good math phd programs

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.

Guide to Graduate Studies

The PhD Program The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one’s own way. For this reason, a Ph.D. dissertation involving some original research is a fundamental part of the program. The stages in this program may be described as follows:

• Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
• Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
• Making a first original contribution to mathematics within this chosen special area.

Students are expected to take the initiative in pacing themselves through the Ph.D. program. In theory, a future research mathematician should be able to go through all three stages with the help of only a good library. In practice, many of the more subtle aspects of mathematics, such as a sense of taste or relative importance and feeling for a particular subject, are primarily communicated by personal contact. In addition, it is not at all trivial to find one’s way through the ever-burgeoning literature of mathematics, and one can go through the stages outlined above with much less lost motion if one has some access to a group of older and more experienced mathematicians who can guide one’s reading, supplement it with seminars and courses, and evaluate one’s first attempts at research. The presence of other graduate students of comparable ability and level of enthusiasm is also very helpful.

University Requirements

The University requires a minimum of two years of academic residence (16 half-courses) for the Ph.D. degree. On the other hand, five years in residence is the maximum usually allowed by the department. Most students complete the Ph.D. in four or five years. Please review the program requirements timeline .

There is no prescribed set of course requirements, but students are required to register and enroll in four courses each term to maintain full-time status with the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Qualifying Exam

The department gives the qualifying examination at the beginning of the fall and spring terms. The qualifying examination covers algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. Students are required to take the exam at the beginning of the first term. More details about the qualifying exams can be found here .

Students are expected to pass the qualifying exam before the end of their second year. After passing the qualifying exam students are expected to find a Ph.D. dissertation advisor.

Minor Thesis

The minor thesis is complementary to the qualifying exam. In the course of mathematical research, students will inevitably encounter areas in which they have gaps in knowledge. The minor thesis is an exercise in confronting those gaps to learn what is necessary to understand a specific area of math. Students choose a topic outside their area of expertise and, working independently, learns it well and produces a written exposition of the subject.

The topic is selected in consultation with a faculty member, other than the student’s Ph.D. dissertation advisor, chosen by the student. The topic should not be in the area of the student’s Ph.D. dissertation. For example, students working in number theory might do a minor thesis in analysis or geometry. At the end of three weeks time (four if teaching), students submit to the faculty member a written account of the subject and are prepared to answer questions on the topic.

The minor thesis must be completed before the start of the third year in residence.

Language Exam

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. Almost all important work is published in one of these four languages. Accordingly, students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination. Students are asked to translate one page of mathematics into English with the help of a dictionary. Students may request to substitute the Italian language exam if it is relevant to their area of mathematics. The language requirement should be fulfilled by the end of the second year. For more information on the graduate program requirements, a timeline can be viewed at here .

Non-native English speakers who have received a Bachelor’s degree in mathematics from an institution where classes are taught in a language other than English may request to waive the language requirement.

Upon completion of the language exam and eight upper-level math courses, students can apply for a continuing Master’s Degree.

Teaching Requirement

Most research mathematicians are also university teachers. In preparation for this role, all students are required to participate in the department’s teaching apprenticeship program and to complete two semesters of classroom teaching experience, usually as a teaching fellow. During the teaching apprenticeship, students are paired with a member of the department’s teaching staff. Students attend some of the advisor’s classes and then prepare (with help) and present their own class, which will be videotaped. Apprentices will receive feedback both from the advisor and from members of the class.

Teaching fellows are responsible for teaching calculus to a class of about 25 undergraduates. They meet with their class three hours a week. They have a course assistant (an advanced undergraduate) to grade homework and to take a weekly problem session. Usually, there are several classes following the same syllabus and with common exams. A course head (a member of the department teaching staff) coordinates the various classes following the same syllabus and is available to advise teaching fellows. Other teaching options are available: graduate course assistantships for advanced math courses and tutorials for advanced undergraduate math concentrators.

Final Stages

How students proceed through the second and third stages of the program varies considerably among individuals. While preparing for the qualifying examination or immediately after, students should begin taking more advanced courses to help with choosing a field of specialization. Unless prepared to work independently, students should choose a field that falls within the interests of a member of the faculty who is willing to serve as dissertation advisor. Members of the faculty vary in the way that they go about dissertation supervision; some faculty members expect more initiative and independence than others and some variation in how busy they are with current advisees. Students should consider their own advising needs as well as the faculty member’s field when choosing an advisor. Students must take the initiative to ask a professor if she or he will act as a dissertation advisor. Students having difficulty deciding under whom to work, may want to spend a term reading under the direction of two or more faculty members simultaneously. The sooner students choose an advisor, the sooner they can begin research. Students should have a provisional advisor by the second year.

It is important to keep in mind that there is no technique for teaching students to have ideas. All that faculty can do is to provide an ambiance in which one’s nascent abilities and insights can blossom. Ph.D. dissertations vary enormously in quality, from hard exercises to highly original advances. Many good research mathematicians begin very slowly, and their dissertations and first few papers could be of minor interest. The ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren’t known; and (2) a somewhat fatalistic attitude concerning “creative ability” and recognition that hard work is, in the end, much more important.

PhD Program

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

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

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

• real analysis
• geometry and topology
• applied mathematics

Course Requirements for students starting prior to Autumn 2023

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

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

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

Course Requirements for students starting in Autumn 2023 and later

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

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

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

Years 4&5

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

Throughout the PhD Program

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

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

Mathematics

Undergraduate Program

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

The Bachelor of Liberal Arts degree is designed for industry professionals with years of work experience who wish to complete their degrees part time, both on campus and online, without disruption to their employment. Our typical student is over 30, has previously completed one or two years of college, and works full time.

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

graduate program

Ucla math commencement ceremony, program overview.

Virtually every core area of mathematics is strongly represented in the UCLA Math Graduate Program. In the U.S. News & World Report’s 2018 Best Graduate Schools rankings (most recent), the UCLA Mathematics Graduate Program maintained its highest historical ranking of seven (shared) overall in the nation. In seven research specialties, the Program ranked in the top ten: Analysis (#1), Applied Math (#2), Logic (#2), Algebra/Number Theory/Algebraic Geometry (#8), Discrete Mathematics and Combinatorics (#11), Geometry (#12), and Topology (#7). For more information about the rankings of the entire UCLA Department of Mathematics, read the 2020 Academic Ranking of World Universities for Mathematics . 

As of fall 2020, the graduate program has 152 PhD candidates. The 24 PhD graduates of 2019-2020 are continuing their research studies in postdoctoral positions or as tenured faculty at premier institutions such as Princeton, Carnegie Mellon University, Rutgers, the National Geospatial Intelligence Agency,  and the Institute for Basic Science, Center for Geometry and Physics. Other graduates are beginning their careers in industry for companies including Google, Morgan Stanley, Facebook, and Dreamworks Animation. 

The graduate program is located in the Mathematical Sciences Building, which is centrally situated on the UCLA campus. The MS building houses classrooms, administrative offices, faculty offices, graduate student offices, the graduate student lounge and several computer labs. PC’s are available in all graduate student offices. The department also maintains a Linux based “Beowulf” cluster for parallel computing.

Additional facilities include:

• The Graduate Reading Room, which  has a large non-circulating collection of books, over 9,000 monographs, and subscribes to 150 mathematical journals.
• The Applied Computing Lab (ACL) in MS 6187 (available to all Applied Math graduate students) consists of six machines running Linux and eight machines running Windows 7. A high-speed/volume printer is available as well.
• The Graduate Computing Lab (GCL ) in MS 3347 has linux/windows machines and a high-speed/volume printer. 

quick links

2023 Open House Information

Financial Support

Housing Information

Program Requirements

The Online Application Process

Workforce Programs

Annual Support Plan and Offers of TA Appointments

CCLE Course Webpages

Courses Overview

Exit Survey for Graduating Students

Fall 2021 New Student Information

Feedback Form

Formatting Your Thesis

Graduate Handbook

Graduate Students Travel Stipends

Graduate Tentative Schedules

Qualifying Exam Dates & System

Teaching Assistant Manual

Teaching Preferences

Academic Student Employee Union

Arthur Ashe Student Health and Wellness Center

Center for Accessible Education (CAE)

Commencement

Counseling and Psychological Services (CAPS)

Graduate Division

Graduate Student Association

Graduate Student Outreach

Graduate Student Resource Center

Math/Physical Sciences Council

Title IX Compliance Training for Graduate Students

UCLA Ombuds Office

graduate staff

Graduate Advisor

[email protected]

(310) 825-4971

Sanim Rishan

[email protected]

Monday - Friday 9 - 11 AM & 1 - 3 PM

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.

• University of Pennsylvania
• School of Arts and Sciences
• Penn Calendar

Department of Mathematics

Search form.

Mathematics Graduate Program

Thinking of applying to graduate school 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?

2024 Best Mathematics Doctor's Degree Schools

Choosing a great mathematics school for your doctor's degree, a great overall school, early-career earnings, other factors we consider, one size does not fit all, featured mathematics programs, best schools for doctorate students to study mathematics in the united states, 17 top schools for a doctorate in math, additional noteworthy schools.

Mathematics by Region

Other Rankings

Best associate degrees in mathematics, best master's degrees in mathematics, best value in mathematics, best for non-traditional students in mathematics, best online in mathematics, most popular online in mathematics, best bachelor's degrees in mathematics, best overall in mathematics, highest paid grads in mathematics, best for veterans in mathematics, most popular in mathematics, most focused in mathematics, mathematics related rankings by major, math focus areas.

Most Popular Related Majors

Notes and References

Popular reports, compare your school options.

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.  

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. 

………… return to top

Ohio State navigation bar

• BuckeyeLink
• Search Ohio State

Doctor of Philosophy (PhD)

Program synopsis and training.

 The Doctor of Philosophy (PhD) in mathematics is the highest degree offered by our program. Graduates will have demonstrated their ability to conduct independent scientific research and contribute new mathematical knowledge and scholarship in their area of specialization. They will be well-supported and well prepared for research and faculty positions at academic institutions anywhere in the world. Owing to their independence, analytic abilities, and proven tenacity, our PhD graduates are also sought after by private and government employers.

Our PhD program offers two tracks, one for Theoretical Mathematics and one for Applied Mathematics . The tracks differ only in the course and  qualifying requirements during the first two years. Applicants are required to decide on one of the tracks and applications will be evaluated subject to respective criteria described below.

Once students have passed their Qualifying Requirements, the two tracks merge and there is no distinction in later examinations and research opportunities. In particular, the candidacy exam for both tracks consists of a research proposal, the graduate faculty available for advising is the same, and the final degree and thesis defense are independent of the initially chosen track.

Expected Preparations for Admission

Competitive applicants to the theoretical track are expected to have strong foundations in Real Analysis and Abstract Algebra, equivalent to our Math 5201 - 5202  and Math 5111 - 5112 sequences.

Expected preparations for the applied track include the equivalents of a rigorous Real Analysis course (such as Math 5201 ), a strong background in Linear Algebra, as well as an introductory course in Scientific Computing.

Besides these basic requirements, competitive applicants in either track submit evidence for a broad formation in mathematics at the upper-division or beginning graduate level. Relevant coursework in other mathematical or quantitative sciences may also be considered, especially for the applied track.

Prior research experiences are not required for either track, and we routinely admit students without significant research background. Nevertheless, applicants are encouraged to include accounts of research and independent project endeavors as well as letters of supervising mentors in order to be more competitive for fellowship considerations. The research component is likely to have greater weight in applications to the applied track.

These prepared documents serve to provide our admission committee with a narrative overview of the applicant's mathematical trajectory. Their primary focus should, therefore, be to enumerate and describe any evidence of mathematical ability and mathematical promise. The information included in the documents should be well-organized, comprehensive, informative, specific, and relevant. This will help our committee to properly and efficiently evaluate the high number of applications we receive each year.

Our Graduate Recruitment Committee will generally  not  consider GRE test scores for this Autumn 2024 admissions. If you have already taken the test, please do not self-report the scores to us. In exceptional circumstances students may have the option to report unofficially. 

International students whose native language is not English and are not exempt should score at least a 20 on the Speaking portion of the TOEFL or at least 6.5 on the IELTS Speaking portion.  We also recommend an overall score of at least 95 on TOEFL or at least 7.0 on IELTS.  For a list of exempt countries, please see  https://gpadmissions.osu.edu/intl/additional-requirements-to-apply.html

Qualifying Requirements by Track

The qualifying requirements for the theoretical track are fulfilled by passing our Abstract Algebra course sequence  ( Math 6111 , Math 6112 ) and  our Real Analysis course sequence ( Math 6211 , Math 6212 ), each with at least an A-, or  by passing a respective examination.

The qualifying requirements for the applied track combine a mandatory Scientific Computing course ( Math 6601 ), one of the algebra or analysis courses, and three additional courses chosen from  Math 6602 , Math 6411 ,  Math 6451 , and the courses comprising the algebra and analysis sequences.

The breadth requirements in the applied track are more flexible than in the theoretical track, but also include a mandatory graduate course in a non-math STEM department from an approved list. 

You can find more information about our PhD program requirement here .

Opportunities & Outcomes

The research opportunities and academic outcomes of our doctoral program are described in detail in the Graduate Program Prospectus  [pdf]. 

Our department has about 80 active graduate faculty on the Columbus and regional campuses. Virtually every area of mathematics is represented in our program, with a sampling displayed below.

• Commutative, Non-commutative, & Quantum Algebra
• Analytic, Algebraic, Computational Number Theory
• Algebraic Geometry, Tropical Geometry
• Applied Mathematics, Mathematical Physics
• Real and Complex Analysis
• Functional Analysis, Operator Algebras
• Combinatorics and Graph Theory
• Differential Geometry
• Dynamical Systems and Ergodic Theory
• Financial and Actuarial Mathematics
• Logic and Foundations
• Probability Theory, Statistical Mechanics
• Mathematical Biology
• Ordinary and Partial Differential Equations
• Representation theory
• Scientific Computing
• Topology, Topological Data Analysis

See also our  Applied Mathematics Topics List  [pdf].

Our program offers many support opportunities without teaching duties as well, to allow more time for scientific endeavors. These opportunities include university fellowships, external funding, and departmental fellowships and special assignments. See the  Financial Support  page for more details.

The median time to degree completion in our program is below six years but also varies significantly among our students, with as little as four years for students entering with substantial prior preparations. Funding is guaranteed for six years and can be extended to seven years with advisor support and the permission of the Graduate Studies Committee.  

Most of our graduates continue their careers in academia. Post-doctoral placements in the last two years include, for example, UCLA, Stanford, ETH-Zürich, Brown University, University of Michigan, Northwestern University, University of Vienna, EPF Lausanne, Free University at Berlin, Purdue University, and University of Utah. In recent years our graduates also went to Princeton University, IAS, University of Chicago, Yale University, University of Michigan, Cal-Tech, Northwestern University, University of Texas, Duke University, SUNY Stony Brook, Purdue University, University of North Carolina - Chapel Hill, and Indiana University. Recent non-academic placements include Google, Facebook, Amazon, NSA, and prestigious financial institutions.

Students also have access to training and networking opportunities that prepare them better for careers in private industry and teaching - for example, through the Erdős Institute  - and are regularly offered highly competitive positions in the industry. 

Nearly half of the graduate population consists of domestic students coming from both larger universities and smaller liberal arts colleges with a solid math curriculum. And as a program group member of the National Math Alliance , we are dedicated to enhancing diversity in our program and the scientific community. The International students in our program come from all parts of the world with a wide variety of educational backgrounds.

Prospective students:  [email protected]

Graduate Office Department of Mathematics The Ohio State University 231 W 18th Avenue ( MA 102 ) Columbus, Ohio 43210 United States of America                

Phone: (614) 292-6274 Fax: (614) 292-1479

[pdf] - Some links on this page are to .pdf files. If you need these files in a more accessible format, please email  [email protected] . PDF files require the use of Adobe Acrobat Reader software to open them. If you do not have Reader, you may use the following link to Adobe to download it for free at:  Adobe Acrobat Reader .

Graduate Programs

Mathematics.

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. Students with backgrounds in advanced mathematics will find our program quite flexible. Visits to Brown and direct communication with the director of graduate study are strongly encouraged.

The core courses are in differentiable manifolds, real functions, complex functions, algebra, and topology. Other courses offered each year are in P.D.E., probability, algebraic geometry, number theory and differential geometry.

Additional Resources

The library contains one of the finest mathematical collections available anywhere. The department has extensive computing facilities.

Application Information

Application requirements, gre subject:.

Not required

GRE General:

Dates/deadlines, application deadline, completion requirements.

Advancement to candidacy determined in part by qualification in the basic and advanced courses; teaching experience; examination on an advanced topic; expository talk based on a research paper in that subject; dissertation; and oral defense.

Alumni Careers

Contact and Location

Department of mathematics, mailing address.

• Program Faculty
• Program Handbook
• Graduate School Handbook

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.

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

How should I choose which graduate programs to apply to for the PhD?

This fall I will be an senior mathematics major at a small public liberal arts university. I'm trying to finalize the list of schools to which I will apply (to PhD programs in pure math), but I am finding it somewhat difficult. I know that I am not a candidate for admission at top-tier universities. My school is relatively unknown outside of its state, and the professors who will write my recommendation letters aren't very well-known either (although they do publish somewhat frequently in their respective fields). I have taken two semesters of abstract algebra, one semester of real analysis, and two semesters of topology, and received an A in all. By the time I graduate I'll have taken another semester in real analysis and a course in complex analysis, plus several other applied and discrete math classes. I haven't taken any graduate courses since my school doesn't offer them, but I have completed a research project with one of my professors in the area of math which I hope to study in grad school. My GPA is around 3.85.

I think (and please correct me if I am wrong) that I should focus on applying to "mid-tier" programs, but I find it very difficult to determine which programs are at this level. I know that one student from my school was accepted at a program ranked in the 40's by the U.S. News math grad school rankings.

Essentially, my question is this: Do the U.S. News rankings accurately reflect the selectivity of programs, and if so, is there some point in the rankings at which schools become "mid-tier" or at which I would be competitive for admission?

• graduate-admissions
• mathematics

• 12 I think you should apply to the schools where the professors do the research which you are interested in. You don't want to be in the best school in the world studying something you don't like. –  Nobody Commented Aug 20, 2013 at 6:29

4 Answers 4

Yes , the rankings (roughly) reflect the selectivity of the program, as far as I know. Your choice to focus on mid-tier programs makes sense. (I think defining mid-tier as starting in the 40s is plausible, though I suspect you'll get conflicting answers from different people.) However

Don't confuse the quality of the program overall with the quality of their specialty that you hope to study. Their specialty program could be much better or worse than the program overall. In math departments (as opposed to, say, some computer science departments), students are typically admitted to the department , rather than to a professor's research group or a specialty area. Taking advantage of this could get you into a specialty program that's rated higher than you "deserve".

Don't exclude a school just because it's too highly rated. It's good to apply to a wide range of schools, some "reach" schools that you think it unlikely you'll be admitted to, and some "safety" schools that you would be quite surprised not to be admitted to. All sorts of factors influence how likely it is you'll be admitted to a given school in a given year, many of them completely unknowable to you. For example, maybe a new faculty member will be coming and looking for students (or maybe one will be leaving). Maybe the program has all their TA positions tied up with current students who haven't finished yet, or maybe not. Maybe a dean wants to grow the program, etc. Many of these things you just can't know. Most likely, you won't get into MIT, Harvard, Princeton, or Stanford. But once you get into the 20s, 30s and below, the outlook is less clear.

Focus on fit , rather than solely on ranking . Think about where the school is located. If you plan to live there for 5 or 6 years, you don't want to hate the place. This can include proximity to your family or friends, climate, scenery, nightlife, etc. If you know what specialty you want to study, the school should have at least 1, but hopefully 2 or 3 folks that you would potentially like as an adviser.

Focus on aspects of your application that you can still change . With a transcript no stronger than yours, I got into a top-25 school. The cool part is that for the specialty I chose, they were top-10. At this point, most of your transcript (and much of your application in total) is fixed. But you didn't mention your GRE scores. (The surprising thing about the GRE is that you can do pretty well if you're just really good at Calculus (through multivariable), Dif. Eq., and Linear Algebra.) I think my subject test was something like 65th percentile. That's not terribly good, but I think it was enough to convince the admissions committee that even though I was coming from a small LAC that no one had heard of, I did know something. The other thing I did, which I highly recommend you try, is get a letter of recommendation from a faculty member at that school (where I was admitted). I wrote code for him for 3 or 4 weeks (about 30 hours/week, I think) during Christmas break of my senior year. In exchange, he wrote a recommendation for me. I'm sure it didn't say that I was a math wunderkind, but whatever it said added just enough to my application to get me in.

• 2 +1 for point 3! This is one of the main deciding factors for us (I have a wife, and a daughter on the way, so the neighborhood is almost more important than the selectivity of the program.) –  Jonathan E. Landrum Commented Aug 20, 2013 at 14:44
• @Dan C: What is a good way of looking for the "right" professors besides looking up the math faculty of each department? Also, I'm international so looking for connections from professors, that I know, is almost non-existent. –  TheLast Cipher Commented Feb 1, 2019 at 4:42
• @TheLastCipher I'm not sure I understand your question. By "right" do you mean someone to do research under? or someone to get a rec letter for (as in 4.)? or something else? Having connections is huge. I went to grad school in the city where I grew up. I don't remember how I got the connection that led to the rec letter, but I think it was through a contact of my father. (My undergrad adviser did not have a strong academic network.) I would suggest that you look through the math faculty of each department. It is a lot of work, but potentially has a big pay off. –  Dan C Commented Feb 2, 2019 at 5:24
• @TheLastCipher If you don't have good contacts, I would recommend first getting a masters degree, at the best place you are admitted with funding. (It is less important that your choice for a masters program satisfy point 3, since you will likely be there no more than 2 years.) Use the time during your masters to attend conferences to try to build your network (with any guidance you can get from your faculty mentors). Then, using those contacts, you may have a better idea of where to go for a PhD program, and who you could work with. –  Dan C Commented Feb 2, 2019 at 5:26
• @Dan C: By "right" I meant to do research under. Thank you for the advice! –  TheLast Cipher Commented Feb 2, 2019 at 15:13

Dan C's answer is great, and I just want to echo some points and add a few things to it.

First, I'm not sure why you've decided you're not a candidate for a "top-teir" school. It sounds like you've been successful in your coursework, and you can likely get strong letters of recommendation. If you don't bomb the GRE, you can certainly get into a "highly-ranked" school! I went to a college just like the one you describe, and my friends and I all did fine when it came to grad school admissions -- one of my friends got into a "top ten" department, and we all got accepted by schools in the top twenty or thirty. So don't count yourself out simply because your school is small and relatively unknown. And, most importantly, if you do get into a prestigious program, be sure to base your decision to enroll on more than the US News rankings!

(I've used the quotation marks above because the rankings are all a bit questionable, and one should really consider the strength of a department in your field of interest, like Dan C said.)

Regarding the professors who will be writing your letters of recommendation: They may not be heavyweights in their fields, but chances are they know some people of influence. Take a look at some departments, get a feel for what you'd like to study, and possibly with whom, and then talk to your letter writers. It may happen, when you mention your interest in working with Professor X, that your letter writer was roommates with Professor X in grad school. These little personal connections won't get you admitted, but they will help ensure that your application gets a fair evaluation despite your school's relative obscurity.

Good luck! Aim high.

I'll just note that my credentials weren't so different from yours when I graduated from college (obscure liberal arts college with little track record, etc.) and I got in to Berkeley, Michigan and Northwestern. Of course, I can't actually compare our cases (and this was a decade ago), but I don't think you should hesitate to apply to, say, Wisconsin, or UT Austin or Rutgers (depending on your regional preferences). If you doubt it, you can always contact the graduate coordinator and ask if they think you're a plausible candidate.

As Dan says, a good range is the best approach; apply at least one place you can't quite believe you'll get in, and at least one place where you feel absolutely confident, and a few in between. This stuff is indeed incredibly unpredictable, but there are a lot of slots in reasonable graduate programs, and fewer good candidates than you might think.

I'll only address the question of deciding what "mid-tier" means. There's one coarse classification that could be helpful to you.

There are 48 math departments considered as Group I under the AMS classification (the older one, deprecated as of last year but the most useful one in my opinion). There's obviously a lot of variation within this group, but I think it's safe to assume that the programs at these 48 schools are stronger than the 56 math departments in Group II . (The bottom of Group I is probably not separated from the top of Group II by too much, however, so don't stress too much about the cutoff.) However I have a lot less confidence in the division between the bottom of Group II and the top of Group III; in this region the AMS's case for switching to the new groupings seems quite strong to me.

You must log in to answer this question.

Not the answer you're looking for browse other questions tagged graduate-admissions mathematics ..

• Featured on Meta
• Bringing clarity to status tag usage on meta sites
• We've made changes to our Terms of Service & Privacy Policy - July 2024
• Announcing a change to the data-dump process

Hot Network Questions

• Is it OK to make an "offshape" bid if you can handle any likely response?
• How do I safely remove a mystery cast iron pipe in my basement?
• Can my players use both 5e-2014 and 5e-2024 characters in the same adventure?
• In theory, could an object like 'Oumuamua have been captured by a three-body interaction with the sun and planets?
• Change color/style of vertical line between block start-end in algorithm2e
• How does one go about writing papers as a nobody?
• How does current in the cable shield affect the signal in the wires within
• Inconsistent “unzip -l … | grep -q …” results with pipefail
• What's the proper way to shut down after a kernel panic?
• If Miles doesn’t consider Peter’s actions as hacking, then what does he think Peter is doing to the computer?
• Is it possible to create a board position where White must make the move that leads to stalemating Black to avoid Black stalemating White?
• Why do we reduce a body to its center of mass when calculating gain/loss of gravitational potential energy?
• There are at least 3 versions of a quote, with 2 having different attributions. What is the original, who said it, and what does the quote mean?
• If more collisions happen with more resistance, why less heat is generated?
• Flight left while checked in passenger queued for boarding
• How to make a ParametricPlot3D into solid shape
• using a tikz foreach loop inside a newcommand
• Which cards use −5 V and −12 V in IBM PC compatible systems?
• Why does Russia strike electric power in Ukraine?
• Unable to locate package epstopdf
• How many kms do alu rims last when ridden in city and/or road conditions?
• If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
• My PC takes so long to boot for no reason
• Why, if gravity were higher, would designing a fully reusable rocket be impossible?

• Academic Programs

Graduate Program

Learn about our programs.

Our graduate mathematics program is one of the largest in the country — and one of the best. The Department of Mathematics offers programs leading to the degrees of Master of Science and Doctor of Philosophy. Recent changes in the graduate program were aimed at improving opportunities for our students to develop in areas that suit their goals. We invite prospective students to visit to meet faculty and current students and to see first hand what Purdue has to offer.

Program and Course Information

• Course Schedules
• Course Descriptions
• Computational Science & Engineering Program
• Computational Life Sciences

Funding Opportunities

• Fellowships
• Purdue Graduate School Fellowships
• Teaching Assistantships
• Student Travel Funds
• Frequently Asked Questions (FAQ)
• Introduction to Departmental Accounts
• Graduate Student Handbook (PDF)
• Mathematics Graduate Student Representatives
• Purdue Graduate School

Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067

Phone: (765) 494-1901 - FAX: (765) 494-0548   Contact Us

© 2024 Purdue University | An equal access/equal opportunity university | Copyright Complaints | DOE Degree Scorecards

Trouble with this page? Accessibility issues ? Please contact the College of Science .

Maintained by Science IT

• The Student Experience
• Financial Aid
• Degree Finder
• Undergraduate Arts & Sciences
• Departments and Programs
• Research, Scholarship & Creativity
• Centers & Institutes
• Geisel School of Medicine
• Guarini School of Graduate & Advanced Studies
• Thayer School of Engineering
• Tuck School of Business

Campus Life

• Diversity & Inclusion
• Athletics & Recreation
• Student Groups & Activities
• Residential Life
• [email protected] Contact & Department Info Mail
• Frank J. Guarini '46
• Board of Advisors
• Guarini School Impact and Initiatives
• Visual Identity
• From the Dean
• Visiting Dartmouth
• Get Involved
• Living Here
• Student Services
• Guarini Student Survey
• Sarah Cornelius, Guarini
• Rachel Garlick, Guarini '21
• Dylan Green, PhD '24
• Ansh Gupta, MS '24
• Kayla Iuliano, Postdoc
• Tongtong Li, Guarini Postdoc
• Karina Madzari, MALS '24
• Catherine Miller, Guarini
• Camella Pham, Guarini '23
• Stephen Pike, Guarini
• Behishta Sadaat, MALS
• Sharanya Sarkar, Guarini
• Jasmine Shirey, MALS Thesis Award
• Rebecca Valls, PhD '24
• James Washington, Jr., MALS
• Huan Zhao, Guarini
• Pradipta Debnath, International Graduate Student Mentor Program
• News & Events
• Investiture and Commencement
• Mental Health Awareness Month
• Ethics Training Sessions
• Orientation
• Graduate Student Appreciation Week
• Postdoc Appreciation Week
• Academic Requirements
• Academic Standing
• Transcript Requests
• Enrollment Verification
• Academic and Conduct Regulations
• Academic Policies
• Thesis and Dissertation Forms
• Admissions & Financial Aid
• Cognitive Neuroscience
• Comparative Literature
• Computer Science
• Earth Sciences
• Ecology, Evolution, Environment and Society
• Health Policy and Clinical Practice
• Integrative Neuroscience
• Master of Arts in Liberal Studies (MALS)

Mathematics

• Molecular and Cellular Biology
• Physics and Astronomy
• Psychological and Brain Sciences
• Quantitative Biomedical Sciences
• Sonic Practice
• PhD Innovation Program at Dartmouth
• IvyPlus Exchange Scholar Program
• Internship and Experiential Dartmouth Learning Courses - Graduate Students
• Interdisciplinary Programs
• Summer Research Opportunities
• Postbac Research Education Program (DPREP)
• Admissions Information
• Admissions FAQ
• Fellowships
• Awards & Grants
• Tuition & Living Costs
• Childcare Subsidy
• Emergency Loan Funds
• Institutional Financial Aid
• International Students
• Non-Degree Applicants
• Economic Benefits
• Student Support
• Graduate Student Council Resource Guide
• Grievance Policy
• Mental Health
• Title IX Office
• Dartmouth Compliance and Ethics Hotline
• Ethics Training
• Professional Development
• Language Support for International Graduate Students and Postdocs
• Disability-related Accommodations
• Teaching Support
• CVs and Resumes
• Correspondence
• Individual Development Plan (myIDP)
• Interview Practice & Techniques
• Student Professional Development Groups
• Academic Jobs
• Non-Academic Jobs
• For Employers
• Finding Funding
• Get in Touch
• First-Generation Students
• LGBTIQA+ Persons
• Students with Disabilities
• Service Members and Veterans
• Campus Diversity Initiatives
• Recruitment
• Postbac Research Education Program (Dartmouth PREP)
• International Scholars
• Affiliated Fellows
• Postdoc Research Day
• National Postdoc Association Core Competencies
• Professional Affiliations
• Professional Development Award
• National Postdoc Association
• Mentoring Resources
• Dartmouth Postdoc Community Resources

Search form

• Applying to Dartmouth
• Collective Bargaining Agreement Updates

Contact the mathematics department.

Learn more about the mathematics department.

Application Requirements

All application materials must be submitted directly through the online application system. We do not accept paper application materials. Official transcripts should not be sent to the Guarini School office during the application process.

Application Fee

English language proficiency .

• Language proficiency test scores are required for non-US citizens, with the exception of those who are earning or have earned a degree from institutions in the US or Canada, or whose primary language of instruction at their non-US institution was English.
• We accept TOEFL, IELTS, and Duolingo 
• The ETS code for the Guarini School is 3351

Personal Statements

• 2 required personal statement prompts.

Recommendation Letters

• 3 required, up to 4 accepted.

Transcripts

• Your most recent unofficial transcripts should be uploaded as part of your application. Official transcripts are not needed during the application process.

Program Supplement

Please upload a list of upper-level mathematics courses you have taken, specifying which textbooks you have used.

Research Areas

Indicate your interest in pursuing each research area during your graduate study. For more information about our various research groups, click here .

Learn more about the mathematics department faculty.

Questions About the Admissions Process

Admissions information can be found here.

Admissions FAQ.

Mathematics Department Website

Application Deadline: December 15, 2024

Degree Offered: PhD

PhD Program

Take on the big challenges.

Earning a PhD takes courage. There will be obstacles, uncertainty and ambiguity. But it’s the vision of better patient care that sustains you, drives you. That’s what drives us, too.

The Duke Difference

High-impact research.

Field-defining work in imaging, genetic medicine, biomaterials, light-based technologies and more.

Mentoring, from Day One

Be surrounded by a team invested in your success.

Uniquely Interdisciplinary

Duke BME’s superpower. Experience our innovative learning and research ecosystems.

Comprehensive Mentorship & Support

Mentoring, really, even before Day One. During the Duke BME admission process we’ll begin an immersive discussion about your interests. Based on those discussions, once accepted you’ll be admitted directly to a lab. Your Advising Team will including your program director, a team of faculty members and senior PhD students as well as dedicated resources available through the Graduate School at Duke.

Additional High-Value Resources

• Conference and travel support
• Grant supported traineeship programs
• Graduate certificate programs in tissue engineering, nanoscience and photonics

Entrepreneurship: Duke Design Health

Discover. Design. Deploy.

When you join a Duke Design Health team you identify needs that impact human health, and then create effective, equitable solutions.

Doctor of Philosophy in Biomedical Engineering

30 Credits of Coursework

• Life Science course—3 credits
• Advanced Mathematics course—3 credits
• Additional courses—24 credits

2 Semesters of Teaching Assistantship (TA)

Responsible Conduct of Research (RCR)

• Orientation
• 4 RCR forums

Thesis and Defense

Sample Timeline

The minimum required amount of coursework is 30 units.

The program of coursework, including the applicability of any  transfer credits , is determined by the student, their advisor and their committee.

Each committee meeting should include an update on progress towards coursework requirements. The student’s committee retains the power to approve the coursework or request that the student take additional courses.

The advanced math (3 units required) and life science (3 units required) courses, and up to one (1) independent study class may be used toward the 30-credit requirement. See a list of potential life science and advanced math courses . Students are not limited to the courses listed.

Important Notes

• Ungraded seminars do not count toward the 30-unit requirement. Students are encouraged to discuss class selection with their advisor upon matriculation and frequently throughout their course of study
• Students seeking a master’s degree en route to a PhD must satisfy the degree requirements for the master’s degree. These are not necessarily aligned with the PhD coursework requirements, and so special consideration should be taken

Two semesters of BME Seminar are required. New matriculants take BME 702’s (Fall only).

Second-year students take BME 701’s (Spring only).

Teaching Assistantship

Two (2) semesters aare required. Duke BME PhD students typically fulfill their teaching assistant (TA) assignments in years 2 to 5.

Students must:

• Complete a TA training session
• And sign up for a Teaching Assistantship Seminar during the semesters in which they TA

Responsible Conduct of Research

RCR training at Duke challenges students to engage in ethical decision-making through active learning—by using realistic scenarios and current issues.

One (1) orientation session and 4 forums are required.

More about RCR at Duke .

PhD Contacts

Jamel Forbes

Staff Specialist, PhD Program

Danielle Giles

Assistant Director of Graduate Studies

Kathryn Radabaugh Nightingale

Director of Graduate Studies, Theo Pilkington Distinguished Professor of BME

Research Themes

Biomechanics & Mechanobiology, Biomedical Imaging & Biophotonics

Research Interests

Ultrasonic and elasticity imaging; image-guided therapies; biomechanical tissue modeling; ultrasonic bioeffects.