

All entering Ph.D. students will be considered for Graduate Student Instructorships, which normally require four classroom hours of teaching per week plus additional office hours during the Fall and Winter terms. The stipend for such an appointment in 2021-2022 is $11,598 per term. In addition, Graduate Student Instructors receive a full tuition waiver. Teaching duties may involve teaching a section of a first-year calculus or pre-calculus course or serving as an instructor for recitation sections attached to a faculty lecture in multivariable calculus or elementary differential equations. The Department of Mathematics has many fellowship opportunities, including the Copeland, Glover, Rainich, and Shields Fellowships which may provide a stipend, tuition waiver and in some cases a reduced teaching load. Other fellowships administered by the Rackham Graduate School can be found at their  Fellowships office .  The University of Michigan is part of the CIC consortium, which also awards fellowships to outstanding underrepresented applicants. Also available are prestigious Rackham Science Award’s given out by the Rackham Graduate School.

After Admission

All new Graduate Student Instructors are required to attend an orientation and training program which is held the week before classes begin. New Graduate Student Instructors whose Undergraduate Degree is not from an English speaking University must pass an English Evaluation which tests the specific oral skills needed for classroom teaching and are required to attend a three-week cultural orientation program starting in July.

Research Assistantships are awarded mainly to senior Ph.D. students to relieve them of teaching duties during the final part of their dissertation research. Students at this point may also compete for Rackham Dissertation Fellowships, which provide full support for one year, or Research Partnerships. A small number of positions as paper-graders for the larger advanced courses is available each term.

Some additional funds are often available for support during the summer. More advanced students who are actively involved in research may be supported from NSF grants awarded to faculty members. For other students there is a limited number of Departmental fellowships and a few teaching positions are available. No advanced graduate courses are offered in either the Spring or Summer half-terms and students are encouraged to spend some of their summers attending workshops, doing research, working in government, or seeking internships in industry.

Marjorie Lee Browne (MLB) Scholars Program - an MS bridge to PhD program for diverse students

The Department of Mathematics at the University of Michigan is pleased to offer the Marjorie Lee Browne (MLB) Scholars Program. The program is named for Dr. Marjorie Lee Browne, who in 1949 became the first African-American woman to earn a Ph.D. in Mathematics at the University of Michigan. The MLB Scholars Program is an enhanced option for the M.S. degree in either Mathematics or Applied and Interdisciplinary Mathematics that is designed to give students professional knowledge of pure or applied mathematics in order to prepare them for continuing toward a Ph.D.  Please see this Marjorie Lee Brown Scholars webpage for eligibility and details.

If you have any questions regarding the application process, please contact the Department of Mathematics at [email protected].

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The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.

Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.

Research Areas and Potential Supervisors

Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.

We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.

Before making an application to study with us we recommend you:

• Investigate our areas of research and consider how they fit with your interests and ambitions.

A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.

• Identify 2 or 3 appropriate supervisor(s) with whom you might work.

Applicants should indicate one or more proposed supervisor(s) in their application. The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.

If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.

• Give some thought to your intended research and why you want to study with us.

On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.

Research areas

Click on a research area to find out more about available supervisors and their research:

Please note that a  large majority of the successful applicants for PhD studentships with  the High Energy Physics, and General Relativity & Cosmology (GR) groups   will have taken Part III of the Mathematical Tripos.

Funding Opportunities

Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.

All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:

Note for PhD applicants:

We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.

Note for MPhil applicants:

We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Most interviews are expected to take place in the second half of January.

The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.

Not all applicants will be selected for interview.

If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:

• the location of the interview (it may be in-person or on-line dependent upon interviewer availability, your distance from Cambridge, as well as individual preferences),
• the interview format and whether you should prepare anything specific in advance,
• the approximate duration of the interview,
• who you will be meeting.

Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.

Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.

Decision timeline

Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.

To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.

Communication of outcomes

You will be notified of the formal outcome of your application via the Applicant Portal.

Following an interview, you can normally expect to receive notification of the outcome within a week or two.

If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.

We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.

Take a look at our frequently asked questions for PhD applicants.

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• The PhD Journey - Stages of a Doctoral Degree

The PhD Journey

Written by Mark Bennett

A PhD typically involves between three and four years of full-time study, culminating in a thesis which makes an original contribution to your field.

The process of getting a PhD is made up of quite a few components and milestones, from the literature review and writing up your dissertation right through to the viva examination at the end.

This section is a guide on how to do a PhD, providing in-depth advice and information on some of the main challenges and opportunities you’ll meet along the way!.

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7 stages of the PhD journey

A PhD has a few landmark milestones along the way. The three to four year you'll spend doing a PhD can be divided into these seven stages.

• Preparing a research proposal
• Carrying out a literature review
• Conducting research and collecting results
• Completing the MPhil to PhD upgrade
• Participating in PhD teaching, conferences and publications
• Writing your thesis
• Defending your PhD results at a viva voce

We've expanded on what you can expect from each stage below.

1. Preparing a research proposal

Strictly speaking, your research proposal isn’t part of your PhD. Instead it’s normally part of the PhD application process.

The research proposal sets out the aims and objectives for your PhD: the original topic you plan to study and / or the questions you’ll set out to answer.

It also explains why your work is worthwhile and why it fits with the expertise and objectives of your university.

Finally, a PhD proposal explains how you plan to go about completing your doctorate. This involves identifying the existing scholarship your work will be in dialogue with and the methods you plan to use in your research.

All of this means that, even though the proposal precedes the PhD itself, it plays a vital role in shaping your project and signposting the work you’ll be doing over the next three or more years.

2. Carrying out a literature review

The literature review is normally the first thing you’ll tackle after beginning your PhD and having an initial meeting with your supervisor.

It’s a thorough survey of work in your field (the current scholarly ‘literature’) that relates to your project or to related topics.

Your supervisor will offer some advice and direction, after which you’ll identify, examine and evaluate existing data and scholarship.

In most cases the literature review will actually form part of your final PhD dissertation – usually setting up the context for the project, before you begin to explain and demonstrate your own thesis.

Sometimes a literature review can also be evaluated as part of your MPhil upgrade .

Research vs scholarship

Research and scholarship are both important parts of a PhD. But they aren't the same thing - and it's helpful to know the difference. Research is the original work you produce with your thesis. Scholarship is the expert understanding of your subject area that enables you to conduct valuable research.

3. Conducting research and collecting results

Once you’ve carried out your literature review, you’ll move from scholarship to research .

This doesn’t mean you’ll never read another academic article or consult someone else’s data again. Far from it. You’ll stay up to date with any new developments in your field and incorporate these into your literature review as necessary.

But, from here on in, your primary focus in your PhD process is going to be investigating your own research question. This means carrying out organised research and producing results upon which to base your conclusions.

Types of PhD research

The research process and the type of results you collect will depend upon your subject area:

• In Science, Technology, Engineering and Mathematics (STEM) subjects you’ll focus on designing experiments, before recording and analysing their outcomes. This often means assembling and managing complex numerical datasets – sometimes in collaboration with the rest of your laboratory or workshop.
• In Social Science subjects you’ll be more focussed on designing surveys or conducting case studies. These will produce quantitative or qualitative data, depending on the nature of your work.
• In Arts and Humanities subjects you’ll often have less raw data, but that doesn’t mean you won’t be working with ‘hard’ factual information. You’ll analyse texts, sources and other materials according to an accepted methodology and reflect upon the significance of your findings.

Whatever subject you’re in, this research work will account for the greater part of your PhD results. You’ll have regular meetings with your supervisor, but the day-to-day management of your project and its progress will be your own responsibility.

In some fields it’s common to begin writing up your findings as you collect them, developing your thesis and completing the accompanying dissertation chapter-by-chapter. In other cases you’ll wait until you have a full dataset before reviewing and recording your conclusions.

4. Completing an MPhil to PhD upgrade

At UK universities it’s common to register new PhD students for an MPhil before ‘ upgrading ’ them to ‘full’ doctoral candidates. This usually takes place after one year of full-time study (or its part-time equivalent).

Forcing you to register for a ‘lesser’ degree may seem strange, but it’s actually an important part of the training and development a PhD offers:

• As an MPhil student you’re able to comprehend your field and produce new research.
• As a PhD student you’re able to go that crucial step further and produce the significant original contribution to knowledge that defines a doctorate.

The MPhil upgrade is when you take the step from the former to the latter.

The MPhil upgrade exam

Upgrading from MPhil to PhD registration usually involves a form of oral exam – similar to the viva voce that concludes a PhD. But, unlike a full viva, the MPhil upgrade is less formal and only covers part of your thesis.

In most cases you’ll submit a small amount of the material you’ve produced so far. This could be a draft of your first chapter (or part of it) and / or your literature review. You could also be asked to reflect on your progress in general.

You’ll then sit down with your supervisor and someone else from your department (familiar with your field, but unrelated to your project). They’ll offer feedback on the quality of your work and ask questions about your findings.

The aim of the process won’t be to examine your drafts so much as to confirm that your project has the potential to justify a PhD – and that you’re on track to complete it on time.

‘Failing’ a PhD upgrade is actually quite rare. Your university may ask you to repeat the procedure if they are concerned that you haven’t made sufficient progress or established a viable plan for the rest of your project.

What is an MPhil?

The MPhil (Master of Philosophy) is also a research degree, but its scope is more limited than a PhD (Doctor of Philosophy). And no, just like a PhD, an MPhil isn’t necessarily a Philosophy qualification. Our guide covers all you need to know about the difference between a MPhil and PhD .

5. PhD teaching, conferences and publications

During the PhD process, you’ll have lots of opportunities to take part in extra-curricular activities, such as teaching, academic conferences and publications.

Although it isn’t usually compulsory to participate in these, they can be an incredibly rewarding experience and will look great on your CV.

Teaching during a PhD normally involves hosting undergraduate seminars or supervising students in the lab, as well as marking work and providing feedback.

Academic conferences are an excellent way to network with like-minded colleagues and find out the latest developments in your field. You might even be able to present your own work to your peers at one of these events.

Publishing during a PhD will help you increase your academic profile, as well as give you experience of the peer review process. It’s not normally a requisite of your PhD, but publications will certainly help if you plan on applying for postdoc positions.

6. Writing your thesis

As the culmination of three or more years of hard work, the thesis (or dissertation) is the most important part of the procedure to get your PhD, presenting you with the opportunity to make an original scholarly contribution to your discipline.

Our guide to writing your thesis covers everything you need to know about this lengthy research project, from structure and word count to writing up and submission.

We’ve also written a guide to the PhD dissertation abstract , which is an important part of any thesis.

7. Defending your PhD results at a viva voce

Unlike other degrees, a PhD isn’t normally marked as a piece of written work. Instead your dissertation will be submitted for an oral examination known as a viva voce (Latin for ‘living voice’).

This is a formal procedure, during which you ‘defend’ your thesis in front of appointed examiners, each of whom will have read your dissertation thoroughly in advance.

Examiners at a viva voce

A PhD is normally examined by two academic experts:

• One will be an internal examiner, usually appointed from elsewhere in your faculty and department. They won’t be directly associated with your project, but will have sufficient expertise to assess your findings.
• The other will be an external examiner. They will be a recognised expert in the area you are researching, with a record of relevant research and publication. Most universities in the UK allow you to invite an external examiner of your choice, provided there is no existing conflict of interest.

Your supervisor will help you prepare for the viva and will offer advice on choosing an external examiner. However, they will not normally be present during the examination.

The PhD timeline

Ready to take the next step?

There's lots more information about how to get a PhD in our advice section . Or, if you're ready to start looking at different projects, why not check out one of the thousands of current PhD opportunities in our database?

Not sure how PhD study will differ from a Masters? In this guide, we take a look at how the two qualifications compare, including applications, course structure, assessment and more.

Every student will need to write an abstract for their PhD dissertation. Here's everything you need to know about what an academic abstract is and how to write one.

What can you expect from a PhD? What's life actually like as a postgraduate student? Read our guides to the doctoral research experience.

The viva voce is the final oral exam at the end of a PhD degree. Our guide explains the usual viva format, covers common questions and explains how to prepare.

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Department of Mathematics

Thanks to its international focus, the Department of Mathematics offers doctoral students the best possible start to a career in academic or industrial research. A doctorate usually takes between three and five years.

The Department of Mathematics offers a broad spectrum of research areas for doctoral students ranging from pure mathematics, such as algebra, analysis, geometry, number theory or probability, to more applied mathematics, such as insurance mathematics, finance, mathematical physics, numerical analysis, operations research and statistics.

About twenty to thirty doctoral students complete their doctoral thesis at the Department every year: overview of upcoming and successfully passed doctoral examinations.

Research environment

Doctoral students work as scientific assistants and are employed for up to six years. They attend the external page Zurich Graduate School in Mathematics.

The benefits are:

• internationally highly respected professors
• research funded by the external page Swiss National Science Foundation
• offices in the ETH Zurich Main Building
• access to the Mathematics Library and the ETH Library , access to online publications
• conferences organised by the Forschungsinstitut für Mathematik to support the scientific exchange of ideas

Teaching activities

Passing on knowledge to future mathematicians, other scientists and engineers is a key part of doing doctoral studies at ETH Zurich. The teaching workload depends on the doctoral student's salary level. Teaching generally comprises:

• teaching exercise classes
• organising exercises for a lecture
• assisting in student seminars
• interacting with the lecturer and/or teaching assistants (undergraduate students)
• providing assistance for lectures ranging from basic mathematics for biologists to advanced lectures for mathematicians
• coordinating and correcting exams

Additional courses

Research lives from acquiring knowledge about current theory and discussing it with experts. During the regular doctoral studies, at least 12 ECTS credits must be acquired to cover the following objectives:

• Deepening of knowledge in the research field of the doctoral thesis and expansion of knowledge beyond the original discipline
• Acquisition of transferable skills
• Integration into the scientific community  

Courses and seminars:

• wide variety of high-level lectures, minicourses and student seminars: see ETH Zurich Course Catalogue or external page graduate courses offered by the Zurich Graduate School in Mathematics
• Reseach seminars organised by professors and research groups where experts from different mathematical fields give talks and exchange their knowledge
• The FIM - Institute for Mathematical Research and the Institute for Theoretical Studies invite academic guests for scientific exchange

Life in Zurich

• largest city in Switzerland with a top ranking for quality of life
• charming medieval old town very close to the ETH Main Building and the Department
• fantastic water activities, winter sports or hiking because of the lake and the Alps within close proximity
• variety of cultural events and night life, very cosmopolitan  

Further activities

• The external page Zurich Graduate School of Mathematics (ZGSM) organises language courses and social events such as barbecues and fondue dinners.
• The Association of Scientific Staff at ETH (AVETH) and the Association of Academic Staff at the D-MATH (VMM) represent the interests of doctoral students and organise events.
• The external page Academic Sports Association Zurich (ASVZ) offers a wide range of sports that fulfil every wish.

More Information

• chevron_right ETH Zurich – Doctorate
• chevron_right Student portal – Doctorate
• chevron_right Welcome Center
• chevron_right Continuing education in university teaching
• external page call_made German courses (ZGSM)
• external page call_made Language center

Legal matters

• chevron_right Ordinance on Doctoral Studies at ETH Zurich
• chevron_right Rector’s Implementation Provisions for the Ordinance on Doctoral Studies 2021

Associations

• protected page lock VMM – Association of the academic mid-level faculty at D-MATH
• chevron_right AVETH – Association of Scientific Staff at ETH
• chevron_right AVETH – Survival Guide

Mathematics (PhD)

Program description, dual-degree.

The Department of Mathematics is part of the Courant Institute of Mathematical Sciences , an independent division of New York University . Based in Warren Weaver Hall, at the heart of New York University’s Washington Square campus, it is one of the top-ranked Mathematics departments worldwide (#4 in the US and #9 in the world as per the Shanghai rankings ; #6 in the US and #8 in the world as per the QS rankings ).

For more on the Courant Institute and its pioneering history in the field of applied mathematics (our department is consistently ranked #1 in applied mathematics as per USNews), see the history page .

The study of mathematics can lead to a variety of exciting professional careers. Basic research, engineering, finance, business, and government service are among the opportunities open to those with mathematical training.  Moreover, with the increasing importance of basic science and information technology, prospects for careers in the mathematical sciences are very good. Mathematical analysis and computational modeling are important for solving some of the most pressing problems of our time - new energy resources, climate change, risk management, epidemiology, to name a few. We must strive to maintain our technological edge; mathematical skills will be crucial to this effort.

Some more specific business positions include portfolio analysis, design studies, statistical analysis, computer simulation, software design and testing, and other areas of operations research. There are extensive opportunities for mathematics in finance, the actuarial fields, and economic forecasting.

Many laboratories, both government and private, maintain independent research staffs that include mathematicians. Their work often deals with the development of new technology, including research in basic physics and software development, as well as applied mathematics. Numerical simulation, such as weather and climate forecasting, depends heavily on the use of supercomputers.

Practical considerations aside, there is the pleasure of learning, applying, and creating mathematics. Real world issues pose problems that can be studied by formulating and analyzing mathematical models. In some cases applications may lead to new mathematics, and a new branch of the science is born. In other cases abstract theory finds unexpected practical purpose. Working on research problems is exciting; solving difficult problems successfully is, for many, satisfaction enough.

All applicants to the Graduate School of Arts and Science (GSAS) are required to submit the  general application requirements , which include:

• Academic Transcripts
• Test Scores  (if required)
• Applicant Statements
• Résumé or Curriculum Vitae
• Letters of Recommendation , and
• A non-refundable  application fee .

See Mathematics for admission requirements and instructions specific to this program.

The Mathematics Department offers a dual-degree with the NYU School of Law: Mathematics PhD/Law JD.

Program Requirements

Written comprehensive examination, oral preliminary examination, dissertation defense, departmental approval.

The program requires the completion of 72 credits. It is possible, with departmental permission, to take courses relevant to students’ course of study in other departments at NYU or at other universities. A minimum of 32 credits must be completed at the Department of Mathematics.

Additional Program Requirements

The examination tests the basic knowledge required for any serious mathematical study; it is comprised of three individual examinations in Advanced Calculus, Complex Variables, and Linear Algebra, and is given on three consecutive days, twice a year, in early September (or, sometimes, late August) 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. Students may take the written examination twice; a third and final time requires the permission of the Director of Graduate Studies.

This examination is usually taken after two years of full-time study. Its purpose is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. 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. Students may take the oral examination twice; a third and final time requires the permission of the Director of Graduate Studies. All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points. It is recommended that students attempt the examinations well before this deadline.

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.

All Graduate School of Arts & Science doctoral candidates must be approved for graduation by their department for the degree to be awarded.

Sample Plan of Study

Following completion of the required coursework for the PhD, students are expected to maintain active status at New York University by enrolling in a research/writing course or a Maintain Matriculation ( MAINT-GA 4747 ) course.  All non-course requirements must be fulfilled prior to degree conferral, although the specific timing of completion may vary from student-to-student.

Learning Outcomes

Upon successful completion of the program, graduates will have:

• Mastery of the fundamental methods of basic areas in mathematics broadly related to their future research.
• Deep working knowledge of the theories, concepts and open questions in the selected area of research.
• Mastery in written communication sufficient for writing research articles acceptable for publication in peer-reviewed journals.
• Proficiency in oral communication sufficient to give lectures and presentation at scientific conferences and symposiums.
• Lecturing skills which enables them to teach courses in the future in broad areas in mathematics.
• Mastery of the modern tools and classical methods in the selected area of research.
• The ability to formulate sound research programs and bring a research project to fruition in the form of a peer-reviewed publication.

NYU Policies

Graduate school of arts and science policies.

University-wide policies can be found on the New York University Policy pages .

Academic Policies for the Graduate School of Arts and Science can be found on the Academic Policies page . 

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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 .

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• PhD Mathematics Education Program Timeline | Curriculum & Instruction | College of Education | University of Wyoming
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Program Timeline for Ph.D. in Mathematics Education

Annual review of progress/program timeline.

The following provides a framework to specify general expectations and be suggestive of the scope and sequence of the program, while realizing that all specific courses will be selected in consultation with the Major Professor and approved by the Doctoral Committee to satisfy the individual goals and needs of the student. An overall GPA of 3.0 must be maintained.

Year 1 (minimum 18 hours)

• Complete two mathematics education courses, receiving at least a B in each.
• Complete at least one college-wide core course (e.g., EDCI 5870 Introduction to Doctoral Studies)
• Complete at least one appropriate graduate mathematics course
• Complete two research methodology courses
• Completion of electives as recommended
• Identify and establish the choice of Major Professor; in consultation develop a program of study; establish the Doctoral Committee
• At year-end, submit preliminary proposal of research interests and ideas, and an annual self-evaluation; begin development of Reading List

Year 2 (minimum 18 hours)

• Complete at least one college-wide core course
• In Fall, conduct initial Doctoral Committee meeting; discuss and approve program of study; preliminary discussion of research interests
• Maintain and extend the Reading List; by mid-Spring, share it with the Doctoral Committee for review and feedback
• At year-end, submit an updated proposal of potential dissertation research, and an annual self-evaluation
• Submit a proposal to write and present a scholarly paper to a recognized mathematics education research conference (typically in collaboration with other graduate students and/or one or more faculty members)
• Conduct Doctoral Committee meeting to finalize Reading List and to frame and plan for completion of the written comprehensive exams before the end of Fall term

Year 3 (minimum 18 hours)

• Complete all additional courses on the approved Program of Study
• Enroll in at least 6 hours of dissertation research to conceptualize and develop the dissertation research proposal (which may include a pilot or preliminary study)
• Complete oral exams, and the defense and approval of the dissertation research proposal; obtain IRB approvals as needed
• Begin dissertation research project: complete detailed plans, collect data, engage analyses, begin writing as appropriate
• Submit a scholarly manuscript to a recognized mathematics education research journal (typically in collaboration with other graduate students and/or one or more faculty members)
• Submit an annual status report and self-evaluation

Year 4/Year 5 (as needed)

• Enroll in at least 6 hours of dissertation research each semester
• Continue toward completion of the dissertation research
• Finish writing, and defend the dissertation research; present your research at a Mathematics Education colloquium
• As feasible, begin developing one or more scholarly manuscripts based upon the dissertation
• Conduct search and interviews for seeking a post-doctoral position

In the culture of our program, we seek to function as faculty and students in a dynamic community of active scholars. As such, we acknowledge that many significant developmental experiences for doctoral students must and will take place outside formal course venues. Therefore, all students and faculty are expected to be vitally involved in ongoing research, development, and outreach projects and activities in which continuous interaction and collaboration occurs, within Mathematics Education and other disciplines.

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Is a PhD in mathematics worth it?

I know the answer to this depends on so so many factors but I would really appreciate to hear what people think about this. Maybe you’ve finished a PhD, are currently doing one, or considering to do one in the future.

I’ll provide some specific topics below to generate discussion:

Enjoyment, fulfilment, contributing to collective human knowledge.

Stress, mental health, burn out.

Career prospects (academia vs industry), salary, opportunity cost.

I finished a masters in applied maths this summer and have since started a job in data science. I’m trying to decide if it is worth taking 3/4 years out to pursue a PhD before probably coming back to work in industry.

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PhD Timeline and Milestones

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There is no specific length of time associated with earning a PhD. Across disciplines and campuses, the average amount of time to earn the degree is between four and five years, although individual time varies widely.

The education program was planned to span at least three years and was designed for students who already have undertaken graduate work and already demonstrated competence and interest in educational research. The length of the program, however, is based on the student’s progress in mastering subject matter, preparing for examinations, preparing research proposals, and conducting original research. The nature of these activities differs and makes for considerable time variability among students in the same program.

Year-by-Year Guideline

A general guideline for planning your graduate program is described below.

During the first year, students normally complete any prerequisites that are deemed necessary by the admissions committee, the graduate advisor, or faculty advisor. General program prerequisites are noted on the Advising Form in this handbook.

In addition to prerequisites, in the fall all PhD students are required to complete the one-quarter, 4-unit Proseminar In Education (EDU 291).

All students will take the following methodology core courses:

• EDU 201 Qualitative Methods (4) Winter
• EDU 204A Quantitative Methods in Educational Research: Analysis of Correlation and Design (4) Spring

Second year

During the second year of the program, students complete any remaining background course work or required course work. The rest of the second year is devoted to completing courses in your area of specialization. At least 32 units (approximately eight courses) are required for the area of specialization; these are selected with the assistance of the faculty advisor. You should also complete at least two advanced methodology courses.  Students will also complete the Preliminary Examination by the end of the second year.

Second/Third year

During the second and third year, students prepare for and complete the qualifying examination. The student and his or her qualifying examination committee will design a qualifying examination to assess readiness to complete the dissertation.

Fourth year plus

PhD dissertations must satisfy the standards and format of the Graduate Studies Office and those of an appropriate publications manual, for example, that of the American Psychological Association (latest edition). In general, the style and format of the journals by the AERA should be used in written work in this program.

The Office of Graduate Studies will assign a three-person committee to guide the dissertation, with one member serving as chair. Normally a student’s dissertation advisor will be the chair. All three members of the committee must approve the dissertation.

When the committee approves the dissertation, the student makes a public presentation of the dissertation results. The details of place and time for dissertation presentations will be publicly posted, and any member of the University community may attend and raise questions at this exit seminar. This presentation is not an examination, but an opportunity for students to inform members of the graduate group and others about their research. Participation in the process of research dissemination is viewed as a scholarly activity.

Expected Timeline for Completing Program Milestones


Students entering the Ph.D. program in Education are expected to make timely progress toward completing their doctoral studies. We have defined timely progress in terms of several program milestones. The table below specifies the time that students should take to complete each milestone. Students are encouraged to complete program milestones sooner than indicated, but not at the expense of producing quality work.

Students who do not complete program milestones within a normal time period are considered by the GGE faculty to be at risk of not completing the program successfully and will be counseled by their advisor to help them get back on track as quickly as possible.

Program Milestone Years to Completion


MILESTONE #1: Course requirements completed, Preliminary Exam passed, & Qualifying Exam committee formed two to three years from beginning of program

MILESTONE #2: Completion of both of the following two separate steps:

• Qualifying exam completed
• Dissertation proposal approved (Advancement to Candidacy) One year past Milestone #1, not to exceed four years from beginning of program

MILESTONE #3: Dissertation completed within four years past Milestone #2, not to exceed a total of seven years in the program.

We expect students to complete each milestone within the specified period of time. We recognize, however, that students come into the program with varied backgrounds and interest, and these will be reflected in somewhat different timelines through and between program milestones. We also recognize that exceptional circumstances can make it difficult for students to complete a program milestone within the normal period of time.

Progress in completing program milestones is an important criterion in shaping faculty evaluations of student work, including evaluations for fellowship and travel support, teaching assistantships, and research assistantships. GGE faculty also look for indications of each student’s course completion record, writing and reading ability, and writing and research productivity.

Faculty members also view the PhD program as a point of entry for students into the educational research community. Evidence that students are taking some initiative in joining this community - through collegial engagement with faculty, other doctoral students, and educational researchers in other venues (conferences, associations, journals, etc.) – is regarded very favorably by faculty members, not only on its own merits but as a resource to students in developing professional skills and dispositions. Evidence that students are not engaged in collegial relations of this sort is viewed by faculty members as a liability for students who hope to complete the program successfully and in a timely manner.

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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.

PhD Timeline

--> Also see the separate pages with on-boarding information for new PhD students <--   Information and Resources for New Graduate Students Wiki site for incoming PhD students (behind Harvard Key)

First Year (G1)

• Notify your financial aid officers of any external funding. Contact:  Erin Bishop  in SEAS Finance and  Emily Fingerle  in GSAS Financial Aid.
• Make note of the course registration deadline. (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
• Register for courses before the deadline  (previously known as "Study Card Day")
• Mid-January: Deadline for submitting materials to be reviewed at the January CHD meetings .
• Late-January: Course registration deadline (previously known as "Study Card Day").
• G1s: Your  Prospective Program Plan  due to the Office of Academic Programs on this day.
• Transfer of up to 3 classes of coursework may be allowed. Include the  Application for Credit for Work Done Elsewhere  with your Prospective Program Plan. 
• April 1:   Research Advisor Selection Form /Research Assistant appointment form due to Office of Academic Programs.
• Note: The April CHD meeting is the last CHD meeting in all academic year. CHD does not meet over the summer. Remember to plan ahead.

Second year (G2)

Throughout year.

• G2’s are required to serve as a Teaching Fellow in either the Fall or Spring semester.
• Make sure you complete the  TF form once you line up a TF position! 
• G2’s are required to take their qualifying exam in either the Fall or Spring terms.
• Email quals_defenses@seas  to book a room. If you book your own room (e.g., external to SEAS) you must still email  quals_defenses@seas  well in advance in order for your required documentation to be ready, else your exam cannot take place.
• Upon completion of the exam, students are required to submit the  Designation of Research Committee  form to OAP.
• If you plan to request a delay of the qualifying exam, complete a  Request to Delay Qual Exam  form. Note that delays until September (i.e. start of G3 year) are typically approved as a matter of course
• Mid-September: Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
• Mid-October :  Final Program Plan  due to OAP; see the  CHD page  for dates.
• Late-January : Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
• May 1 : Advising Agreement form due to OAP.
• May:   Commencement and diploma options for Masters en Route / Continuing Master’s students - You can apply to receive your S.M. degree en route to your PhD after you have completed eight of your core courses (this requirement may depend on area). You will receive your S.M. diploma, and participate in the Commencement if you choose to. However since you will be considered a non-terminal degree recipient, you will not be able to join the ceremony in Sander's Theater. 

Third year (G3+) and beyond

• Meet with your Research Committee at least annually, as indicated by your area's expectations.
• Send any changes to your Final Program Plan to the CHD for review. See the  CHD page  for submission dates.   Note that   the Committee on Higher Degrees expects students not to petition for a revised Program Plan less than a year prior to the final defense  in case additional coursework is required, so it's important to keep your plan up to date with your courses as actually taken.
• Inform OAP of any  changes to your research committee . 
• PhD candidates can review their eligibility to receive an SM en route . 
• Early-September:  Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
• Late-January: Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar
• May 1 :  RA reappointment  form due to OAP.

Completing your degree

Degree application.

• Check out FAS degree-completion information  here  (Registrar) and deadlines  here  (GSAS calendar)
• Complete the  degree application  via my.harvard by the Registrar's deadline.
• If you schedule your own room (e.g., external to SEAS) you must still email quals_defenses@seas   well in advance in order for your required documentation to be ready,  else your defense cannot take place.   You must also get agreement from your full committee to hold your defense in a non-SEAS room.

Dissertation Submission and Commencement

• The best way to share your dissertation with others is by linking to the DASH copy. DASH uses persistent URLs and provides you with download statistics, and the DASH copy of your PDF will not include the signed Dissertation Acceptance Certificate (DAC). If you choose to post or share your PDF in some other way, you should remove the DAC page so that readers do not have access to the scanned signatures.
• Get ready for commencement by updating your email and other contact information via  my.harvard.edu .

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