mathematics in phd

PhD Program

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

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

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

• real analysis
• geometry and topology
• applied mathematics

Course Requirements for students starting prior to Autumn 2023

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

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

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

Course Requirements for students starting in Autumn 2023 and later

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

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

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

Years 4&5

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

Throughout the PhD Program

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

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

Department of Mathematics

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

PhD in Mathematics

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

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

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

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

In addition to the above, PhD students often:

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

Ph.D. Program Overview

Description.

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

Core Courses

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

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

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

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

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

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

"What is...?" Seminar

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

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

Special Committee

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

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

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

Current Advising Committee

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

Admission to Candidacy

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

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

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

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

Masters Degree in the Minor Field

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

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

Graduate Student Funding

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

Special Requests

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

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Ph.D. Program in Mathematics

Degree requirements.

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

NYU Shanghai Ph.D. Track

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

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

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

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

Probability

PDE/Analysis

The Written Comprehensive Examination

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

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

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

The Oral Preliminary Examination

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

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

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

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

The Dissertation Defense

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

Summer Internships and Employment

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

Mentoring and Grievance Policy

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

Visiting Doctoral Students

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

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A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to discrete mathematics and combinatorics. These are the best graduate-level math programs. Each school's score reflects its average rating on a scale from 1 (marginal) to 5 (outstanding), based on a survey of academics at peer institutions. Read the methodology »

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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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PhD in Mathematics

Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at  Doctoral Programs . The requirements for all these programs consist of three components:  coursework ,  examinations , and  dissertation  in accordance to the guidelines described in the  GT Catalogue .

Completion of required coursework, examinations, and dissertation normally takes about five years. During the first one or two years, students concentrate on coursework to acquire the background necessary for the comprehensive examinations. By the end of their third year in the program, all students are expected to have chosen a thesis topic, and begin work on the research and writing of the dissertation.

The program of study must contain at least 30 hours of graduate-level coursework (6000-level or above) in mathematics and an additional 9 hours of coursework towards a minor. The minor requirement consists of graduate or advanced undergraduate coursework taken entirely outside the School of Mathematics, or in an area of mathematics sufficiently far from the students area of specialization.

Prior to admission to candidacy for the doctoral degree, each student must satisfy the School's comprehensive examinations (comps) requirement. The first phase is a written examination which students must complete by the end of their second year in the graduate program. The second phase is an oral examination in the student's proposed area of specialization, which must be completed by the end of the third year.

Research and the writing of the dissertation represent the final phase of the student's doctoral study, and must be completed within seven years of the passing of comps. A final oral examination on the dissertation (theses defense) must be passed prior to the granting of the degree.

The Coursework

The program of study must satisfy the following  hours ,  minor , and  breadth  requirements. Students who entered before Fall 2015 should see  the old requirements , though they may opt into the current rules described below, and are advised to do so.

Hours requirements.  The students must complete 39 hours of coursework as follows:

• At least 30 hours must be in mathematics courses at the 6000-level or higher.
• At least 9 hours must form the doctoral minor field of study.
• The overall GPA for these courses must be at least 3.0.
• These courses must be taken for a letter grade and passed with a grade of at least C.

Minor requirement.  The minor field of study should consist primarily of 6000-level (or higher) coursework in a specific area outside the School of Math, or in a mathematical subject sufficiently far from the student’s thesis work. A total of 9 credit hours is required and must be passed with a grade of B or better. These courses should not include MATH 8900, and must be chosen in consultation with the PhD advisor and the Director of Graduate Studies to ensure that they form a cohesive group which best complements the students research and career goals. A student wishing to satisfy the minor requirement by mathematics courses must petition the Graduate Committee for approval.  Courses used to fulfill a Basic Understanding breadth requirement in Analysis or Algebra should not be counted towards the doctoral minor. Upon completing the minor requirement, a student should immediately complete the  Doctoral Minor form .

Breadth requirements.  The students must demonstrate:

• Basic understanding of 2 subjects must be demonstrated through passing the subjects' written comprehensive exams.  At least 1 of these 2 exams must be in Algebra or Analysis.
• Basic understanding of the third subject may be demonstrated either by completing two courses in the subject (with a grade of A or B in each course) or by passing the subject's written comprehensive exam.
• A basic understanding of both subjects in Area I (analysis and algebra) must be demonstrated.
• Earning a grade of A or B in a one-semester graduate course in a subject demonstrates exposure to the subject.
• Passing a subject's written comprehensive exam also demonstrates exposure to that subject.

The subjects.  The specific subjects, and associated courses, which can be used to satisfy the breadth requirements are as follows.

• Area I subjects:​
• Area II subjects:​

Special Topics and Reading Courses.

• Special topics courses may always be used to meet hours requirements.
• Special topics courses may be used to meet breadth requirements, subject to the discretion of the Director of Graduate Studies.
• Reading courses may be used to meet hours requirements but not breadth requirements.

Credit Transfers

Graduate courses completed at other universities may be counted towards breadth and hours requirements (courses designated as undergraduate or Bachelors' level courses are not eligible to transfer for graduate credit).  These courses do not need to be officially transferred to Georgia Tech. At a student’s request, the Director of Graduate Studies will determine which breadth and hours requirements have been satisfied by graduate-level coursework at another institution.  

Courses taken at other institutions may also be counted toward the minor requirement, subject to the approval of the Graduate Director; however, these courses must be officially transferred to Georgia Tech.

There is no limit for the transfer of credits applied toward the breadth requirements; however, a maximum of 12 hours of coursework from other institutions may be used to satisfy hours requirements. Thus at least 27 hours of coursework must be completed at Georgia Tech, including at least 18 hours of 6000-level (or higher) mathematics coursework.

Students wishing to petition for transfer of credit from previous graduate level work should send the transcripts and syllabi of these courses, together with a list of the corresponding courses in the School of Math, to the Director of Advising and Assessment for the graduate program.

Comprehensive Examinations

The comprehensive examination is in two phases. The first phase consists of passing two out of seven written examinations. The second phase is an oral specialty examination in the student's planned area of concentration. Generally, a student is expected to have studied the intended area of research but not necessarily begun dissertation research at the time of the oral examination.

Written examinations.  The written examinations will be administered twice each year, shortly after the beginning of the Fall and Spring semesters. The result of the written examination is either pass or fail. For syllabi and sample exams see the  written exams page .

All students must adhere to the following rules and timetables, which may be extended by the Director of Graduate Studies, but only at the time of matriculation and only when certified in writing. Modifications because of leaves from the program will be decided on a case-by-case basis.

After acceptance into the PhD Program in Mathematics, a student must pass the written examinations no later than their fourth administration since the student's doctoral enrollment. The students can pass each of the two written comprehensive exams in separate semesters, and are allowed multiple attempts.

The Director of Graduate Studies (DGS) will be responsible for advising each new student at matriculation of these rules and procedures and the appropriate timetable for the written portion of the examination. The DGS will also be responsible for maintaining a study guide and list of recommended texts, as well as a file of previous examinations, to be used by students preparing for this written examination.

Oral examination.  A student must pass the oral specialty examination within three years since first enrolling in the PhD program, and after having passed the written portion of the comprehensive exams. The examination will be given by a committee consisting of the student's dissertation advisor or probable advisor, two faculty members chosen by the advisor in consultation with the student, and a fourth member appointed by the School's Graduate Director. The scope of the examination will be determined by the advisor and will be approved by the graduate coordinator. The examining committee shall either (1) pass the student or (2) fail the student. Within the time constraints of which above, the oral specialty examination may be attempted multiple times, though not more than twice in any given semester. For more details and specific rules and policies see the  oral exam page .

Dissertation and Defense

A dissertation and a final oral examination are required. For details see our  Dissertation and Graduation  page, which applies to all PhD programs in the School of Math.

Mathematics, PhD

Zanvyl krieger school of arts and sciences.

The goal of our PhD program is to train graduate students to become research mathematicians. Each year, an average of five students complete their theses and  go on to exciting careers  in mathematics both inside and outside of academia.

Faculty research interests  in the Johns Hopkins University Department of Mathematics are concentrated in several areas of pure mathematics, including analysis and geometric analysis, algebraic geometry and number theory, differential geometry, algebraic topology, category theory, and mathematical physics. The department also has an active group in data science, in collaboration with the  Applied Math Department .

The Department values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from all interested parties.

A brief overview of our graduate program is below. For more detailed information, please see the links at the right.

Program Overview

All students admitted to the PhD program receive full tuition fellowships and teaching assistantships. Teaching assistant salaries for the 2022-2023 academic year are $33,000, and exceptional applicants are also considered for supplementary fellowships. Students making satisfactory progress can expect to be supported for six years.

PhD candidates take two or three courses per semester over the first several years of the program. These are a mix of required and intermediate-level graduate courses, independent studies, and special topics classes offered by our faculty.

By the beginning of their second year, students are asked to demonstrate competency in algebra and in analysis by passing written qualifying exams in these two broad areas. Students are then expected to choose an advisor, who will supervise their dissertation and also administer an oral qualifying exam to be taken in the second or third year. More specifics about all these requirements are described on the  requirements page .

All graduate students are invited to attend  weekly research seminars in a variety of topic areas  as well as regular department teas and a weekly wine and cheese gathering attended by many junior and senior members of the department. A graduate student lunch seminar series provides an opportunity for our students to practice their presentation skills to a general audience.

PhD students will gain teaching experience as a teaching assistant for undergraduate courses. Most of our students lead two TA sections per week, under the supervision of both the faculty member teaching the course and the director of undergraduate studies. Students wanting more classroom experience (or extra pay) can teach their own sections of summer courses. First-year students are given a reduced TA workload in the spring semester, in preparation for the qualifying exams.

In addition to their stipend, each student is awarded an annual travel allowance to enable them to attend conferences for which limited funding is available or visit researchers at other institutions.

Financial Aid

Students admitted to the Ph.D. program receive teaching assistantships and full tuition fellowships. Exceptional applicants become candidates for one of the university's George E. Owen Fellowships.

William Kelso Morrill Award

The William Kelso Morrill Award for excellence in the teaching of mathematics is awarded every spring to the graduate student who best exemplifies the traits of Kelso Morrill: a love of mathematics, a love of teaching, and a concern for students.

Excellence in Teaching Awards

Three awards are given each year to a junior faculty member and graduate student teaching assistants who have demonstrated exceptional ability and commitment to undergraduate education.

Admission Requirements

Admission to the PhD program is based on primarily on academic records, letters of recommendation, and a personal statement. The Department of Mathematics values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from all interested parties.

Via the online application , applicants should submit:

• A Statement of Purpose
• An optional Personal Statement
• Transcripts from all institutions attended
• Three letters of recommendation
• Official GRE scores for both the general and the subject test
• Official TOEFL scores (if English is not your first language)

The required Statement of Purpose discusses your academic interests, objectives, and preparation. The optional Personal Statement describes your personal background, and helps us create a more holistic understanding of you as an applicant. If you wish you may also discuss your personal background in the Statement of Purpose (e.g. if you have already written a single essay addressing both topics), instead of submitting separate statements.

Application fee waivers are available based on financial need and/or participation in certain programs .

Many frequently asked questions about the graduate admission process are answered here .

No application materials should be mailed to the department. All application materials are processed by the Graduate Admissions Office .

Undergraduate Background

The following is an example of what the math department would consider a good background for a student coming out of a four-year undergraduate program at a college or university in the U.S. (assuming a semester system):

• Calculus in one variable (two semesters, or AP credits)
• Multivariable Calculus (one semester)
• Linear Algebra (one semester)
• Complex analysis (one semester)
• Real analysis (two semesters)
• Abstract algebra (two semesters)
• Point-set topology (one semester)

Many admitted students have taken upper-level undergraduate mathematics courses or graduate courses. Nevertheless, the department does admit very promising students whose preparation falls a little short of the above model. In such cases, we strongly recommend that the student start to close the gap over the summer, before arriving for the start of the fall semester.

Financial Support   

Students admitted to the PhD program receive full tuition fellowships and teaching assistantships. Teaching assistant salaries for the 2022–2023 academic year are $33,000. Students making satisfactory progress can expect to be supported for six years. Exceptional applicants are considered for supplementary fellowships of $6,000 each year for three years.

Students from underrepresented groups may be eligible for other university-wide supplemental fellowships. Summer teaching is available for students seeking extra income.

Additional Information for International Students

Student Visa Information:  The Office of International Services at Homewood  will assist admitted international students in obtaining a student visa.

English Proficiency: Johns Hopkins University requires students to have adequate English proficiency for their course of study. Students must be able to read, speak, and write English fluently upon their arrival at the university. Applicants whose native language is not English must submit proof of their proficiency in English before they can be offered admission and before a visa certificate can be issued. Proficiency can be demonstrated by submitting results from either the Test of English as a Foreign Language (TOEFL) or the IELTS . Johns Hopkins prefers a minimum score of 100 on the TOEFL or a Band Score of 7 on the IELTS. Results should be sent to Johns Hopkins directly by TOEFL or IELTS. Applicants taking the IELTS must additionally upload a copy of their score through the application system. However, do not send the student copy or a photocopy of the TOEFL.

Program Requirements

Course requirements.

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

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

Qualifying Exams

Candidates must pass written qualifying exams by the beginning of their second year in Analysis (Real & Complex) and in Algebra. Exams are scheduled for September and May of each academic year, and the dates are announced well in advance.

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

PhD Dissertation

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

Our PhD program does not have a foreign language requirement.

Graduate Program

Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we urge independent work and research, there exists a real sense of camaraderie among our graduate students. As a result, the atmosphere created is one of excitement and stimulation as well as of mentoring and support. Furthermore, there exists a strong scholarly relationship between the Math Department and the Institute for Advanced Study, located just a short distance from campus, where students can make contact with members there as well as attend the IAS seminar series.  Our program has minimal requirements and maximal research and educational opportunities. We offer a broad variety of advanced research topics courses as well as more introductory level courses in algebra, analysis, and geometry, which help first-year students strengthen their mathematical background and get involved with faculty through basic course work. In addition to the courses, there are several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the Department Colloquium give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students for graduate students, creating a vibrant mathematical interaction among them; and, (3) What’s Happening in Fine Hall (WHIFH) seminar where faculty give talks in their own research areas specifically geared towards graduate students. Working or reading seminars in various research fields are also organized by graduate students each semester. First-year students are set on the fast track of research by choosing two advanced topics of research, beyond having a strong knowledge of three more general subjects: algebra, and real and complex analysis, as part of the required General Examination. It is the hope that one, or both, of the advanced topics will lead to the further discovery of a thesis problem. Students are expected to write a thesis in four years but will be provided an additional year to complete their work if deemed necessary. Most of our Ph.D.'s are successfully launched into academic positions at premier mathematical institutions as well as in industry .

Chenyang Xu

Jill leclair.

Overview of the PhD Program

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

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

General Ph.D. Requirements

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

Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

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

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

In Applied Mathematics

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

The department offers programs covering a broad range of topics leading to the Doctor of Philosophy and the Doctor of Science degrees (the student chooses which to receive; they are functionally equivalent). Candidates are admitted to either the Pure or Applied Mathematics programs but are free to pursue interests in both groups. Of the roughly 120 Ph.D. students, about 2/3 are in Pure Mathematics, 1/3 in Applied Mathematics.

The two programs in Pure and Applied Mathematics offer basic and advanced classes in analysis, algebra, geometry, Lie theory, logic, number theory, probability, statistics, topology, astrophysics, combinatorics, fluid dynamics, numerical analysis, mathematics of data, and the theory of computation. In addition, many mathematically-oriented courses are offered by other departments. Students in Applied Mathematics are especially encouraged to take courses in engineering and scientific subjects related to their research.

All students pursue research under the supervision of the faculty , and are encouraged to take advantage of the many seminars and colloquia at MIT and in the Boston area.

Degree Requirements

Degree requirements consist of:

• Oral qualifying exam
• Classroom teaching
• Original thesis and defense

Prospective students are invited to consult the graduate career timeline for more information, and to read about the application procedure .

Graduate Co-Chairs

Graduate Student Issues, math graduate admissions

Jonathan Kelner , Davesh Maulik , and Zhiwei Yun

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

Mathematics

Undergraduate Program

Mathematics is the science of order, and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations. The concentration in Mathematics is designed to acquaint the student with the most important general concepts underlying the three branches of modern mathematics. Concentration in mathematics will provide an adequate basis for further study in either pure or applied mathematics. Students are also eligible to apply for an A.B./A.M. degree program.

The graduate Mathematics Program at Harvard is designed for students who hope to become research mathematicians and show definite promise in this direction. Once the student has demonstrated a command of basic mathematical concepts by passing the qualifying examination, the emphasis is on getting to the frontiers of some field by independent reading, advanced courses, and seminars. The Cambridge area is one of the most active centers of mathematics in the world. Harvard, Brandeis, and Northeastern Universities and the Massachusetts Institute of Technology have an especially close association in mathematics, and the Harvard University Center of Mathematical Sciences and Applications hosts conferences, seminars, and workshops.

Department of Mathematics

• Prospective Graduate Student FAQ
• Graduate Board Oral Exam
• Graduate Courses
• Qualifying Exams
• Recent PhD Theses
• Graduate Awards

The goal of our PhD program is to train graduate students to become research mathematicians. Each year, an average of five students complete their theses and go on to exciting careers in mathematics both inside and outside of academia.

Faculty research interests in the Johns Hopkins University Department of Mathematics are concentrated in several areas of pure mathematics, including analysis and geometric analysis, algebraic geometry and number theory, differential geometry, algebraic topology, category theory, and mathematical physics. The department also has an active group in data science, in collaboration with the Applied Math Department .

The Department values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from all interested parties.

A brief overview of our graduate program is below. For more detailed information, please see the links at the right.

Program Overview

All students admitted to the PhD program receive full tuition fellowships and teaching assistantships. Students making satisfactory progress are guaranteed support for five years. A sixth year is generally possible for students who are on track to complete their Ph.D. and would benefit from the additional year.

PhD candidates take two or three courses per semester over the first several years of the program. These are a mix of required and intermediate-level graduate courses, independent studies, and special topics classes offered by our faculty.

By the beginning of their second year, students are asked to demonstrate competency in algebra and in analysis by passing written qualifying exams in these two broad areas. Students are then expected to choose an advisor, who will supervise their dissertation and also administer an oral qualifying exam to be taken in the second or third year. More specifics about all these requirements are described on the requirements page .

All graduate students are invited to attend weekly research seminars in a variety of topic areas as well as regular department teas and a weekly wine and cheese gathering attended by many junior and senior members of the department. A graduate student lunch seminar series provides an opportunity for our students to practice their presentation skills to a general audience.

PhD students will gain teaching experience as a teaching assistant for undergraduate courses. Most of our students lead two TA sections per week, under the supervision of both the faculty member teaching the course and the director of undergraduate studies. Students wanting more classroom experience (or extra pay) can teach their own sections of summer courses. First-year students are given a reduced TA workload in the spring semester, in preparation for the qualifying exams.

In addition to their stipend, each student is awarded an annual travel allowance to enable them to attend conferences for which limited funding is available or visit researchers at other institutions.

• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

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

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

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

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

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

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

Browse PhD Opportunities in Mathematics

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

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

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

Additional Learning Modules

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

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

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

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

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

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

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

Tips to Consider when Making Your Application

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

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

How Much Does a Maths PhD Typically Cost?

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

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

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

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

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

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

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

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

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

What Jobs Can You Get with A Maths PhD?

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

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

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

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

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

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

How Much Can You Earn with A PhD in Maths?

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

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

Academic Lecturer

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

Actuary or Finance

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

Aerospace or Mechanical Engineering

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

Data Analyst

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

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

Facts and Statistics About Maths PhD Holders

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

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

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

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

Ruth Lawrence

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

Emmy Noether

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

Other Useful Resources

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

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

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

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

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

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

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

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

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Mathematics, PHD

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

• Location: Tempe campus
• Second Language Requirement: No

Program Description

Degree Awarded: PHD Mathematics

The PhD program in mathematics is intended for students with exceptional mathematical ability. The program emphasizes a solid mathematical foundation and promotes innovative scholarship in mathematics and its many related disciplines.

The School of Mathematical and Statistical Sciences has very active research groups in analysis, number theory, geometry and discrete mathematics.

Degree Requirements

84 credit hours, a written comprehensive exam, a prospectus and a dissertation

Required Core (3 credit hours) MAT 501 Geometry and Topology of Manifolds I (3) or MAT 516 Graph Theory I (3) or MAT 543 Abstract Algebra I (3) or MAT 570 Real Analysis I (3)

Other Requirements (3 credit hours) MAT 591 Seminar (3)

Electives (24-39 credit hours)

Research (27-42 credit hours) MAT 792 Research

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

Additional Curriculum Information Electives are to be chosen from math or related area courses approved by the student's supervisory committee.

Students must pass:

• two qualifying examinations
• a written comprehensive examination
• an oral dissertation prospectus defense

Students should see the department website for examination information.

Each student must write a dissertation and defend it orally in front of five dissertation committee members.

Admission Requirements

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

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

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

All applicants must submit:

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

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

Additional eligibility requirements include competitiveness in an applicant pool as evidenced by coursework in linear algebra (equivalent to ASU course MAT 342 or MAT 343) and advanced calculus (equivalent to ASU course MAT 371), and it is desirable that applicants have scientific programming skills.

Next Steps to attend ASU

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

• Address an original research question in mathematics.
• Able to complete original research in theoretical mathematics.
• Apply advanced mathematical skills in coursework and research.

Career Opportunities

Graduates of the doctoral program in mathematics possess sophisticated mathematical skills required for careers in many different sectors, including education, industry and government. Potential career opportunities include:

• faculty-track academic
• finance and investment analyst
• mathematician
• mathematics professor, instructor or researcher
• operations research analyst
• statistician

Program Contact Information

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

• [email protected]
• 480/965-3951

The Graduate Program

The Department of Mathematics offers Ph.D. programs in Mathematics and Applied Mathematics. The department also supports students in the  Graduate Group in Logic and the Methodology of Science , an interdisciplinary doctoral program shared between the departments of Philosophy and Mathematics. At this time, we no longer offer a terminal Master's degree program.

To review the policies and procedures of the Graduate Program, please refer to our  Graduate Student Handbook .

Please note: Some Mathematics Advising Services have been moved to virtual platforms. You can find the latest information on UC Berkeley’s prevention and response efforts  related to COVID-19 here.

Graduate Program Contacts 

The Graduate Program is overseen by the Departmental Vice Chair for Graduate Affairs and the Graduate Student Affairs Officers. 

• Professor Tom Scanlon, Vice Chair for Graduate Affairs
• Clay Calder, Graduate Student Affairs Officer
• Christian Natividad, Graduate Student Affairs Officer 
• Vicky Lee, Director of Student Services

For Questions Regarding Math Graduate Admissions: Please see the Admissions web page  here . After reviewing the admissions website, if you have further questions please email [email protected] .

The Doctor of Philosophy degree is awarded for superior accomplishment, the attainment of a high level of scholarship and the demonstrated ability, through independent study and research, to carry out an original investigation and present the results of such investigation.

Course requirements

Until the student has selected a major professor, the graduate advisor will assist in planning the doctoral program. The program will be designed to provide the student with competence in several major areas of mathematics and to provide for intensive study and research in the area of specialization.

The student will be expected to complete at least 72 hours of graduate work in mathematics beyond the bachelor’s degree, of which about half should be in courses numbered above 6000. Those students admitted with a master’s degree in pure and/or applied mathematics will be expected to complete at least 54 hours of graduate work in mathematics beyond the master’s degree.

Included in this work, the student will be expected to take (or previously have taken the equivalent of) the following core sequences:

• MATH 5310 - Real Analysis
• MATH 5320 - Real Analysis
• MATH 5410 - Complex Analysis
• MATH 5420 - Complex Analysis
• MATH 5520 - Modern Algebra
• MATH 5530 - Modern Algebra
• MATH 5610 - Topology
• MATH 5620 - Topology

In addition

The student is required to take a broad selection of 6000-level courses, normally at least two 6000-level courses in each of the areas of algebra, analysis and topology.

Qualifying examinations

Before enrolling in the dissertation seminar, the student must pass qualifying examinations over two areas chosen from algebra, topology, real analysis, complex analysis, probability and statistics, and applied mathematics. The doctoral advisory committee is appointed upon successful completion of the qualifying examinations.

Dissertation and final examination

The candidate must submit a dissertation exhibiting independent research on a topic approved by the doctoral committee. After the completion of the dissertation, a final comprehensive oral examination that will be primarily a defense of the dissertation will be given.

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Mathematics Education (Ph.D.)

Why pursue a Ph.D. in mathematics education at UNH?

Earning a Ph.D. in mathematics education prepares you to work in academia as a professor of mathematics education, mathematics or education;to take on leadership roles in mathematics education;and to be involved in cutting-edge research. The uniqueness of the Ph.D.program at UNH is that it provides you with a strong mathematical background comparable to that of the pure mathematics Ph.D. You will complete coursework alongside graduate students of pure and applied mathematics, as well as specialized coursework in mathematics education. To expand and broaden your preparation you will also pursue study in a related minor field, such as statistics, educational psychology, research methods or STEM disciplines.

Program highlights

You will work alongside accomplished mathematics education researchers, mathematicians and statisticians who are professionally active. You will gain an understanding of the breadth of the field of mathematics education while also engaging in original research. You will have the opportunity to work on externally funded projects and teach courses for prospective teachers. Graduates of our programs find jobs at both mathematics and education departments at the top universities across the U.S.and beyond.

Potential careers

• Curriculum supervisor/developer
• Educational software developer
• Mathematics education consultant
• Mathematics educator in government/research/academia
• Mathematics teacher
• Mathematics textbook writer/editor/publisher
• Professor of mathematics education or mathematics
• Researcher in mathematics education

Rita Hibschweiler

Request information.

Contact Information

Curriculum & Requirements

Program description.

The program is designed to provide students with depth and breadth in the fields of both mathematics education and mathematics, preparing students for educational and research leadership. The program is designed to advance forefront knowledge in mathematics education.

Admission Requirement

Applicants to the Ph.D. in Mathematics Education degree must have BA or BS from an accredited college or university. Successful candidates typically have a bachelor’s degree in mathematics or mathematics education and/or advanced coursework in mathematics.

Please visit the  Graduate School website  for detailed instructions about applying to the program.

Requirements for the Program

Students are advanced to candidacy after meeting the following requirements:

Successful completion of written comprehensive examinations in algebra, analysis, mathematics education and an elective subject.

Successful completion of a minor program of study (usually a related one, such as educational psychology or research methodology, but possibly in an area of mathematics) followed by the minor presentation.

Successful completion of a dissertation proposal defense in the major field of mathematics education. 

Experience in teaching equivalent to at least half-­time for one year typically through assistantship assignments.

Dissertation

Students must complete and submit a dissertation that involves original research in mathematics education.

Student Learning Outcomes

• Demonstrate deep knowledge of graduate level mathematics content: algebra, analysis, topology.
• Demonstrate competency in the minor field of study different from, but related to mathematics education (e.g., mathematics, statistics, linguistics, research methods, other sciences, STEM disciplines).
• Demonstrate the ability to conduct and communicate foundations of mathematics education research, theories of mathematics teaching and learning, and mathematics curriculum.

Application Requirements & Deadlines

Applications must be completed by the following deadlines in order to be reviewed for admission:

• Fall : Feb. 15 (for funding); April 1 (recommended US; final international); July 1 (final)
• Spring : Dec. 1 , Nov. 1 for international students
• Summer : N/A
• Special : N/A

Application fee : $65

Campus : Durham

New England Regional : CT ME VT RI

Accelerated Masters Eligible : No

New Hampshire Residents

Students claiming in-state residency must also submit a Proof of Residence Form . This form is not required to complete your application, but you will need to submit it after you are offered admission or you will not be able to register for classes.

Transcripts

If you attended UNH or Granite State College (GSC) after September 1, 1991, and have indicated so on your online application, we will retrieve your transcript internally; this includes UNH-Durham, UNH-Manchester, UNH Non-Degree work and GSC. 

If you did not attend UNH, or attended prior to September 1, 1991, then you must upload a copy (PDF) of your transcript in the application form. International transcripts must be translated into English.

If admitted , you must then request an official transcript be sent directly to our office from the Registrar's Office of each college/university attended. We accept transcripts both electronically and in hard copy:

• Electronic Transcripts : Please have your institution send the transcript directly to [email protected] . Please note that we can only accept copies sent directly from the institution.
• Paper Transcripts : Please send hard copies of transcripts to: UNH Graduate School, Thompson Hall- 105 Main Street, Durham, NH 03824. You may request transcripts be sent to us directly from the institution or you may send them yourself as long as they remain sealed in the original university envelope.

Transcripts from all previous post-secondary institutions must be submitted and applicants must disclose any previous academic or disciplinary sanctions that resulted in their temporary or permanent separation from a previous post-secondary institution. If it is found that previous academic or disciplinary separations were not disclosed, applicants may face denial and admitted students may face dismissal from their academic program.

Letters of recommendation: 3 required

Recommendation letters submitted by relatives or friends, as well as letters older than one year, will not be accepted.

Personal Statement/Essay Questions

Prepare a brief but careful statement regarding:

• Reasons you wish to do graduate work in this field, including your immediate and long-range objectives.
• Your specific research or professional interest and experiences in this field.

Important Notes

All applicants are encouraged to contact programs directly to discuss program-specific application questions.

International Applicants

Prospective international students are required to submit TOEFL, IELTS, or equivalent examination scores. English Language Exams may be waived if English is your first language. If you wish to request a waiver, then please visit our Test Scores webpage for more information.

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Charles Wexler prize recipient finds passion for math at ASU

Jacob Cooper is the recipient of the Charles Wexler Mathematics Prize, the highest honor an undergraduate in the School of Mathematical and Statistical Sciences can receive. He is graduating with a Bachelor of Science in mathematics this May and plans to pursue a PhD in mathematics at ASU next.

Editor’s note:  This story is part of a series of profiles of  notable spring 2024 graduates .

Jacob Cooper initially enrolled as a computer science major at Arizona State University, but after taking MAT 300 just out of curiosity, he felt a spark of interest in mathematics so strong he decided to switch majors.

This month, Cooper is graduating with a Bachelor of Science in mathematics and was selected as the recipient of the Charles Wexler Mathematics Prize , the highest honor an undergraduate in the School of Mathematical and Statistical Sciences can receive.

“It feels incredibly mind-blowing,” said Cooper. “I remember when I first joined the math program, texting my friends back home that I was scared, and that I wasn’t sure if I was going to be able to integrate myself into the community, since I had such a hard time in the computer science program.

“But over time, I found that it was a really wonderful community of incredibly talented mathematicians, all of whom I think would have been great recipients for this award.”

Cooper, who grew up in Flagstaff, Arizona, hadn’t had the best grades in high school and was worried he wouldn’t meet the GPA requirements of many scholarships. He discovered that ASU allowed students to qualify based on test scores and was pleased to be accepted with a President’s Scholarship.

Assistant Professor Malena Español first met Cooper in her numerical analysis course, where he received an A-plus. As part of the course, he worked on an interdisciplinary team of four on a final project titled “Audio Classification.”

“During this project, Jacob showed that he has strong computational and mathematical backgrounds, works well with others, has excellent written and oral communication skills, and can lead a team project,” said Español.

Cooper took advanced linear algebra with Assistant Professor Jonathan Montaño , where he earned another A-plus grade. Cooper approached Montaño last August asking if he could join fellow undergrad Ethan Leventhal in his Barrett honors thesis project on the multidegrees of binomial edge ideals, which is work that connects graph theory and algebraic geometry.

“I explained to him that Ethan had already spent a semester learning the prerequisites for the project, but Jacob did not shy away from the challenge,” Montaño said. “This reflects Jacob’s strong commitment and work ethic. They have been working together since then and have made important progress. They have already obtained good results that in my opinion are publishable.”

Cooper also worked with other faculty members, including Assistant Professor Molly Simon on science identity and sense of belonging in an introductory geology course, and served as a grader and instructional aide for a number of math courses.

Last summer he worked with the Joaquin Bustoz Math-Science Honors Program as a class supervisor. He managed four tutors and 25 students while working alongside Associate Teaching Professor Frank Arthur . Program manager Cynthia Romero explained that students in the program — which allows high school students to take a college-level mathematics or science course at ASU at no cost — are “underrepresented in STEM, first-generation collegebound and/or from low-socioeconomic households.”

“They can often feel overwhelmed due to being away home, culture shock of being at a large university or the high level of academic rigor,” Romero said. “Jacob created a fun and inclusive class environment full of music, cat memes and inspirational talks that helped him establish trust with his students. Jacob focused on both the student's mental well-being in addition to their academic success.”

After graduation, Cooper plans to pursue a PhD in mathematics at ASU. We asked him to share more about his journey as a Sun Devil.

Question: What’s something you learned while at ASU — in the classroom or otherwise — that surprised you, that changed your perspective?

Answer: I was always really intimidated by professors, and while it’s silly, it surprised me just how human they were. They all have fun stories and are so interesting to get to know, and have such wonderful insight and experiences.

Q: What’s the best piece of advice you’d give to those still in school?

A: Be nice to yourself and find ways to take little steps forward. Failure is inevitable, and it’s impossible to be perfect.

Q: What is most misunderstood about mathematics by the general public?

A: A lot of people think math is about finding the correct answer, and I think that is because of how it’s taught. But I think that it’s the opposite: Math is about exploring all the ways to do the same thing, and how those changes in perspective change your way of thinking.

Q: What was your favorite spot on campus?

A: The rooftop of PSH (Bateman Physical Sciences Center, H-wing) while observing the stars.

Q: Which clubs, activities, or community service projects are you involved in?

A: I am currently the treasurer of the Astronomy Club at ASU, and I’ve done a considerable amount of hours volunteering for outreach events for them. I also served as secretary/treasurer for the Math Bio Club, was an active member of the ASU Student Chapter of the Association for Women in Mathematics, and helped found the Scholars of Physical Mathematics, which aims to bring together students of both disciplines. My proudest activity was being a class supervisor and lead tutor for the Joaquin Bustoz Math-Science Honors Program.

Q: What do you like to do in your spare time?

A: Music is really important to me, and sometimes when I was bored (or procrastinating) on campus, I would find my way into the practice rooms in the music hall to play piano. I also enjoy playing with my two cats. I also try to find time to play games with my friends.

Q: If someone gave you $40 million to solve one problem on our planet, what would you tackle?

A: Education is a human right, and I would want to use that money to try and make education more accessible. I think that there are a lot of people who would excel in academia and have an amazing time in college, but can’t because the costs and barriers are too high.

Q: What were your favorite memories of your time in the School of Mathematical and Statistical Sciences?

A: Working as an IA for Associate Teaching Professor Beth Schlenker and trying to spread enthusiasm for math to the business students. Taking MAT 371 with President’s Professor Matthias Kawski , and making my first friends in the math department. Going to Coffee Break and socializing when my schedule wasn’t in the way. Attending lectures for my first graduate-level class with Associate Professor Julien Paupert . Attending the 2022 and 2023 AWSiM conferences. Volunteering for the school during Open Door and the Homecoming Block Party. …

I really couldn’t have asked for a better experience (at ASU). … This department is full of so many incredible people and mathematicians, and I see just how much effort and passion we all have for math. As much as I love math, I don’t think that it’s worth anything without the human aspect, and without the connection it brings to those who enjoy it.

More Sun Devil community

Dean's medalist plans to pursue PhD in mathematics

Editor’s note: This story is part of a series of profiles of notable spring 2024 graduates. Scottsdale, Arizona, native Ethan Leventhal started as a math major because he loved math but wasn’t sure…

ASU innovation in society graduate aims to ensure that the future is for everyone

Editor’s note: This story is part of a series of profiles of notable spring 2024 graduates. For Idaho native Ava Steckel, having diverse passions is a strength. So when she attended Arizona State…

ASU sustainable food systems grad is a leader in food advocacy

Editor’s note: This story is part of a series of profiles of notable spring 2024 graduates. From communications and research to policy frontline, Elizabeth Reilly is working toward contributing to a…

• Doctor of Philosophy in Mathematics (PhD)
• Graduate School
• Prospective Students
• Graduate Degree Programs

Canadian Immigration Updates

Applicants to Master’s and Doctoral degrees are not affected by the recently announced cap on study permits. Review more details

Go to programs search

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics. The PhD program trains students to operate as research mathematicians. The focus of the program is on substantial mathematical research leading to the PhD dissertation. Students also develop their skills in presenting and teaching mathematics and its applications.

For specific program requirements, please refer to the departmental program website

What makes the program unique?

UBC has one of the largest and most vigorous departments of mathematics in Canada. Our faculty routinely win national and international awards for their research and teaching achievements. We have an engaged and sociable cohort of graduate students who are essential members of a broad selection of active research groups. Each group holds a variety of seminars and events that allow graduate students, postdoctoral fellows, visitors and faculty to enjoy regular interaction.

UBC is the headquarters for the Pacific Institute of Mathematical Sciences (PIMS). PIMS hosts a plethora of mathematical events such as conferences and summer schools, greatly enriching the scientific environment in the quantitative sciences at UBC. Our mathematics students are also regular participants at the nearby Banff International Research Station for Mathematical Innovation and Discovery. Finally, our Institute for Applied Mathematics provides options for interdisciplinary studies for PhD students who wish to work in applied and computational mathematics.

I chose UBC because of the reputation of the university and mathematics department, the alignment of my research interests with my advisor’s expertise, and my love for Canada!

Ethan White

Quick Facts

Program enquiries, admission information & requirements, 1) check eligibility, minimum academic requirements.

The Faculty of Graduate and Postdoctoral Studies establishes the minimum admission requirements common to all applicants, usually a minimum overall average in the B+ range (76% at UBC). The graduate program that you are applying to may have additional requirements. Please review the specific requirements for applicants with credentials from institutions in:

• Canada or the United States
• International countries other than the United States

Each program may set higher academic minimum requirements. Please review the program website carefully to understand the program requirements. Meeting the minimum requirements does not guarantee admission as it is a competitive process.

English Language Test

Applicants from a university outside Canada in which English is not the primary language of instruction must provide results of an English language proficiency examination as part of their application. Tests must have been taken within the last 24 months at the time of submission of your application.

Minimum requirements for the two most common English language proficiency tests to apply to this program are listed below:

TOEFL: Test of English as a Foreign Language - internet-based

Overall score requirement : 100

IELTS: International English Language Testing System

Overall score requirement : 7.0

Other Test Scores

Some programs require additional test scores such as the Graduate Record Examination (GRE) or the Graduate Management Test (GMAT). The requirements for this program are:

The GRE is not required.

2) Meet Deadlines

3) prepare application, transcripts.

All applicants have to submit transcripts from all past post-secondary study. Document submission requirements depend on whether your institution of study is within Canada or outside of Canada.

Letters of Reference

A minimum of three references are required for application to graduate programs at UBC. References should be requested from individuals who are prepared to provide a report on your academic ability and qualifications.

Statement of Interest

Many programs require a statement of interest , sometimes called a "statement of intent", "description of research interests" or something similar.

Supervision

Students in research-based programs usually require a faculty member to function as their thesis supervisor. Please follow the instructions provided by each program whether applicants should contact faculty members.

Instructions regarding thesis supervisor contact for Doctor of Philosophy in Mathematics (PhD)

Citizenship verification.

Permanent Residents of Canada must provide a clear photocopy of both sides of the Permanent Resident card.

4) Apply Online

All applicants must complete an online application form and pay the application fee to be considered for admission to UBC.

Tuition & Financial Support

Financial support.

Applicants to UBC have access to a variety of funding options, including merit-based (i.e. based on your academic performance) and need-based (i.e. based on your financial situation) opportunities.

Program Funding Packages

All full-time students who begin a UBC-Vancouver PhD Mathematics program in September 2018 or later will be provided with a funding package of at least $24,256 for each of the first four years of their PhD. The funding package may consist of any combination of internal or external awards, teaching-related work, research assistantships, and graduate academic assistantships.

Average Funding

• 52 students received Teaching Assistantships. Average TA funding based on 52 students was $13,784.
• 48 students received Research Assistantships. Average RA funding based on 48 students was $11,580.
• 3 students received Academic Assistantships. Average AA funding based on 3 students was $1,814.
• 54 students received internal awards. Average internal award funding based on 54 students was $13,279.
• 4 students received external awards. Average external award funding based on 4 students was $27,083.

Scholarships & awards (merit-based funding)

All applicants are encouraged to review the awards listing to identify potential opportunities to fund their graduate education. The database lists merit-based scholarships and awards and allows for filtering by various criteria, such as domestic vs. international or degree level.

Graduate Research Assistantships (GRA)

Many professors are able to provide Research Assistantships (GRA) from their research grants to support full-time graduate students studying under their supervision. The duties constitute part of the student's graduate degree requirements. A Graduate Research Assistantship is considered a form of fellowship for a period of graduate study and is therefore not covered by a collective agreement. Stipends vary widely, and are dependent on the field of study and the type of research grant from which the assistantship is being funded.

Graduate Teaching Assistantships (GTA)

Graduate programs may have Teaching Assistantships available for registered full-time graduate students. Full teaching assistantships involve 12 hours work per week in preparation, lecturing, or laboratory instruction although many graduate programs offer partial TA appointments at less than 12 hours per week. Teaching assistantship rates are set by collective bargaining between the University and the Teaching Assistants' Union .

Graduate Academic Assistantships (GAA)

Academic Assistantships are employment opportunities to perform work that is relevant to the university or to an individual faculty member, but not to support the student’s graduate research and thesis. Wages are considered regular earnings and when paid monthly, include vacation pay.

Financial aid (need-based funding)

Canadian and US applicants may qualify for governmental loans to finance their studies. Please review eligibility and types of loans .

All students may be able to access private sector or bank loans.

Foreign government scholarships

Many foreign governments provide support to their citizens in pursuing education abroad. International applicants should check the various governmental resources in their home country, such as the Department of Education, for available scholarships.

Working while studying

The possibility to pursue work to supplement income may depend on the demands the program has on students. It should be carefully weighed if work leads to prolonged program durations or whether work placements can be meaningfully embedded into a program.

International students enrolled as full-time students with a valid study permit can work on campus for unlimited hours and work off-campus for no more than 20 hours a week.

A good starting point to explore student jobs is the UBC Work Learn program or a Co-Op placement .

Tax credits and RRSP withdrawals

Students with taxable income in Canada may be able to claim federal or provincial tax credits.

Canadian residents with RRSP accounts may be able to use the Lifelong Learning Plan (LLP) which allows students to withdraw amounts from their registered retirement savings plan (RRSPs) to finance full-time training or education for themselves or their partner.

Please review Filing taxes in Canada on the student services website for more information.

Cost Estimator

Applicants have access to the cost estimator to develop a financial plan that takes into account various income sources and expenses.

Career Outcomes

88 students graduated between 2005 and 2013: 1 is in a non-salaried situation; for 19 we have no data (based on research conducted between Feb-May 2016). For the remaining 68 graduates:

Sample Employers in Higher Education

Sample employers outside higher education, sample job titles outside higher education, phd career outcome survey, career options.

A great majority of our PhD graduates move on to postdoctoral fellowships and faculty positions at universities and research institutes in North America and around the world. However, a significant fraction of students move into careers in industry. Students considering non-academic careers are encouraged to complete an industrial internship (for instance through the Mitacs Accelerate program - headquartered at UBC) during their studies.

Enrolment, Duration & Other Stats

These statistics show data for the Doctor of Philosophy in Mathematics (PhD). Data are separated for each degree program combination. You may view data for other degree options in the respective program profile.

ENROLMENT DATA

Completion rates & times, upcoming doctoral exams, monday, 27 may 2024 - 12:30pm - room 203, thursday, 30 may 2024 - 10:00am - 203, mathematics building, 1984 mathematics road, friday, 5 july 2024 - 9:00am - room 200.

• Research Supervisors

Advice and insights from UBC Faculty on reaching out to supervisors

These videos contain some general advice from faculty across UBC on finding and reaching out to a supervisor. They are not program specific.

This list shows faculty members with full supervisory privileges who are affiliated with this program. It is not a comprehensive list of all potential supervisors as faculty from other programs or faculty members without full supervisory privileges can request approvals to supervise graduate students in this program.

• Adem, Alejandro (Cohomology of finite groups, orbifolds, stringy topology, algebra, sporadic simple group, group actions, arithmetic groups, K-theory, homotopy theory, spaces of homomorphisms)
• Angel, Omer (Probability theory, percolation, random graphs, random walks, particle processes, scaling limits)
• Bachmann, Sven (Mathematics and statistics; Mathematical Analysis; quantum phenomena; Mathematical physics; Quantum statistical physics; Topological states of matter)
• Balmforth, Neil (Fluid mechanics, nonlinear dynamics and applied partial differential equations)
• Behrend, Kai (Moduli spaces, Gromov-Witten invariants, string theory, Donaldson-Thomas invariants, Euler characteristics, categorification)
• Bennett, Michael (Number Theory, Diophantine Approximation and Classical Analysis)
• Bryan, Jim (Algebraic and differential geometry; Algebraic geometry, moduli spaces, enumerative invariants related to theoretical physics.)
• Cautis, Sabin (Mathematics and statistics; Geometry)
• Chau, Albert (Differential Geometry and Partial Differential Equations)
• Chen, Jingyi (Algebraic and differential geometry; Differential Geometry, Partial Differential Equations)
• Colliander, James (hamiltonian dynamical systems; partial differential equations; harmonic analysis)
• Coombs, Daniel (Mathematical biology; Cellular immunology; Complex physical systems; Epidemiology (except nutritional and veterinary epidemiology); Cell Signaling and Infectious and Immune Diseases; Cell biophysics; Disease models; Epidemiology; Immune cell signalling; Mathematics)
• Cytrynbaum, Eric (Bacterial cell division, Microtubule and cellular organization, Wave propagation in excitable media)
• Dao Duc, Khanh (Genomics; Mathematical biology; Neurocognitive patterns and neural networks; Agricultural spatial analysis and modelling; combine mathematical,computational and statistical tools to study fundamental biological processes; regulation and determinants of gene expression and translation; Machine Learning for Biological Imaging and Microscopy; Database development and management; Biological and Artificial Neural Networks for geometric representation)
• Doebeli, Michael Walter (Mathematical ecology and evolution, evolution of diversity, adaptive speciation, evolution of cooperation, game theory, experimental evolution in microorganisms)
• Feng, James (Chemical engineering; Mathematics and statistics; Biophysics; Complex fluids; Fluid mechanics; Mathematical biology)
• Fraser, Ailana (Differential Geometry, Geometric Analysis)
• Friedlander, Michael (numerical optimization, numerical linear algebra, scientific computing, Scientific computing)
• Frigaard, Ian (Fluid mechanics (visco-plastic fluids))
• Ghioca, Dragos (Drinfeld modules, isotrivial semiabelian varieties, Lehmer inequality)
• Gordon, Julia Yulia (Representation theory of p-adic groups and motivic integration; Trace Formula and its applications)
• Gustafson, Stephen James (Mathematics and statistics; Mathematical Analysis; Differential Equation; Global and Non-Linear Analysis; Mathematical physics; Nonlinear partial differential equations; Nonlinear waves; Topological solitons)
• Hauert, Christoph (Mathematics and statistics; Modelization and Simulation; Evolution and Phylogenesis; Biological Behavior; dynamical systems; evolution; game theory; social dilemmas; stochastic processes)
• Hermon, Jonathan (probability theory; Markov chains and the cutoff phenomenon; particle systems; percolation)
• Holmes-Cerfon, Miranda (Mathematical modelling and simulation; Computational methods in statistics; Numerical analysis; Thermodynamics and statistical physics)

Doctoral Citations

Sample thesis submissions.

• On a completion of cohomological functors generalizing Tate cohomology
• Distribution of integral points on varieties
• Effective and explicit S-unit equations with many terms
• Classifying space for commutativity and unordered flag manifolds
• Finite-size scaling of a few statistical physics models in high dimensions
• Residual supersingular Iwasawa theory and μ-invariants for Zₚ²-extensions
• Numerical methods for biological flows laden with deformable capsules and solid particles
• The construction of blow-up solutions for some evolution equations
• Topics in discrete analysis
• Inviscid damping phenomena in some fluid models
• Gibbs measures and factor codes in symbolic dynamics
• Deep reinforcement learning agents for industrial control system design
• Structure-preserving numerical schemes for phase field models
• Enumerative geometry problems for Calabi-Yau manifolds with an action
• Tamagawa numbers of symplectic algebraic tori, orbital integrals, and mass formulae for isogeny class of abelian varieties over finite fields

Related Programs

Same specialization.

• Master of Science in Mathematics (MSc)

At the UBC Okanagan Campus

Further information, specialization.

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics.

UBC Calendar

Program website, faculty overview, academic unit, program identifier, classification, social media channels, supervisor search.

Departments/Programs may update graduate degree program details through the Faculty & Staff portal. To update contact details for application inquiries, please use this form .

Nicholas Richardson

Having grown up outside of Toronto and completed my undergrad and master's degree at the University of Waterloo, I was ready to change the scenery and go study somewhere else. I joke that is it the farthest I could move without leaving Canada, but more truthfully it was the campus that felt "right...

Gabriel Currier

I quite like the kind of math that people do here, and enjoy working with my supervisors. The campus is also a beautiful place and the graduate student community is pretty laid back and friendly.

Nathan Lawrence

Many factors contributed to my choice of UBC for graduate school. I was attracted to Vancouver’s geographical similarities to Portland in the pacific northwest. Also, I have family in the area. However, most importantly, I was intrigued and inspired by my professors and advisors to take on the...

Curious about life in Vancouver?

Find out how Vancouver enhances your graduate student experience—from the beautiful mountains and city landscapes, to the arts and culture scene, we have it all. Study-life balance at its best!

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