Department of Mathematics

Requirements for the ph.d. degree.

In order to qualify for the Mathematics Ph.D., all students are required to:

  • Complete eight term courses at the graduate level, at least two with Honors grades.
  • Pass qualifying examinations on their general mathematical knowledge;
  • Submit a dissertation prospectus;
  • Participate in the instruction of undergraduates ;
  • Be in residence for at least three years;
  • Complete a dissertation that clearly advances understanding of the subject it considers.

All students must also complete any other  Graduate School of Arts and Sciences degree requirements  as they appear in the Programs and Policies bulletin.

The normal time for completion of the Ph.D. program is five to six years. Requirement (1) normally includes basic courses in algebra, analysis, and topology.  Students typically complete the eight-course requirement by the end of their third year.  The Honors grades of (1) must be achieved within the first two years.  A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term.  All qualifying examinations must be passed by the end of the second year.  There is no limit to the number of times that students can take the exams, and so they are encouraged to take them as soon as possible.

The dissertation prospectus should be submitted during the third year. 

The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)–(5) and obtaining an adviser.

In addition to all other requirements, students must successfully complete MATH 991a, Ethical Conduct of Research, prior to the end of their first year of study. This requirement must be met prior to registering for a second year of study.

Master’s Degrees :

The M.Phil. and M.S. degrees are conferred only en route to the Ph.D.; there is no separate master’s program in Mathematics.

M.Phil.   Please refer to the Graduate School Degree Requirements

M.S.   A student must complete six term courses with at least one Honors grade, perform adequately on the general qualifying examination, and be in residence at least one year.

Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

  • Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
  • Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
  • Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
  • Complete a seminar, giving a talk of at least one-hour duration
  • Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
  • Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

Overview of the Application Procedure

Welcome to the MIT Mathematics Graduate Admissions page. This page explains the application process in general. For complete details, go to the on-line application which is available mid-September to December. These instructions are repeated there.

MIT admits students starting in the Fall term of each year only. Admission is to the PhD program only; there is no Masters program. There is no separate application for financial support; all admitted students are offered support.

Submitting GRE scores is entirely optional: We will accept scores if submitted (and are most interested in the Math Subject test result, if any) but it will not hurt your application if not included.

To apply, follow these steps:

Fill out the on-line application by 23:59, EST, December 15.

You will be submitting:

  • Field(s) of interest
  • Personal information/addresses
  • International student data
  • Three or more names and e-mail addresses of letter writers
  • Educational and work history, including IELTS/TOEFL scores (preferably from this year), and honors
  • Grades in math/science/engineering courses and overall
  • Statement of objectives
  • Outside financial support and potential outside support
  • Credit/debit card payment of $75
  • The Math department requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Arrange for submission of (official reports only)

  • Letters of recommendation
  • For international students, IELTS (or TOEFL iBT)

We recommend that before November 15 you notify your letter writers that you will be needing evaluations from them, so that they have time to prepare them and submit them by December 15. Once you have submitted your on-line application, instructions to your letter writers will be generated for you. You are responsible for making sure that your letter writers have copies of these instructions.

You self-reported your grades in step 1, but we require an official transcript for all admitted students. If/when we request this, arrange for an official copy of your college transcript to be sent to:

Academic Services, Room 2-110 Dept of Mathematics, MIT 77 Massachusetts Ave. Cambridge MA 02139-4307 USA

TOEFL reporting codes Institution code: MIT = 3514 Mathematics Department code: 72

International Students

IELTS is the English language proficiency test we prefer, but we also accept the TOEFL iBT . (On the other hand, we generally do not accept the TOEFL PBT.) To have IELTS results reported, indicate "Mathematics Department, Massachusetts Institute of Technology (MIT)" on your IELTS test application; no code or address is needed. To have TOEFL iBT results reported, use the codes above (3514 for MIT, and 72 for Mathematics).

If you are an international student, you should take the IELTS (or TOEFL iBT) by December 31. If you will receive an undergraduate degree from an English-language university in an English-speaking country after attending it for at least three years, then the Math Department will waive the English language proficiency test requirement.

Paper Forms

If for some reason, you are unable to use the on-line system, you may use paper forms. But note that on-line documents allow us to consider your application more quickly and conveniently. Your letter writers may also use paper forms, if necessary.

Please address questions about the application process to [email protected] . You can find more information about MIT graduate admissions in general at the MIT Graduate Admissions site .

Computational Science and Engineering

Students with primary interest in Computational Science may also consider applying to the interdisciplinary Computational Science and Engineering (CSE) program, with which the Mathematics Department is affiliated. For more information, see https://oge.mit.edu/programs/computational-science-and-engineering-phd/ .

Department of Mathematics

Mathematics phd program.

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

Questions? Email [email protected]

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

The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy.

The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government. Admission is limited and highly selective. Successful applicants have typically pursued an undergraduate major in mathematics.

In the first year of PhD studies, students must pass written examinations in the areas of the basic . In the second year an oral examination on two selected topics must be passed. Subsequent years are devoted to seminars, research, and the preparation of a dissertation. Students are required to serve as a teaching assistant or instructor for four years beginning with the second year of study. All students must serve as a primary instructor for at least one semester; all others semesters students will serve as a teaching assistant. En route to the Ph.D., students will earn three degrees: a Master of Arts (after year one), a Master of Philosophy (after year four), and the Doctorate of Philosophy (after a successful thesis defense).

There are also allied doctoral programs in , , and .

The Mathematics Department is housed in a comfortable building containing an excellent , computing and printing facilities, faculty and graduate student offices, a lounge for tea and conversation, and numerous seminar and lecture rooms.

The department has a broad fellowship program designed to help qualified students achieve the PhD degree in the shortest practicable time. Each student admitted to the PhD program is appointed a fellow in the Department of Mathematics for a period of five years, contingent on good progress. A fellow receives a stipend for the nine-month academic year and is exempt from payment of tuition.

A fellow in the Department of Mathematics may hold a fellowship from a source outside Columbia University. When not prohibited by the terms of the outside fellowship, the University supplements the outside stipend to bring it up to the level of the University fellowship. Candidates for admission are urged to apply for fellowships for which they are eligible (e.g., National Science Foundation, Ford and Hertz Foundations).

All students admitted to the PhD program become fellows in the Department and are exempt from tuition. Students may be responsible for certain : a student activity fee and transcript fee.

Students in the PhD program are entitled to affordable University housing near the Department in Morningside Heights. This makes it possible to live comfortably in the University neighborhood on the fellowship stipend.

The PhD program in mathematics has an enrollment of approximately 60 students. Typically, 10-12 students enter each year. While students come from all over the world, they form an intellectually cohesive and socially supportive group.

New York City is America’s major center of culture. Columbia University’s remarkably pleasant and sheltered , near the Hudson River and Riverside Park, is situated within 20-30 minutes of Lincoln Center, Broadway theaters, Greenwich Village, and major museums. Most department members live within a short walk of the University.

Since receiving its charter from King George II in 1754, Columbia University has played an eminent role in American education. In addition to its various faculties and professional schools (such as Engineering, Law, and Medicine), the University has close ties with nearby museums, schools of music and theology, the United Nations, and the city government.

The application deadline is typically early December for admission the following September. Precise details on requirements and deadlines can be found . Applicants must submit all required documents by the posted deadline. Students whose undergraduate degree was not from an English-speaking country must also submit scores from the TOEFL or IELTS.  Applications must be filed .

 

:

Graduate School of Arts and Sciences
Columbia University
Office of Student Affairs
107 Low Library, MC 4304
New York, NY 10027
212-854-6729

Michael Harris
Director of Graduate Studies
Department of Mathematics
Columbia University
2990 Broadway
509 Mathematics, MC 4406
New York, NY 10027


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.

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.

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

how to get phd in mathematics

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.  

PhD Qualifying Exams

The requirements for the PhD program in Mathematics have changed for students who enter the program starting in Autumn 2023 and later. 

Requirements for the Qualifying Exams

Students who entered the program prior to autumn 2023.

To qualify for the Ph.D. in Mathematics, students must pass two examinations: one in algebra and one in real analysis. 

Students who entered the program in Autumn 2023 or later

To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: 

  • real analysis
  • geometry and topology
  • applied mathematics

The exams each consist of two parts. Students are given three hours for each part.

Topics Covered on the Exams:

  • Algebra Syllabus
  • Real Analysis Syllabus
  • Geometry and Topology Syllabus
  • Applied Mathematics Syllabus

Check out some Past and Practice Qualifying Exams to assist your studying.

Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take either or both of the exams in the autumn. If they pass either or both of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing either of the exams.

Students must pass both qualifying exams by the autumn of their second year. Ordinarily first-year students take courses in algebra and real analysis throughout the year to prepare them for the exams. The exams are then taken at the beginning of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Students who started in Autumn 2023 and later

Students must choose and pass two out of the four qualifying exams by the autumn of their second year. Students take courses in algebra, real analysis, geometry and topology, and applied math in the autumn and winter quarters of their first year to prepare them for the exams. The exams are taken during the first week of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Exam Schedule

Unless otherwise noted, the exams will be held each year according to the following schedule:

Autumn Quarter:  The exams are held during the week prior to the first week of the quarter. Spring Quarter:  The exams are held during the first week of the quarter.

The exams are held over two three-hour blocks. The morning block is 9:30am-12:30pm and the afternoon block is 2:00-5:00pm.

For the start date of the current or future years’ quarters please see the  Academic Calendar

Upcoming Exam Dates

Spring 2024.

The exams will be held on the following dates:

Monday, April 1st

Analysis Exam, Room 384H

Wednesday, April 3rd

Algebra Exam, Room 384I

Thursday, April 4th 

Geometry & Topology Exam, Room 384I

Friday, April 5th

Applied Math Exam, Room 384I

Department of Mathematics

Phd requirements.

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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.

Teaching Seminar

Candidates must take, attend, participate in, and pass the course 110.771 (GTA Teaching Seminar). The seminar is an important part of the preparation for classroom teaching, and thus an essential part of mathematics graduate education. The seminar is generally required in a student’s first year at JHU. A student supported by an external fellowship may delay taking the seminar until the spring before they are required to TA (but may not postpone the seminar entirely).

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. More information as well as old exams and syllabi can be found on the Qualifying Exams page .

Candidates must pass an oral qualifying examination in the student’s chosen area of research by April 10th 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.

The MA Degree

Although the Department of Mathematics does not admit students seeking a terminal MA degree, students in the PhD program may earn an MA degree.

MA candidates must complete:

  • Four graduate courses given by the Hopkins Department of Mathematics
  • Two additional courses at the graduate or 400 level, other than 110.401, 110.405 and 110.415, given by the Hopkins Department of Mathematics, or with the permission of the graduate program director, graduate mathematics courses given by other departments or universities.

All courses used to satisfy the requirements must be completed with a grade of B- or better. (Advanced graduate courses completed with a grade of P can also be used to satisfy the requirements.)

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Graduate Program

Thinking of applying to graduate school in mathematics.

how to get phd in mathematics

Penn was ranked 8th among all US universities in a leading national study , and our mathematics graduate program was recently highest in a study of graduate programs in arts and sciences at Penn. We have a very active and involved mathematics faculty , diverse course offerings and a broad seminar schedule , with a variety of research projects and strengths in algebra, analysis, geometry-topology, combinatorics, logic, probability, and mathematical physics. We have a supportive atmosphere, with personal attention from the faculty and extensive interaction among graduate students. Our grad students can take courses not only in the Mathematics Department but also elsewhere at Penn, and the wide resources of the university are available. Our former graduate students have gone on to mathematical careers both in academia and in industry.

Our full-time Ph.D. students receive a generous and competitive support package including

  • five years of funding with a combination of fellowships and teaching assistantships;
  • a stipend and a full tuition scholarship;
  • no teaching responsibilities for at least two years (generally including the first and fourth year);
  • health insurance coverage provided at no cost to the student.

We invite you to learn about our graduate program, our math department, our university and living in Philadelphia, a cosmopolitan city and a true mathematical hub, with easy access to nearby mathematics departments and research institutes.

We are looking for interested, mathematically talented and dedicated students to be a part of our group of excellent future mathematicians. Consider applying to Penn for your graduate education. Questions?

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How to get into a top mathematics PhD program?

I'm a first year student undergraduate at a top US university, and I'm going to major in math. Of course, I still don't really know what I want to do with my life, but I'm really excited about going on to a PhD in math. What does one have to do to get into a top PhD program in mathematics? When I say top, I mean absolute top - like Princeton or MIT. Please understand that I'm not being presumptuous in asking this: I don't know whether I'll ever be good enough to do a PhD at an institution such as these, but I'm just asking for reference - and out of curiosity.

I've read a lot of threads about similar topics, but answers there are fairly vague ("good letters of recommendation", "advanced coursework", etc). What exactly do these terms mean, and what should I - as a first year student - already start doing to at least stand a chance sometime in the future to even dream of being in a program such as the ones I mentioned?

  • graduate-admissions
  • mathematics
  • undergraduate
  • research-undergraduate

gtoques's user avatar

  • 1 Get good grades and apply when you have finished final year... –  Solar Mike Mar 28, 2019 at 6:28
  • 6 Let me be blunter than I or most mathematicians would like to be. There is such a thing as mathematical talent, and, starting where you are and given the level you're aiming for, it matters (though many other things also matter!) Let me make an analogy to making the NBA. One could make a list of things that most basketball players have to do to make the NBA, but almost all of the basketball players who try to do most of these things still won't make the NBA. In fact, so few of them will make it that calling such a list a guide to making the NBA would be ridiculous. –  Alexander Woo Mar 28, 2019 at 8:00
  • 2 I think a lot of it has to do with opportunities taken at a young age. Enrolling in a program to skip part of high school and start college early is an example. Basically, one initial requirement would probably be access to math beyond what one typically sees. Another example is participating in the Ross program. Or working with highly motivated students on challenging math. If you can forgo everything and focus on math, that would probably help. Go to a top college and take as much math as possible. It helps to have mathematician parents. –  user74089 Mar 28, 2019 at 9:05
  • 1 @AlexanderWoo The problem with the NBA analogy is that there are much clearer ways to measure talent and performance in basketball than in mathematics. Even if "mathematical talent" were a one-parameter quantity, it's more than a little dubious that Princeton and MIT are particularly good at identifying it. –  Elizabeth Henning Mar 28, 2019 at 17:11

2 Answers 2

First off, I have a PhD in a top 20 - not top 3. I believe my school was 16 or 17 when I was doing my PhD. So I'm below what you are aiming for. So feel free not to read this post.

First of all, I'm puzzled by your comment:

fairly vague ("good letters of recommendation", "advanced coursework", etc). What exactly do these terms mean, and what should I - as a first year student - already start doing to at least stand a chance sometime

Good letters of recommendation: You will need to get about 3 profs to write good letters of recommendation when you apply to grad school. That means you need them to say you are smart as in PhD-smart.

Advanced coursework: Take ALL the higher level courses if possible. Take some graduate level courses if possible.

Now about grad school: don't think about the top 1 or 2 or even 3 for now. If your goal is math, then your goal is math, not the school. Just focus on math for now.

I do not know you, so whatever I said below might be useless and meaningless.

What can you do as a first year student? Get a good GPA, as close to 4.0 as you can. You want to take as many math courses as you can right? So do some self-study and test out of your gen ed courses. I had a student who tested out about 8 so that he can have time to take ALL the higher level courses.

Are you taking any math courses now? Then focus on them and do well. Doing well does not mean just getting an A. It means being near the top of the class. Your prof knows. Not all profs will take note. But some do.

You have to figure out which profs are interested in growing PhD students. Profs who care will be open to chat with you and guide you. The only way you can catch their attention and learn from them is to be at the top of your class. Ask questions in class (if possible, when appropriate). Do you study ahead? Talk to them during office hours and ask questions so that they know you are interested and are studying your textbook ahead of the class.

When I was an undergraduate I always study ahead. While studying all the courses, I will pick one book and study ahead until I'm done with the book for that course. Then I'll pick another one and study ahead. Etc. Don't just read the book. Do the problems.

It's also a good idea to think about your favorite area in math and study it on your own. Unfortunately if you are not very deep into math, you might not know where to go with this. That's why knowing a prof well will help. He can guide you.

If you have time and if you have not done so, I suggest you look at the textbooks for math olympiads. Study them and do all the problems. Try to finish as much as you can so that you have some time to try some putnam competition books. Math problems in the math olympiad and the putnam are very different from the type of problems you will solve in your regular math classes. In many ways they are closer to research-type math problems. Again, I do not know you. Maybe you have already done lots of math olympiad training.

Another very important thing to note is that it is your responsibility to keep your level of interest in your area (i.e. math) as high as possible. That means spending some time reading up on the biographies of famous mathematicians. Don't do too much of that since you do have to study math.

Books are the most important resource for you right now. Ask your profs for good recommendations. Do not be surprised that your class textbook might not be the best textbook on that subject. It's just one that's convenient and easy to use. I have no idea where you are in your math education. But if you are in Calculus, then you can for instance study "Calculus" by Michael Spivak. If you are very strong in math and have already studied that, you can go on to other books.

Check your math library and see if you can find magazines you can understand. Try the American Mathematical Monthly and the Mathematical Intelligencer.

See if there's a math club you can join. Make sure it's a math club and not just a social gathering for math majors. Nothing wrong with socializing, but if the club does not have math related activities, then it won't help your goal.

If you work very hard in the first 2 years, you might know what area you want to go into. (But it might change.) And if you take some grad level course(s) in that area in your third year, you might be able to attend the research seminar in that area, which might be a weekly meeting. You might be able to start doing some research during your senior year.

spoock7824's user avatar

  • 4 This is good advice except the part about math competitions. Those questions are nothing like research problems. –  Tobias Kildetoft Mar 29, 2019 at 5:43

Roughly: good grades (3.8+ GPA) in difficult courses, good test scores (80+ percentile on math GRE subject test [not the regular GRE math, which you should get a ~perfect score on without studying]), strong research background and good letters corresponding to it.

That will get you into schools in the top ~30. To get into the very top programs, you will need to meet this standard and also have either (1) a very nice research background / letters, or (2) something "interesting", such as impressive accomplishments outside of math

Disclaimer: not a mathematician

cag51's user avatar

  • 1 Can the downvoters explain? Not a mathematician, will delete if I'm off-base, but I got into a top-10 physics program with basically this formula... –  cag51 ♦ Mar 28, 2019 at 5:52
  • 1 I understand that. What exactly do you mean by accomplishments "outside of math" though? What kind of accomplishments? –  gtoques Mar 28, 2019 at 6:18
  • 4 Voted this up - can't see why it gets downvotes... –  Solar Mike Mar 28, 2019 at 6:50
  • 7 This advice is far too generic. Good grades (3.8 GPA)? There is no mention of the caliber of courses. Median Princeton admit probably has a 4.0 GPA with stellar performance in numerous graduate level courses like differential geometry or algebraic topology. 95+ percentile on GRE is probably a given although I doubt top programs put much weight on it at all. Most importantly, it really helps if a respected mathematician gives an absolutely glowing recommendation regarding your research potential. Impressive accomplishments outside math count for very little. –  zoidberg Mar 28, 2019 at 7:06
  • 3 @zoidberg surely the advice has to be generic - the OP is nowhere near completion, has no grades to speak of and not applied to any institution yet.... –  Solar Mike Mar 28, 2019 at 7:14

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Choosing a Graduate School Path that Fits You

Graduate school is an advanced program of study beyond a bachelors degree, leading to a specialized degree in a variety of mathematical sciences disciplines, including theoretical and applied mathematics, statistics, data science, and computer science. On this page we answer frequently asked questions and provide some useful resources.to help you choose the graduate school path that is the best fit for you . 

Why consider graduate school?

With a graduate degree, you will develop deeper expertise which will qualify you for a variety of careers. If you love mathematics, graduate school is also a chance to learn more, and to do more with what you learn.

What kinds of jobs does a graduate degree lead to?

A graduate degree in the mathematical sciences will lead you to a variety of interesting careers, including jobs in business, government, research, non-profit institutions, and teaching. Not all students apply to graduate school because they know exactly where they want it to lead (and those who do often change their minds!). Some students apply to graduate school because they like math and want to learn more, or even because they aren't ready to look for a job or don't know what else they want to do. Regardless of why you apply, we have lots of information and tools to help you choose your direction.

Explore the range of careers for people with training in mathematics:

  • BEGIN Career Initiative  includes AMS resources on jobs in Business, Industry, and Government.
  • BIG Math Network provides information on careers in Business, Industry and Government for students in the mathematical sciences.
  • 101 Careers in Mathematics is a book with over 100 career profiles written by people with degrees and backgrounds in mathematics.
  • See our Mathematical Moments to see the many exciting discoveries and applications of mathematics.
Following the 2018 midterm elections, 22 Congressional Representatives and 2 Senators have doctoral degrees, one in Mathematics! — Source: Capital Currents blog

The AMS Employment Services provides job listings for people with PhDs or close to completing one.

The Bureau of Labor Statistics is an agency of the U.S. Department of Labor that provides comprehensive employment and salary data.

Which area of math is right for you?

You don't need to know exactly the career path you want to pursue, although the resources above might help you narrow your focus.

The mathematical sciences are comprised of a broad array of disciplines. Look for graduate programs that can take you in a direction that interests you. Universities often have separate graduate programs or even separate departments of mathematics, applied mathematics, computer science, statistics, and data science, or some combination of these.

Learn more about specific mathematical sciences and related careers from these professional societies:

  • The American Statistical Association and This Is Statistics
  • Society for Industrial and Applied Mathematics (SIAM)
  • Data Science Association
  • Mathematical Association of America
  • Informs: Institute for Operations Research and the Management Sciences

Most graduate programs offer several options, so you can narrow your focus or even change direction as you work your way through your studies.

Master's? PhD?

Some master's degrees prepare you to enter a PhD program, while others are professional degrees, which prepare you to enter a specific career outside of research, such as teaching. Some are a combination of both.

Some students enter doctoral programs as soon as they finish a bachelor's degree, while others get a master's first. A master's degree usually requires two years of full-time coursework, and sometimes a research-based thesis or other capstone project. With a master's you can still continue on to more advanced study.

Doctoral degrees usually prepare you for mathematics research in academic, government, or business institutions. They give you the training needed to work with complex mathematical applications in any of these settings. A PhD typically requires 2-3 years of coursework, comprehensive exams, and independent research to create new knowledge, guided by your advisor. This research, written as your PhD thesis, is called your dissertation. Your PhD degree may take anywhere from 5-7 years to complete.

Paying for graduate school

Financial aid is available for graduate school, and many graduate students don't pay any tuition at all! Most graduate students finance their education through a combination of funding sources. Financial aid is available for graduate school, often in forms of grants or jobs. As a PhD student in the mathematical sciences, you will typically work as a teaching or research assistant, which pays a stipend and covers all or most of your tuition.

The median annual salary of mathematical scientists in May 2019 was \$92,030, with 10% earning more than $162,060 . — Source: Bureau of Labor Statistics

Assistantships are campus-based work assignments that provide you with valuable professional experience in teaching or research, and an opportunity to work with students and faculty. Assistantships are usually awarded by departments as part of the admission process, and typically provide a stipend (a small salary) and waive tuition and some fees.  

Fellowships are typically granted to individuals to cover their living expenses and tuition while they carry out research or work on a project. Awards are usually based on an individual's merit as measured by grades, GRE scores, publications, and letters of recommendation. For some fellowships, you need to apply to organizations tat are independent of your university, such as the National Science Foundation (NSF).

Grants are most often awarded to cover expenses associated with carrying out research or other specific projects, such as travel, materials, or computers.

You can explore funding opportunities at these resource sites:

  • The AMS Awards, Fellowships, and other Opportunities list includes opportunities for students and other mathematical scientists. You can filter to find information about fellowships and grants.
  • National Science Foundation Graduate Research Fellowship Program recognizes and supports outstanding graduate students in NSF-supported science, technology, engineering, and mathematics disciplines who are pursuing research-based Master's and doctoral degrees at accredited United States institutions.
  • Graduate Fellowships for STEM Diversity (GFSD)  are provided by a partnership between government agencies and laboratories, industry, and higher education institutions. GFSD's goal is to increase the number of American citizens with graduate degrees in STEM fields, emphasizing recruitment of a diverse applicant pool. Any U.S. citizen can apply, regardless of race or gender.

What should you think about in choosing where to apply?

Once you have a general idea of where you want this journey to take you, do some research to identify the academic programs that are the best fit for you. A grad school that is highly specialized or has a strong reputation in an area you're interested in might be the best fit for you, but it might not be . In addition to choosing an academic program, you are also choosing where you will spend the next several years of your life, and you'll be most successful where you can thrive as both a student and as an individual.

Admission requirements

Is the GRE subject test required? What coursework do you need? What resources are available to students who need to fill gaps in their background? Even if you don't meet all of the requirements, you can still apply. There might be something else in your application that makes you stand out. On the other hand, be realistic about whether you feel prepared for what the program will require of you.

Not sure if you're ready?

If your interest is piqued but you're not sure you're ready for graduate school, consider applying to a post-baccalaureate program..These programs allow students to strengthen their backgrounds and fill in gaps in their coursework before applying to graduate school, typically through one year of coursework following the bachelor's degree. There are also summer bridge programs.  This is a partial list and others can be found through internet searching. Some students who want to earn a PhD start with a master's degree first.

Summer and post-baccalaureate programs can help you prepare for graduate school if you're not quite ready. You can find a list at the AMS Find a Graduate Program  and at the Math Alliance  

Mathematical specializations

Do the faculty work on mathematical topics that interest you? Look at their websites to see the kinds of courses they teach and research they do. If you are not sure about your interests, you may want to find a department that is larger and more varied, so that you have more options to explore. Look carefully at the range of options available in each program. Different mathematical disciplines are sometimes in separate academic departments, or sometimes in the same department. Even within a department, students often have choices about specializing.

Quality of the program

It's tempting to look at online graduate school rankings, but keep in mind that the rankings may be based on criteria that are different from yours. Many deans and advisors question the validity of ranking systems. Instead, look for information about the faculty-student ratio, the acceptance rate, average time to degree, the percent of students who complete their intended degree, and the kinds of jobs alumni move on to. How big is the program, and how many students complete degrees each year? If you can't find that information online, you can ask the department's graduate director.

Doctoral students often work as teaching assistants (TAs) or research assistants. As a TA, you might lead discussion sections, grade papers, or do other teaching-related work. In exchange, part or all of your tuition is waived and you receive a regular paycheck, called a stipend. At some state schools, tuition waivers may not cover the out-of-state portion of the tuition. You can also apply for f ellowships and scholarships . Ask how much TAs earn, and for how many years would you be guaranteed a stipend? Will you have to pay tuition? Is health insurance included?

Getting a PhD is usually free! Many doctoral students work as teaching or research assistants, which earns them full tuition and a stipend.

Department composition

Who are the faculty, students, and staff? If your race, gender, ethnicity, or other identities are important factors for you, do you feel comfortable in the department environment? Are there affinity groups on or off campus that are a fit for you? Will you be able to find a welcoming peer group? 

Research training

Do graduate students have opportunities to get involved in research? Do they gain experience making research presentations, writing research papers, and attending conferences? Does the department provide funding for travel to conferences?

Student life

Investigate the diversity of students, student organizations, housing, and campus support services. Is childcare available and what does it cost? Is there a religious or cultural community on campus or in the broader community? What other activities and communities are available on and off campus? What is the quality of campus facilities such as libraries, computer labs, and sports facilities? What computer resources will you have access to?

Program requirements

What are the requirements to get a degree? Ask about courses, qualifying exams, and any other requirements you need to meet. How many courses are required and how often are they offered? How many courses are offered in the areas that most interest you? Will the coursework help you meet your professional or educational goals? Do students work together in study groups for coursework and exams? 

Do you want to be in a specific geographic region to be near (or far from) home? Will studying in a particular location help you meet personal or professional goals? Will you enjoy living in an urban or suburban environment? Be prepared for a new climate, but don't let it intimidate you!

Speaking of community…

What kind of student community is there? Do students work collaboratively, individually, or competitively? Can you find a community of peers in the department or elsewhere on campus? Is there an AMS Graduate Student Chapter ? Students who feel like they are part of a community are more successful in graduate school. There are some tools for finding a mathematical community on our Equity, Diversity and Inclusion page.

Where are graduates of the program working? Are they going into careers that you might be interested in? What resources are available to help you connect with jobs in academia, business, or government? Are internships available? Required?

Overall employment of mathematicians and statisticians is projected to grow 33 percent from 2019 to 2029, much faster than the average for all occupations. — Source: Bureau of Labor Statistics

Where can you learn more?

We suggested many questions for you to ask as you make the exciting decision about pursuing  more advanced education in the mathematical sciences. Here are some resources to help you find some answers!

A good starting point is Find a Graduate Program in Mathematical Sciences which allows you to search for graduate programs in the United States based on degree level, geography, specialization, and other characteristics. Some graduate programs place display ads on that page to better explain their programs to prospective students. From there, look at the websites of any programs you are interested in. The websites for the university itself can have some helpful information on it as well.,  

Also look at the Survey of Graduate Students and Postdoctorates in Science and Engineering from the National Science Foundation.

Contact the department's Graduate Program Director (or someone with a similar title) by phone or email to ask more questions, including any of the questions we describe above.

Talk with current and former students. Do they like the program? What are its strengths and weaknesses? Are they content with their choice of grad program? You might be able to find student contact info on the department website, or you can ask the Graduate Program Director for some students to connect with. Your professors might have some information to guide you as well.

If you're able to visit the school, sit in on a few classes and attend some seminars. Spend some informal time with the grad students. How do the students interact with each other? How do students and faculty interact? Spend time exploring the department and get a feel for the people and the local professional culture.

The annual Fall Graduate School Fair and the Graduate School Fair at the Joint Mathematics Meetings  gives meeting participants the opportunity to speak with representatives from 40-50 U.S. graduate programs.

There is no such thing as the "best" graduate program. You are looking for the program that is best for you .

And when you are ready, our guide on Applying to Graduate School can help you prepare applications that highlight your strengths. 

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how to get phd in mathematics

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Best Doctorates in Mathematics: Top PhD Programs, Career Paths, and Salaries

Given that only a small proportion of the general population holds a PhD in Mathematics, there aren’t many people pursuing doctoral studies in the math field. It requires a high level of intelligence and mathematical ability which a typical person doesn’t possess. It also requires a decent work ethic and the ability to commit five to seven years to research and study.

However, PhD in Mathematics salaries are high. If you’re interested in pursuing a PhD in Mathematics, check out our article to find the best mathematics PhDs and what mathematics jobs you can get. First, let’s find out what a PhD in Mathematics is.

Find your bootcamp match

What is a phd in mathematics.

A PhD in Mathematics is a doctoral degree obtained by a graduate student in mathematics. This kind of mathematics graduate program allows students to develop their research capabilities in mathematics and its potential applications.

PhD in Mathematics can be a Doctor of Philosophy, Doctor of Science, or Doctor of Applied Mathematics degree. Students need to submit their PhD thesis in order to complete the math degree program they are pursuing. Math doctorate programs can take between three and six years to complete, depending on how much time is dedicated to the thesis and its required research.

How to Get Into a Mathematics PhD Program: Admission Requirements

The requirements to get into a mathematics PhD program typically include application fees, school transcripts, a professional resume, three letters of recommendation, and a statement of academic purpose. The admission process for most mathematical PhD programs is similar.

Some schools also require that students have mastered the material roughly equivalent to the undergraduate mathematics major, such as several semesters of calculus and experience with differential equations. Other doctoral math programs require applicants to submit essays or a minimum GPA score as entrance requirements.

PhD in Mathematics Admission Requirements

  • Professional CV or resume
  • Statement of academic purpose
  • Application fee
  • At least three recommendation letters
  • Undergraduate and graduate school transcripts

Mathematics PhD Acceptance Rates: How Hard Is It to Get Into a PhD Program in Mathematics?

It is extremely hard to get into a PhD program in Mathematics. For example, the Harvard PhD acceptance rate is 4.59 percent and the University of Wisconsin has a zero percent PhD acceptance rate over a five-year median. Doctoral studies in mathematics are rigorous and have a low acceptance rate, making it difficult to get into and obtain a Doctorate in Mathematics.

How to Get Into the Best Universities

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Best PhDs in Mathematics: In Brief

School Program Online Option
Columbia University Mathematics PhD No
Harvard University Mathematics PhD No
Massachusetts Institute of Technology Doctor of Philosophy or Doctor of Science Mathematics Degree No
Princeton University Applied and Computational Math PhD No
Rochester Institute of Technology Mathematical Modeling PhD No
Stanford University Mathematics PhD Program No
University of California, Berkeley PhD Program in Applied Mathematics No
University of Michigan – Ann Arbor Applied & Interdisciplinary Mathematics PhD No
University Of Wisconsin Mathematics, PhD No
Yale University PhD in Applied Mathematics No

Best Universities for Mathematics PhDs: Where to Get a PhD in Mathematics

The best universities for mathematics PhDs are Harvard University, Massachusetts Institute of Technology, Princeton University, Stanford University, University of California, Berkeley, and Yale University.

Other universities also have excellent PhD in Mathematics programs that we haven’t mentioned in our list, like Johns Hopkins University, Colorado State University, University of California, Los Angeles, and University of Chicago.

Columbia University is a private Ivy League research university founded in 1754 as King's College. It is among the top five national universities and is known as the oldest institution of higher education in New York. At Columbia University, students can find doctoral studies in biological sciences, astronomy, chemistry, economics, music, psychology, and religion.

Mathematics PhD

The PhD mathematics program is designed for full-time students interested in research and teaching at the university level. It is an intense course also meant for students that seek careers in quantitative research and development in business or government. It covers subjects like analysis and probability, Riemann surfaces, cumulative algebra, and modern geometry.

Mathematics PhD Overview

  • Program Length: 4 years
  • Acceptance Rate: 6%
  • Tuition and Fees: $25,248/semester
  • PhD Funding Opportunities: Department of Defense Funding, NIH Fellowship Parent Funding 

Mathematics PhD Admission Requirements

  • A completed online application form at the Online Application System
  • $120 application fee
  • Statement of purpose
  • A video essay (to be completed in the Online Application System)
  • A current resume or CV
  • Official transcripts from each university you attended
  • Two letters of reference

Harvard University was established in 1636 by the Puritan clergyman John Harvard. It is known as the oldest institution of higher learning in the US and as one of the most prestigious universities in the world. It offers many PhD programs in subjects such as anthropology, statistics, virology, physics, neuroscience, mathematics, immunology, and history of science.

This doctoral program is intended for students who aspire to be research mathematicians and have demonstrated a strong interest in this field. The math graduate courses cover topics like commutative algebra, advanced real analysis, differential geometry evolution dynamics, Riemann surfaces, and Hodge theory.

  • Program Length: 4-5 years
  • Acceptance Rate: 7%
  • Tuition and Fees: $50,928/first two years of study; $13,240/second two years of study
  • PhD Funding Opportunities: Hertz Foundation, National Defense Science and Engineering Graduate Fellowship Program, National Physical Science Consortium for Minorities and Women, National Science Foundation
  • Application
  • $105 application fee 
  • Transcripts
  • Letters of recommendation
  • Demonstration of English proficiency (for non-native speakers)

Massachusetts Institute of Technology (MIT) is a land-grant research university in Cambridge. Founded in 1861, MIT is best known for its programs in physical science and engineering. It offers a wide array of doctoral studies in aeronautics and astronautics, physics, political science, economics, chemical engineering, biology, brain, and cognitive sciences.

Doctor of Philosophy or Doctor of Science Mathematics Degree

In addition to choosing between a Doctor of Philosophy and a Doctor of Science program, students can choose to apply to the Pure or Applied Mathematics programs. Geometry, number theory, algebra, logic, statistics, topology, astrophysics, combinatorics, analysis, probability, numerical analysis, and theoretical physics, are covered in the Pure and Applied Mathematics curricula.

Doctor of Philosophy or Doctor of Science Mathematics Degree Overview

  • Acceptance Rate: N/A
  • Tuition and Fees: $27,755/term
  • PhD Funding Opportunities: Postdoctoral and Senior Research Awards, Faculty Early Career Development Program, Mathematical Sciences Postdoctoral Research Fellowships (MSPRF)

Doctor of Philosophy or Doctor of Science Mathematics Degree Admission Requirements

  • Fill out the online application
  • Transcripts including grades in math/science/engineering courses
  • At least three names and email addresses of recommendation letter writers
  • Educational and work history
  • Statement of objectives
  • Outside financial support and potential outside support
  • Credit/debit card payment of the $75 application fee
  • Self-reported grades
  • Arrange for submission of official transcripts and letters of recommendation

Princeton University is a private Ivy League research university that was founded in 1746. It is known as the fourth-oldest institution of higher education in the US. Princeton University has many PhD programs in subjects like philosophy, mechanical and aerospace engineering, electrical and computer engineering, and neuroscience.

Applied and Computational Math PhD

In this program, students gain a thorough understanding of areas of mathematics critical to scientific and engineering applications, such as numerical analysis and other computational approaches. In the first year, students choose three topics from six applied mathematics categories. At the end of the first year, students need to take a preliminary exam. 

Before the third year, students need to pass the general examination which culminates in a seminar on a research topic. The final requirement for this program is the doctoral dissertation which can be a mathematical contribution to one field of science or engineering.

Applied and Computational Math PhD Overview

  • Tuition and Fees : $58,790/year 
  • PhD Funding Opportunities: University, departmental, and program fellowships, research and teaching assistantships, external financial support

Applied and Computational Math PhD Admission Requirements

  • $75 application fee
  • Recommendation letters
  • Fall semester grades (for students currently enrolled in master’s degree programs)
  • English language tests (for international students)

Established in 1829, Rochester Institute of Technology is known for its excellent technology, engineering, and computing programs. It offers PhDs in Astrophysical Sciences and Technology, Biomedical and Chemical Engineering, Color Science, Imaging Science Sustainability, and many more disciplines.

Mathematical Modeling PhD

Students in this program plan their own trajectory based on required coursework, research, and their selected concentration. They can select from concentrations in the areas of applied inverse problems, biomedical, and discrete mathematics, among others. Some of the program’s courses cover subjects like numerical analysis and computing for mathematical modeling. 

Mathematical Modeling PhD Overview

  • Acceptance Rate: 74%
  • Tuition: $54,176/year 
  • PhD Funding Opportunities: Federal loans, Outside Scholarships, Yellow Ribbon Program, employment through co-ops, internships, or assistantships

Mathematical Modeling PhD Admission Requirements

  • Online graduate application
  • Copies of official transcripts of all previously completed undergraduate and graduate courses
  • Bachelor’s degree from an accredited university or college
  • Current resume/CV
  • Two letters of recommendation
  • Personal statement of educational objectives
  • TOEFL, IELTS, or PTE score (international students)
  • $65 application fee

Stanford University is well-known for its enterprising student population and high return on investment. Founded in 1885 by California senator Leland Stanford, Stanford University is consistently ranking in the top 10 national universities. Stanford offers many PhD programs in its Graduate School of Engineering, including programs in engineering, medicine, and education.

Mathematics PhD Program

Students in this PhD program take courses in algebraic topology, differential topology, differential geometry, algebraic geometry, theory of probability, real analysis, modern algebra, and mathematical methods of imaging. In the first year, the coursework prepares the students for the qualifying examinations which test them on their skills in algebra and real-world analysis. 

Students must have a dissertation advisor and seek candidacy in their second year. Students will take their Area Examination during their third year, which must be completed by the conclusion of the Winter Quarter. In the fourth and fifth years, students are expected to finish their dissertation research.

Mathematics PhD Program Overview

  • Acceptance Rate: 5.7%
  • Tuition and Fees: $56,487
  • PhD Funding Opportunities: Federal programs, university fellowships, research assistantships, teaching assistantships

Mathematics PhD Program Admission Requirements

  • Bachelor’s degree from a regionally accredited US college or university 
  • Unofficial transcripts/academic records
  • Names and contact information of those who can provide between three and six letters of recommendation
  • Online application
  • $125 application fee or fee waiver

University of California, Berkeley was founded in 1868. UC Berkeley is known for strict academic criteria for its undergraduate programs. The school has more than 130 academic departments and 80 multidisciplinary research areas. UC Berkeley is among the top universities in the world.

PhD Program in Applied Mathematics

The applied mathematics program requires doctoral students with previous graduate study in mathematics must demonstrate exceptional mathematical research skills. Students in this course can learn about linear algebra and differential equations, multivariable calculus, and discrete mathematics. There are also major electives like mathematical biology and statistics.

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PhD Program in Applied Mathematics Overview

  • Program Length: 5-6 years
  • Acceptance Rate: 18%
  • Tuition and Fees: $10,248.75/semester (resident); $17,799.75/semester (non-resident)
  • PhD Funding Opportunities : Berkeley Fellowships, Chancellor’s Fellowships, Cota-Robles Fellowships, Mentored Research Awards, UC Dissertation-Year Fellowships, Conference Travel Grants, Parent and Caregiver Grants

PhD Program in Applied Mathematics Admission Requirements

  • A bachelor’s degree or equivalent from an accredited institution
  • A minimum GPA of 3.0
  • Enough experience in your undergraduate program to complete the program
  • At least three letters of recommendation
  • $120 application fee (California residents); $140 application fee (all other applicants)

The University of Michigan - Ann Arbor is among the top 30 national universities. It was founded in 1817 in Ann Arbor. Some of the most popular majors from this university are business administration, experimental psychology, and economics. It also has good PhD level programs in education, electrical and computer engineering, and computer and information science.

Applied & Interdisciplinary Mathematics PhD

This PhD degree's purpose is to create graduates who are well-prepared to pursue successful careers in the mathematical sciences, whether in government or academia. Students in the applied and interdisciplinary mathematics course can learn about risk management and modeling of financial losses, mathematical theory of probability, and modern mathematics.

Applied & Interdisciplinary Mathematics PhD Overview

  • Program Length: 5-6 years 
  • Acceptance Rate: 26%
  • Tuition and Fees: $25,230.38 (in state); $50,646.38 (out of state)
  • PhD Funding Opportunities: Graduate Student Instructorship (GSI): Mathematics Graduate Student Instructor Teacher Training Program, and Graduate Student Research Assistantship (GSRA)

Applied & Interdisciplinary Mathematics PhD Admission Requirements

  • Three letters of recommendation
  • Personal Statement (500-word limit)
  • TOEFL or IELTS Exam (non-native English speakers)
  • Three semesters of calculus
  • One or two semesters of differential equation courses
  • One semester course in modern algebra, linear algebra, geometry or topology
  • Advanced calculus of one and several variables 
  • $75 application fee (US citizens); $90 application fee (international applicants)

Nelson Dewey, the first governor of Wisconsin, founded the University of Wisconsin in 1848. It has one of the best engineering and business majors. It also has several good graduate degrees from its Department of Mathematics like Doctor of Philosophy, Master of Arts – Foundations of Advanced Studies, and Master of Arts – Foundations for Research.

Mathematics, PhD

The University of Wisconsin’s Doctor of Philosophy program offers a foundation in fundamental and advanced graduate mathematics. Students in this PhD program can learn about linear algebra, abstract algebra, differential equations, knot theory, and real analysis.

Mathematics, PhD Overview

  • Program Length: 5 years
  • Acceptance Rate: 16%
  • Tuition and Fees: $12,176/year (in state); $25,504/year (out of state)
  • PhD Funding Opportunities: Graduate assistantships, fellowships, traineeships, student loans, student jobs, research and travel grants

Mathematics, PhD Admission Requirements

  • Application to the UW–Madison Graduate School
  • Master’s degree in mathematics or a related field
  • Official transcripts
  • Supplementary information form
  • Three academic letters of recommendation and one additional letter
  • Proof of English proficiency (for non-native speakers)
  • One-page statement of purpose

Yale University was founded in 1701 in New Haven, Connecticut. It is among the top 10 national universities and is known for its Ivy League reputation . Yale has many PhD programs like anthropology, applied physics, architecture, biomedical engineering, chemical, and environmental engineering. 

PhD in Applied Mathematics

The applied mathematics program entails the study and application of mathematics to issues prompted by a diverse set of application fields. Students study and apply mathematics concepts to questions driven by a variety of applicable fields.

It covers topics such as discrete algorithms, linear and nonlinear partial differential equations, statistical theory and applications, information theory, econometrics, and classical and modern applied harmonic analysis. This program also covers topics like financial statistics, financial mathematics, econometrics probability theory, and information theory. 

PhD in Applied Mathematics Overview

  • Acceptance Rate: 6.2%
  • Tuition and Fees: $45,700/year
  • PhD Funding Opportunities: Financial aid, university fellowships, dissertation fellowships, teaching fellowships

PhD in Applied Mathematics Admission Requirements

  • A list of all the prior colleges or universities you’ve attended 
  • Unofficial transcripts from each school
  • TOEFL scores (non-native English-speaking applicants)

Can You Get a PhD in Mathematics Online?

Yes, you can get a PhD in Mathematics online. However, there aren’t many online PhD math programs out there because of two reasons. The first reason is that there isn’t a big demand for PhDs in Mathematics, so online universities are not inclined to find ways to make those programs more accessible.

The second reason is that in traditional doctoral studies graduate students in mathematics are used as research and teaching assistants. Usually, math doctoral studies take place within a community in which PhD students are apprentices learning alongside instructors and one another.

Best Online PhD Programs in Mathematics

School Program Length
Atlantic International University Doctorate in Mathematics Custom pace
Edith Cowan University Mathematics PhD 4 years

How Long Does It Take to Get a PhD in Mathematics?

It takes about five years to get a PhD in Mathematics. Depending on the academic institution and the specifications of the program, it can take between three and six years. Some students prefer to have a master’s degree before entering a doctoral program in mathematics, but most programs do not require students to have more than a bachelor’s degree .

Some doctoral mathematics academic programs offer two degrees called dual degree programs. You can begin pursuing a Master’s Degree in Mathematics and begin earning credits for a PhD at the same time.

Is a PhD in Mathematics Hard?

Yes, a PhD in Mathematics is hard. Doctoral studies that require advanced knowledge of mathematics would be extremely difficult for most people. Whether you choose to pursue a PhD in Applied Mathematics or Pure Mathematics, you will encounter complex theoretical concepts.

How Much Does It Cost to Get a PhD in Mathematics?

On average, it costs $12,171 per year to get a PhD in Mathematics . This data is based on the National Center for Educational Statistics’s (NCES) report for the average costs of postgraduate studies at public institutions from 2018 to 2019. According to this data, it would cost a total of $48,684 for four years of studies. The cost to get a PhD in Mathematics has likely risen since 2019.

How to Pay for a PhD in Mathematics: PhD Funding Options

The PhD funding options that students can use to pay for a PhD in Mathematics include research fellowships, teaching assistantships, and tuition waivers. In the previous section, we mentioned the cost of doctoral degrees , but this number is with a deduction in the tuition.

These funding options enable students to lower the cost of tuition. For example, domestic students receive lower tuitions. Without funding options or deductions, a PhD can cost from $20,000 to $30,000 per year.

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What Is the Difference Between a Mathematics Master’s Degree and PhD?

The difference between a Master’s Degree in Mathematics and a PhD is the career opportunities they provide graduates. People who pursue a PhD in Mathematics usually seek jobs in research and academia, while people who pursue master’s degrees are more interested in advancing their professional careers.

A PhD in Math is more research-intensive and focused on historical and current perspectives within the mathematics field. Master’s degrees are a bit broader. Master’s degrees can take up to three years to complete, while PhD can take up to six years. Math PhD students also teach and engage in departmental activities, while master’s students do not.

Master’s vs PhD in Mathematics Job Outlook

It is usually required for postsecondary teachers to have PhDs. According to the Bureau of Labor Statistics (BLS), these professionals have a job outlook of 12 percent , four percent higher than the average for all occupations.

Mathematics and statisticians are usually required to hold a master’s degree and they have a job outlook of 33 percent , nearly three times the average for all occupations. According to these numbers, the job outlook for Master’s Degrees in Mathematics is higher than for PhDs in Mathematics. However, these are just two examples of careers available to master’s and PhD holders.

Difference in Salary for Mathematics Master’s vs PhD

According to PayScale, mathematicians with a master’s degree earn $85,000 per year, and mathematicians with a PhD degree earn $110,000 a year. This is a difference of $25,000 per year for mathematics master’s vs PhD holders.

Related Mathematics Degrees

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Why You Should Get a PhD in Mathematics

You should get a PhD in Mathematics because it expands your academic career opportunities and salary options. With a PhD in Math, you can work for private businesses or government agencies. Many PhD grads work in engineering, medicine, and software development, where they apply the advanced mathematical knowledge they acquired from their doctoral programs.

Reasons for Getting a PhD in Mathematics

  • Specialized skills. A PhD in Mathematics equips you with highly valuable and marketable skills. Aside from subject-specific abilities, you can obtain several transferable skills that will be beneficial in practically any industry, such as exceptional numeracy, logical ability, holistic deduction, and reasoning skills.
  • Higher salary. A PhD is a terminal graduate degree, meaning it is the highest level of academic certification you can achieve in this field. So with a PhD you will gain the highest skills and knowledge in mathematics. High-level skills and knowledge often translate to a high salary.
  • Career opportunities. One of the best advantages math PhDs have is the option of following a variety of employment pathways. To some extent, all sciences are built on basic mathematical principles, so there are many career opportunities with a PhD in Mathematics. With this kind of degree, you can work in finance, academia, or IT.
  • Research opportunities. Doctoral Degrees in Mathematics cover theoretical mathematics which is one of the best areas for research and research methodology. During your doctoral studies in math, you will study and research with some of the smartest people in the world.

Getting a PhD in Mathematics: Mathematics PhD Coursework

a female PhD Student solving a mathematical test

Getting a PhD in Mathematics is not an easy task. Students need to learn different math courses, some of which require advanced knowledge of mathematics. There is some standard mathematics PhD coursework, like classes in mathematical analysis or mathematical logic. Find out more details on common mathematics PhD courses below.

Mathematical Analysis

These kinds of courses explain the principles of mathematical analysis, including differentiability, continuity, sequence and series convergence, the Riemann integral, function sequences, and series. Students can also learn real applications of real-world analysis, including the estimation of indeterminate integrals, Laurent series, WKB theory, Cauchy theorem, and residual theorem.

Differential Topology

Courses in differential topology are a part of the theory of differential forms and De Rham’s theory. Somer differential topology courses teach about multilinear algebra, Stokes’ theorem, and an introduction to cohomology. But, in most cases, these courses teach about winding numbers, vector fields, index, smooth maps, transversality, and differential manifolds.

Discrete Mathematics

Courses in discrete mathematics usually cover finite geometry, finite groups, finite topology, finite fields, fundamental algebraic topology, combinatorics, and graph theory. Students can learn about the symmetry group of the regular icosahedron because it is a reoccurring subject throughout the course.

Theory of Probability

Theory of probability courses introduce students to discrete and continuous random variables, independent random variables, conditional probability, distribution functions, Poisson distributions, Bayes theorem, and joint distribution. Students in this course will learn how to use math principles in the analysis of random phenomena.

Algebraic Geometry

In most cases, algebraic geometry courses teach students about complex algebraic varieties, cohomology, affine, and projective algebraic geometry. They also cover the fundamental concepts of complex analytic varieties, Bezout’s theorem, algebraic curves, and surfaces, the language of schemes, and properties of morphisms.

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How to Get a PhD in Mathematics: Doctoral Program Requirements

Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs. Keep reading to find out more.

PhD students must finish eight or nine-term courses at the graduate level, in most cases maintaining at least a C average grade. The time for completion of a PhD math coursework is four to five years.

The residency requirement can vary from university to university. For most math PhD candidates, the usual residency requirement is around three years. The whole point of residency is to continue the education and training of students in a specialized field of mathematics.

A committee of three faculty members administers the Qualifying Examination, which is an oral test. Each student selects three qualifying test subjects and discusses them with appropriate examiners. Subjects must be in separate, reasonably broad mathematical fields. 

Typically, the primary topic is decided in cooperation with the potential thesis advisor. After completing the qualifying test, students must choose a thesis advisor, who is usually the primary topic examiner.

In academic positions, teaching is important, especially in mathematical doctoral studies. Many people in math PhD programs aspire to academic positions, so teaching is one of the best ways to learn about the mathematics academic profession. It is an excellent way to learn public presentation skills by completing at least one semester of classroom teaching.

Writing and defending a thesis for a PhD in Mathematics is the culmination of this graduate program. Usually, a thesis is anticipated to contain original research of a high enough quality to be published in a high-level research journal. The defense is usually held in the classroom of the Institute and is presented to the Thesis Examination Committee.

Potential Careers With a Mathematics Degree

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PhD in Mathematics Salary and Job Outlook

People with a PhD in Mathematics earn above the average annual salaries and have careers with above the average job growth. For example, actuaries have a 24 percent job growth till 2030. According to the Bureau of Labor Statistics, the average job growth rate for all occupations is 7.7 percent .

Earning a mathematics PhD is difficult but you will graduate with a wide range of job opportunities. People with a PhD in Math earn between $82,360 to $108,660 per year. Overall, people with PhDs in Mathematics have a good salary and job outlook.

What Can You Do With a PhD in Mathematics?

With a PhD in Mathematics, you can work in education or IT and for private, corporate, or government corporations. You can work as a postdoctoral research associate, a math professor in postsecondary or higher education, a director of analytics, a research scientist, a principal software engineer, or an asset manager.

Best Jobs with a PhD in Mathematics

  • Data Scientist
  • Mathematicians and Statistician
  • Operations Research Analyst

What Is the Average Salary for a PhD in Mathematics?

The average salary for a PhD in Mathematics is $110,000 , according to PayScale. The salary range for doctorate-level degree mathematics jobs ranges from $48,690 to $167,040 per year. Lower-earning operations research analysts make an average of $48,690 , while top-earning data scientists earn $167,040 annually, according to the Bureau of Labor Statistics.

Highest-Paying Mathematics Jobs for PhD Grads

Mathematics PhD Jobs Average Salary
Data Scientist
Actuary
Economist
Mathematician or Statistician
Operations Research Analyst

Best Mathematics Jobs with a Doctorate

There are many jobs you can find with a math PhD. The skills you will gain are applicable to almost any field. Find out more about the best PhD in Mathematics jobs below.

Data scientists are specialists who know how to extract and interpret data. They know how to use models and algorithms to analyze massive data repositories. They use various strategies to determine the optimal methods for developing a data model for a business. Data scientist is one of the most in-demand and highest-paid jobs in 2022. 

  • Salary with a Mathematics PhD: $108,660
  • Job Outlook: 22% job growth from 2020 to 2030
  • Number of Jobs: 105,980
  • Highest-Paying States: Washington, California, Delaware, New York, New Jersey

Actuaries are more concerned with the financial implications of risk and uncertainty. Actuaries are financial analysts who analyze past and present financial data and forecast future risks. They assess risk using financial theory, statistics, and math and develop plans that reduce the cost of risk.

  • Salary with a Mathematics PhD: $105,900
  • Job Outlook: 24% job growth from 2020 to 2030
  • Number of Jobs: 27,700
  • Highest-Paying States: Georgia, New Hampshire, New York, Connecticut, Vermont

Some of the main responsibilities economists have are to predict the customer demand for the firm's products and the firm's product sales. They deal extensively with microeconomic issues while researching trends, collecting, evaluating, and analyzing data. Economists also investigate how to efficiently allocate resources like raw materials, labor, land, or machines.

  • Salary with a Mathematics PhD: $105,630
  • Job Outlook: 13% job growth from 2020 to 2030
  • Number of Jobs: 18,600
  • Highest-Paying States: New York, District of Columbia California, New Hampshire, Illinois

In most cases mathematicians and statisticians work in academia and government. Usually, both of the positions require the use of analyzing data or applying statistical and mathematical techniques that help solve problems. 

Statisticians are increasingly involved in statistics and research methodology. Mathematicians are more involved in researching mathematical models or abstractly measuring values and creating results. Mathematics and statistics are the best duos that understand the principles of probability.

  • Salary with a Mathematics PhD: $96,280
  • Job Outlook: 33% job growth from 2020 to 2030
  • Number of Jobs: 44,800
  • Highest-Paying States: District of Columbia, New York, New Jersey, Virginia, Maryland

Operations research analysts utilize mathematics and logic to assist businesses in making informed decisions and solving complex problems. They are high-level problem solvers that use sophisticated approaches such as mathematical modeling and statistical analysis to help companies operate more economically.

  • Salary with a Mathematics PhD: $82,360
  • Job Outlook: 25% job growth from 2020 to 2030
  • Number of Jobs: 104,100
  • Highest-Paying States: Virginia, Alabama, Maryland, Hawaii, New York

Is a PhD in Mathematics Worth It?

Yes, a PhD in Mathematics is worth it if you are interested in solving math problems and analytical thinking. You also have to be willing to commit to the long educational journey and research required to achieve this level of degree.

Exploring the mathematical fields is challenging and demanding but with time it provides excellent career opportunities. Math positions are respected and well-paid with positive job outlooks. Other than its academic difficulty, there aren’t many downsides when it comes to doctoral math degrees because you can go on to work in many fields.

Additional Reading About Mathematics

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PhD in Mathematics FAQ

Yes, a math PhD is useful because it will help you acquire some transferable skills that will be useful in virtually any industry. It is also useful for those interested in mathematics research or academia. If you wonder what you can do with a math degree , a PhD will equip you with many valuable skills.

Yes, a PhD in Mathematics is difficult to learn. It is difficult to be admitted to a doctoral program in mathematics, and it is also difficult and too abstract for most people to grasp advanced mathematical principles taught in PhD studies. Doctoral math studies are objectively difficult, even for those who are naturally strong at math and have excelled at it their whole life.

Mathematicians need several skills like active learning, complex problem-solving, critical thinking, and analytical skills. A good mathematician also needs information ordering and inductive and deductive reasoning abilities.

Mathematicians mainly explore mathematical principles or models and create their own mathematical theories and concepts. Most of the work they do is in the theoretical realm, that is why they mainly want to work in IT, social science, engineering, or financial fields.

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MA, Mathematics – Non-thesis

The Department of Mathematics has one of the highest ranked mathematics graduate programs in the southeast. It is also one of the largest departments at UGA.

Degree Type: Masters

Degree Program Code: MA_MATH_NT

Degree Program Summary:

The Department of Mathematics has one of the highest ranked mathematics graduate programs in the southeast. It is also one of the largest departments at UGA. The Department of Mathematics offers four graduate degrees: Master of Arts (MA), Master of Arts Non-Thesis (MA), Master of Applied Mathematical Science (MAMS), and Doctor of Philosophy (PhD). The Department of Mathematics is in UGA’s Franklin College of Arts and Sciences. It is located in Boyd Graduate Studies Research Center which is situated adjacent to the Science Library on UGA’s south campus. The department offers instruction and research training in the areas of algebra; analysis; applied mathematics; ordinary, partial, and stochastic differential equations; algebraic, differential, and integral geometry; mathematical physics; number theory; numerical analysis; probability and stochastic processes; and topology. Financial aid in the form of assistantships is available to students admitted into the graduate program. This support will be continued for up to six years (five years for students admitted with a Masters degree), as long as the student makes timely progress and maintains a satisfactory academic record.

The purpose of the MA program in mathematics is to offer students who hold a Bachelor’s degree in mathematics an opportunity to broaden their knowledge in several areas of mathematics and its applications. The MA program trains students for careers outside the standard research university environment. This program will prepare a student for teaching at junior colleges or for careers in business, government, or industry. An inadequately prepared PhD applicant may be admitted to the MA program with the possibility of transferring later to the PhD program if he or she makes sufficient progress.

Candidates for the MA Degree with Thesis take 30 credit hours of mathematics-related coursework and write a thesis. It is desirable that the thesis should present original research. However, the thesis may be expository in nature in which case it should be a synthesis of several research articles and books. Candidates must also demonstrate knowledge of one foreign language.

Locations Offered:

Athens (Main Campus)

College / School:

Franklin College of Arts & Sciences

346 Brooks Hall Athens, GA 30602

706-542-8776

Department:

Mathematics

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IMAGES

  1. How To Do Phd In Mathematics

    how to get phd in mathematics

  2. Ph.D. In Mathematics: Course, Eligibility Criteria, Admission, Syllabus

    how to get phd in mathematics

  3. How to do PhD in Mathematics in USA

    how to get phd in mathematics

  4. Best PhDs in Mathematics

    how to get phd in mathematics

  5. How To Do Phd In Mathematics

    how to get phd in mathematics

  6. PhD In Mathematics

    how to get phd in mathematics

VIDEO

  1. GET PhD Thesis and Dissertation Writing Services #phd #thesiswritingservices #phdthesis

  2. Tips to get PhD/Int-PhD admission in IITs, IISER,IISc and other institutes

  3. PhD Mathematics Entrance Exam Result #exam

  4. Rich 🤑Life 4 MATHS Students 💯

  5. The LUMS Podcast I MS & PhD Mathematics

  6. HOW TO GET PHD IN 5 MINS

COMMENTS

  1. Requirements for the Ph.D. Degree

    In order to qualify for the Mathematics Ph.D., all students are required to: Complete eight term courses at the graduate level, at least two with Honors grades. Pass qualifying examinations on their general mathematical knowledge; Submit a dissertation prospectus; Participate in the instruction of undergraduates;

  2. Admissions

    Admissions. Financial Support. Graduate Program Administrator. Marjorie Bell (she/her) 617-496-5211. [email protected]. Science Center Room 331. 1 Oxford Street. Cambridge, MA 02138.

  3. PhD Program

    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 ...

  4. Ph.D. Program

    In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ...

  5. Guide To Graduate Study

    Guide to Graduate Studies. The PhD Program. The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in ...

  6. Admission

    You self-reported your grades in step 1, but we require an official transcript for all admitted students. If/when we request this, arrange for an official copy of your college transcript to be sent to: Academic Services, Room 2-110. Dept of Mathematics, MIT. 77 Massachusetts Ave. Cambridge MA 02139-4307.

  7. 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 ...

  8. Department of Mathematics at Columbia University

    website creator . Program of Study. The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy. The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government.

  9. 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 ...

  10. Harvard Mathematics Department Graduate Information

    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 ...

  11. 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.

  12. 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 ...

  13. PhD Qualifying Exams

    Students who entered the program in Autumn 2023 or later. To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: algebra. real analysis. geometry and topology. applied mathematics. The exams each consist of two parts. Students are given three hours for each part.

  14. PhD 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 ...

  15. Applied Mathematics Doctoral Program

    PhD Program in Applied Mathematics . Students must complete the following requirements in order to earn a PhD in Applied Mathematics. Some specializations have specific course requirements for the doctorate; elective courses are determined in consultation with the program adviser. Successful completion of an approved 30-point program of study ...

  16. How Long Does It Take To Get a PhD in Math?

    Typically, it takes about five years to get a Ph.D. in math. This amount of time is in addition to your undergraduate education, which usually takes about four years to complete. You don't necessarily have to get a master's degree, which takes about two years to complete, to pursue a Ph.D. in math. However, many students choose to earn a master ...

  17. Graduate Program

    Our grad students can take courses not only in the Mathematics Department but also elsewhere at Penn, and the wide resources of the university are available. Our former graduate students have gone on to mathematical careers both in academia and in industry. Our full-time Ph.D. students receive a generous and competitive support package including.

  18. Mathematics

    Mathematics. Ph.D. The Mathematics program is designed to prepare especially able students for a career in mathematical research and instruction. A relatively small enrollment of 30 to 40 students permits small classes and close contact with faculty. Applicants should have a good background in undergraduate mathematics, regardless of their majors.

  19. graduate admissions

    0. Roughly: good grades (3.8+ GPA) in difficult courses, good test scores (80+ percentile on math GRE subject test [not the regular GRE math, which you should get a ~perfect score on without studying]), strong research background and good letters corresponding to it. That will get you into schools in the top ~30.

  20. AMS :: Considering Grad School

    Financial aid is available for graduate school, often in forms of grants or jobs. As a PhD student in the mathematical sciences, you will typically work as a teaching or research assistant, which pays a stipend and covers all or most of your tuition. The median annual salary of mathematical scientists in May 2019 was $92,030, with 10% earning ...

  21. Best PhDs in Mathematics

    How to Get a PhD in Mathematics: Doctoral Program Requirements. Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs.

  22. Mathematics Education PhD

    Mathematics Education PhD; Doctor of Philosophy. The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching ...

  23. Ph.D. Mathematics Course, Eligibility, Entrance Exams, Syllabus

    Ph.D. Mathematics is the program of choice for students who wish to pursue a career in a mathematical research field. The minimum duration of this course is 2-years, whereas you can complete this course in a maximum time span of 3-5 years. Ph.D. Mathematics is a full-time doctoral degree.

  24. MA, Mathematics

    The Department of Mathematics has one of the highest ranked mathematics graduate programs in the southeast. It is also one of the largest departments at UGA. The Department of Mathematics offers four graduate degrees: Master of Arts (MA), Master of Arts Non-Thesis (MA), Master of Applied Mathematical Science (MAMS), and Doctor of Philosophy (PhD).

  25. Take a Course

    Courses Designed for Impact. At Harvard Extension School, our courses are the cornerstone of our academic offerings. You may choose to take a single course — perhaps to build a new skill, explore a passion, or prepare for graduate school. Or you may decide to take courses in pursuit of a degree or certificate. The choice is yours.

  26. What Is Data Analysis? (With Examples)

    What Is Data Analysis? (With Examples) Data analysis is the practice of working with data to glean useful information, which can then be used to make informed decisions. "It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts," Sherlock Holme's proclaims ...

  27. Thinking of Pursuing a PhD in Economics? Info on Graduate School and

    Becoming a PhD economist can provide a fulfilling and financially secure career path. However, getting started in the field can be daunting if you don't know much about the preparation you'll need and the available job opportunities. If you're wondering what it means to be an economics researcher or how to become one, please read on. We'll review how to prepare for a career in ...

  28. How Science, Math, and Tech Can Propel Swimmers to New Heights

    After outlining the evolution of swimming over the past 100 years, the paper explains how an understanding of math and physics, combined with the use of technology to acquire individual-level data, can help maximize performances. Essential to understanding the scientific principles involved with the swimming stroke, the paper says, are Newton ...

  29. When the PhD path leads to career struggles

    Pat Greenhouse/Globe Staff. A doctoral degree is a major commitment. Think carefully. I appreciated reading Kara Miller's The Big Idea column "PhD: Pretty heavily disappointed" (Business ...

  30. High schoolers will need to pass literacy test in Ontario

    Ontario's Education Minister Stephen Lecce unveiled the province's plan on Thursday. Ontario high school students will soon need to pass a financial literacy test in order to graduate — one ...