mathematics phd cornell

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Graduate Study

The Department of Mathematics at Cornell University offers a rigorous graduate program, leading to the Ph.D. degree, that combines study and research opportunities under the direction of an internationally known faculty .

Competitive financial support is available through Graduate School fellowships and some graduate research and teaching assistantships.

Ph.D. Program Content

Learning goals and assessment, application details, financial support.

• Fellowship Opportunities
• Research & Teaching Assistantships
• Funding Opportunities for Travel
• Department Prizes and Awards for Graduate Students

Useful Information for Graduate Students

Non-degree and visiting graduate students.

Related Programs at Cornell: Computer Science , Operations Research , Applied Mathematics , Theoretical and Applied Mechanics , Statistics

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We offer a broad program with opportunities for all Cornell undergraduates. Read more...

Our Ph.D. program trains you to create, teach, and communicate mathematics. Read more...

Our department is known for its stimulating and collegial research atmosphere. Read more...

News Highlights

Professor edward swartz receives donna b. paul advising award.

Strogatz, Bethe research papers named to top-50 list

The APS is celebrating the 125th anniversary of the Physical Review and has selected 50 “milestone” research papers. Steven Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics in the College of Arts and Sciences, is on the list for his 2001 work on random graph theory with postdoctoral researchers Mark Newman and Duncan Watts, Ph.D. ’97.

Éva Tardos Named AWM-SIAM Sonia Kovalevsky Lecturer

The Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM) have selected Éva Tardos to deliver the Sonia Kovalevsky Lecture at the 2018 SIAM Annual Meeting.

Aaron Chen '17, awarded an NSF graduate fellowship

Aaron Chen '17, currently enrolled in the graduate program at the University of Chicago, has been awarded an NSF graduate fellowship.

Upcoming Events

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Requirements

Requirements for admission to candidacy.

The following are required for admission to candidacy for the Ph.D., or to obtain an M.S. degree in Applied Mathematics:

• Prerequisite to the graduate program are familiarity with analysis and algebra at the advanced undergraduate level (e.g., MATH 4130-4140 and MATH 4330-4340). Students lacking either prerequisite (which may be determined by their special committee chair and/or the CAM Director of Graduate Studies), should take the appropriate courses within their first two years of study. No more than two of these courses can count towards meeting other CAM degree requirements.
• Students are required to take at least eight courses in mathematics and its applications that are approved by her/his special committee, at least 4 of which must be numbered 6000 or above. Suggested areas for these courses are given in the list of  Focal Areas  for Applied Mathematics.
• The courses taken to satisfy item (2) must include an advanced course in computational methods (focal area (a)). In order to achieve breadth in Applied Mathematics, courses from at least three other Focal Areas should normally be included. Should a course be listed under more than one focal area, then it will count towards only one such area as chosen by the student's Special Committee.
• Students are required to have minors in Mathematics and in another field relevant to their doctoral research. Note that the course requirements listed above may suffice to satisfy the requirements for a graduate minor in Mathematics.

Exceptions to these requirements can sometimes be made, if approved in advance by the student's Special Committee and the Director of Graduate Studies. All requirement courses must be taken for a letter grade.

Requirements for the Graduate Minor

A student majoring in another graduate field (excluding Mathematics) can obtain a Minor in Applied Mathematics by successfully completing four courses, drawn from at least two of the Focal Areas, each of which contains substantial mathematical content. Two of the courses must be at the graduate level, the others numbered 4000 or above. The courses must be approved by a member of the Field of Applied Mathematics who is a member of the student's Special Committee. Any course used to satisfy requirements of the student's major field of doctoral study may not be used to satisfy the Minor in Applied Mathematics. If field members or students feel that these requirements should be updated or altered, please inform the Director of Graduate Studies.

Graduate Study Guidelines

Selection of committees.

A committee chair (thesis advisor) must be selected by each Ph.D. student  before the end of the second semester  (i.e., before the end of Academic Year 1).

The committee chair will aid the graduate student in selecting a Special Committee, which shall consist of a minimum of three faculty members and which will directly supervise the graduate study and research of a student. The committee chair, who is also the thesis advisor, represents the major field of applied mathematics. The other faculty members represent two minor fields; one of these must be mathematics and the other is a field outside mathematics. This committee must be formed  before the end of the third semester .

Exceptions to the above requirements must be approved by the Director of Graduate Studies (DGS). Failure to comply with the above requirement may result in a hold being placed on your registration by the Graduate School.

A Special Committee Selection and Change form must be submitted to the Graduate School to establish a committee or change/add committee members. This can be done online through Student Center.

Selection of a Special Committee (including the thesis advisor) is a mutual agreement between a student, the chosen faculty members and the DGS. During the pursuit of the degree, changes in circumstances may cause the student and/or faculty members to desire the termination of this commitment.

The A-Exam must be scheduled  before the beginning of the seventh semester  unless a special petition is filed. The A-Exam should be scheduled well in advance of the exam and the appropriate form ( Schedule of Examination  form)  MUST  be submitted to the Graduate School at least 7 calendar days ahead. CAM graduate students are eligible for a Non-Thesis Masters Degree upon completion of the A-Exam. In order for this to be awarded, the Committee Chair must check the relevant box on the  Results of Examination Form . The form must be turned into the Graduate School within 3 days after the exam.

The B-Exam (thesis defense) is scheduled with the same form as the A-Exam and must be submitted to the Grad School at least 7 calendar days ahead.

View the timetable for fulfilling all degree requirements.

Mathematics

As a mathematics major, you can focus on the study of the theoretical aspects of mathematics or explore applications to other fields. You can choose one of seven different concentrations and take a rich variety of courses in analysis, algebra, topology, geometry, probability, statistics and logic to tailor a program that meets your individual needs and interests.

Sample classes

• Statistical Theory and Application in the Real World
• Introduction to Number Theory
• Nonlinear Dynamics and Chaos

All information below is based on the 2022 First-Destination Survey. Lists are not exhaustive, rather they are a sampling of the data. If you would like more information, please email  [email protected]

What can you do with a degree in Mathematics? 

Graduate school:.

In 2022, 50% of mathematics students embarked on graduate school journeys. They pursued various advanced degrees, with 41% focusing on their PhD, 30% working towards an MEng, 19% dedicated to an MS, and more. Their graduate field interest ranges from Computer Science (41%) to Mathematics (19%) and Physics (14%).

These ambitious individuals have chosen to continue their education at prestigious institutions like Stanford University, the University of Oxford, Tufts University, Hong Kong University of Science and Technology, and Carnegie Mellon.

Employment: 

47% of mathematics graduates secured employment, and the majority entered sectors in financial services (31%) and technology (26%). Goldman Sachs and Amazon were the top 2022 employers.

Where 2022 Mathematics Graduates Work

• Department website
• Undergraduate major
• Undergraduate minor
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Associated interests

• Computer Science and Programming
• Math and logic
• Money and finance
• Statistics and data science

Related disciplines

• Sciences and Mathematics

Full list of majors and minors

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Ph.D. Program Application Details

The graduate program in Mathematics leads only to the Ph.D. degree. Students are not accepted for an M.S. degree.

Prerequisites

Mastery of the material required for an undergraduate major in mathematics, including a rigorous course in advanced calculus and real variable theory that will serve as an introduction to measure theory and courses in linear algebra and modern abstract algebra at an advanced level. Applicants should also have some familiarity with applications of advanced calculus. Most successful applicants score 700 or above on their GRE subject test.

Application Guidelines

Students must submit an online application at apply.gradschool.cornell.edu by January 4. The following are submitted with the online application:

• a statement of purpose,
• GRE scores for the general test and subject test in mathematics,
• TOEFL scores (details given below),
• three letters of recommendation.

A transcript must also be submitted by January 4 to the following address: Graduate Admissions, Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853-4201.

Complete the application online at www.gradschool.cornell.edu/admissions/applying/apply-now/ and upload the following by January 4:

• three letters of recommendation,
• transcripts (either official or unofficial) from the institution at which you are currently enrolled and/or from any institution from which you have received or will receive a degree. All transcripts must be combined into one PDF document and uploaded. If it is against an institution’s policy to send official transcripts to you, please request an unofficial copy for yourself and scan that document. Paper copies will be accepted only if the first two options are not available to you. If you are subsequently admitted and accept the offer of admission, we will require a formal and official paper transcript prior to matriculation.

GRE scores for the general test and subject test in mathematics and TOEFL scores (if applicable, details given below) must be received by the Graduate School by January 4.

For more information about Cornell's application process, visit www.gradschool.cornell.edu/admissions/ .

Cornell University expects all applicants to complete their application materials without the use of paid agents, credentials services, or other paid professional assistance. The use of such services violates University policy, and may lead to the rejection of application materials, the revocation of an admissions offer, cancellation of admission, or involuntary withdrawal from the University.

TOEFL Requirement — Test of English as a Foreign Language

TOEFL scores are required for international students whose native language is not English. Only students who have studied full time for two or more years at a college or university located in a country where English is the native language and where English is the language of instruction are exempt from the TOEFL.

The minimum TOEFL requirements are as follows: IBT test (replaced CBT) after September 1, 2009: 20 Writing, 15 Listening, 20 Reading, 22 Speaking. All four scores must be reported. Applicants will not be considered if any minimum score is not met.

The Graduate School requires an overall band score of a 7.0 or higher on the IELTS. Please email [email protected] for information about how to send your scores.

Admission Decisions

Admission decisions are typically made in mid-February. Under the rules of the Council of Graduate Schools, students have until April 15 to make their decisions.

Financial Aid

Everyone who applies for admission to the graduate program in mathematics is automatically considered for financial aid. For many years the field has been able to provide financial support — through a teaching assistantship, fellowship, or graduate research assistantship — to every graduate student who is making satisfactory progress towards the Ph.D. degree, and it expects to continue this practice.

Some of our students have fellowships from the National Science Foundations or other sources. However, most are supported by Teaching Assistantships, which pay $24,104 for 10–15 hours per week in 2014–2015. Duties may be (i) grading for advanced courses, (ii) giving recitation sections, or (iii) teaching a section of calculus. Assignments to courses are made by the Director of Teaching Assistant Programs, Maria Terrell, but are based on the students' requests.

It is our intention to make summer support available to all students who would like to remain in Ithaca during the summer. For students who have completed three years of graduate school, this will typically be in the form of a research assistantship paid for by a professor's grant or by the graduate school. First and second year students will, in general, hold teaching assistant jobs in Summer Session courses. We also encourage students to apply for other forms of summer support that enhance their graduate education.

Equal Opportunity

It is the policy of Cornell University to actively support equality of educational and employment opportunity regardless of race, religion, national or ethnic origin, sex, age, or handicap.

Undergraduate Education

College academic advising, college of engineering.

Cornell Engineering is the largest and most prestigious engineering program in the Ivy League. The college is widely recognized for its rigor, commitment to excellence in education and research, and its longstanding legacy of educating students who go on to become leaders. Cornell Engineering envisions a future in which its student body and faculty reflect the gender, socioeconomic, and racial diversity of society. We endeavor to be a collaborative community of scholars and innovators who leverage the intellectual diversity of Cornell University to push the frontiers of knowledge and to address humanity’s grand challenges. Our graduates will be recognized and valued for their commitment to excellence, enthusiasm for learning, integrity, ethical behavior, and ability to work and thrive in diverse teams.  

College FAQs

Who advises students in your school/college.

Professional Staff Academic Advisors in Engineering Advising: 

The professional staff academic advisors in Engineering Advising provide a variety of professional advising services to help first-and second-year students with academic and personal matters, as well as continued access for upper-class affiliated students. The professional staff academic advisors in Engineering Advising follow an alphabetical cohort model of advising based on the last name of each student.  

Faculty Advisors: 

Students are assigned a faculty advisors when they begin their course of study in the College of Engineering. Faculty advisors help students translate their interests into an appropriate course of study, evaluate their curriculum and workload, monitor their progress toward a degree, and take advantage of the diverse opportunities available at Cornell. 

Peer Advisors: 

Peer Advisors are senior, junior, and sophomore engineering students who assist new students with the academic transition from high school to college. As part of their participation in the Engineering Seminar (ENGRG 1050), all first-year students will interact with their Peer Advisors. 

Directors of Undergraduate Studies:

In each engineering major, a faculty member serves as the Director of Undergraduate Studies who works with students' faculty advisors and with the major's Undergraduate Program Coordinator to assist current and prospective major students. 

Undergraduate Program Coordinators:

Each engineering major has an Undergraduate Program Coordinator who works with the Director of Undergraduate Studies to help support students and faculty with any questions about the major. Undergraduate Program Coordinators help advise students who have affiliated with their engineering major. 

How do I know who's my assigned advisor or advising team?

All engineering students can utilize the services of Engineering Advising. Engineering Advising professional staff academic advisors advise students by alphabetical cohort, based on students' last names. 

Students can view their assigned faculty advisors in Student Center

How do I make an appointment with an advisor?

Students can make a 30-minute (in-person or virtual) appointment with their Engineering Advising professional staff academic advisors online through Chatter . When scheduling an appointment, students should find the Engineering Advising tab listed at the top or in the "More" tab drop-down. Note that other offices also use Chatter and have their own appointment booking pages. 

When should I meet with my advisor?

Students can meet with their advisors at any time and are encouraged to be in touch regularly.  We recommend that students touch base with their advisors at least once a semester, and more regularly if they are experiencing academic or personal difficulty.  All first-year engineering students are required to meet with their faculty advisor at least once in the fall semester and at least once in the spring semester to be cleared for pre- enroll .  

Four Advising Areas

Academic focus.

With 14 different majors and 21 minors, Cornell Engineering offers one of the broadest engineering curricula in the world.  First-year students begin general engineering studies focused on the common curriculum.  They will learn about all the different majors offered at Cornell Engineering, which will allow them to explore their options before applying for affiliation with a major in their second year.  Students can learn more at https://www.engineering.cornell.edu/students/undergraduate-students/curriculum/majors-and-minors .   

Experiential Learning

Engineering Learning Initiatives:  

Engineering Learning Initiatives (ELI) enhances the learning environment by promoting evidence-supported practices in teaching and learning.  ELI programs empower students by facilitating student-centered, inclusive, collaborative, and experiential learning opportunities within supportive and accessible communities.  ELI organizes tutors on call, sponsors Academic Excellence Workshops, and runs the college’s Teaching Assistant Development Program. 

Research:  

Research can enhance the undergraduate experience by allowing students to take the skills and knowledge learned in the classroom and apply them to real situations.  Students can find a mentor, apply for a student grant, enroll in research for credit or be hired for research for pay.  

Engineering Project Teams:  

Cornell Engineering Project Teams offer students a unique, multifaceted learning opportunity. Entirely led and run by undergraduates, project teams collaboratively solve complex problems while gaining real-world engineering experience. Project team participation complements world-class classroom and laboratory learning, providing students with opportunities to hone leadership and professional skills alongside teammates from across the college and university. Innovation and teamwork drive the success of this unparalleled program.  

Study Abroad and Exchange :  

There are a variety of options available for engineering students interested in studying abroad .  The College of Engineering supports five exchange programs: University of Cantabria, University of Comillas -ICAI, Technical University of Denmark (DTU), Hong Kong University of Science and Technology (HKUST), and Technion-Israel Institute of Technology.    

In addition, the  Education Abroad (Office of Global Learning)   manages hundreds of programs for Cornell students and can assist engineering students in finding an experience that meets their needs and interests.  

Engineering Advising will help students think through the process, answer questions about policies and procedures, and along with their faculty advisor, assist students in planning their curriculum.  

Community and Belonging

Diversity Programs in Engineering:

Diversity Programs in Engineering (DPE) offers a comprehensive portfolio of programs at the pre-college, undergraduate, graduate, and faculty levels.  These programs facilitate the recruitment, development, retention, and success of all members of the engineering community with a concentration on those from backgrounds historically underserved and underrepresented in engineering.   

DPE collaboratively works with university and external partners on initiatives enhancing equity for our community in terms of: ethnicity, race, sex, gender, orientation, identity, first generation status, socioeconomic class, and veteran status.  

Engineering Leadership:  

The Engineering Leadership Program develops engineering students as leaders and team members by offering alumni mentoring, leadership skills clinics, professional coaching, and engineering leadership certifications.  

Career Exploration

Engineering Career Center:

The Engineering Career Center’s goal is to empower students to create lifelong career success.  They assist students in exploring careers, internships, co-ops and full-time jobs; preparing for interviews, evaluating and negotiating job offers, and more!  

Nearly 70 students recognized at pinning ceremony

12/15/2023 By | Katya Hrichak , Cornell University Graduate School

The Graduate School welcomed nearly 70 new Dean’s Scholars at a November event to honor students who were nominated and selected for this distinction for their demonstrated commitment to academic excellence and advancing aspects of diversity, access, equity, inclusion, and belonging in the academy and other communities.

At the ceremony, each scholar received a pin with a gold center containing the Cornell seal, representing the scholars’ achievement, surrounded by an outer ring of silver, representing their persistence.

“One of my most important priorities as Dean of the Graduate School is ensuring that all of our students, but particularly those from backgrounds historically excluded from and underrepresented in academia, feel a part of our Cornell community, feel valued, and find success in their graduate studies and their personal and professional pursuits,” said Kathryn J. Boor, dean of the Graduate School and vice provost for graduate education, during her remarks.

She continued, “We all benefit when our campus reflects the rich tapestry of human experience and when our students, faculty, and staff can pursue their work and studies in an environment of acceptance and collaboration.”

Newly pinned students join a community of almost 400 current Dean’s Scholars, providing them with the opportunity to establish and maintain connections across graduate fields by engaging in professional and community development events offered through the Graduate School.

“The Dean’s Scholars community is filled with such caring individuals who are here to welcome you, stand by you, and fight for you,” said Gundeep Singh, a doctoral candidate in biophysics and Dean’s Scholar who gave remarks at the event. “I hope you are able to find lifelong supporters and allies through the fellow members of this community.”

Newly pinned Dean’s Scholars look forward to joining this community, as well as contributing to it themselves.

“Being selected as a Dean’s Scholar is a tremendous honor and a responsibility that I am eager to embrace,” said Josh Felton , a doctoral student in plant biology. “I am excited to fill those same shoes as a role model and near-peer mentor to other, more junior Dean’s Scholars as I progress through my Ph.D., making mistakes and learning about myself and the world to then pass along my knowledge to future generations of scholars.”

Cheyenne I. Reuben-Thomas , a doctoral student in ecology and evolutionary biology and member of the Oneida and Seneca Nations, expressed a similar desire to connect with individuals who share lived experiences and have a positive effect on others.

“I am proud to share this space among the many brilliant minds who are actively changing the norms,” she said. “I look forward to making lifelong friendships and celebrating everyone’s accomplishments, big and small. As someone who is passionate about creating diverse spaces in academia, I am also looking forward to mentoring and uplifting future Dean’s Scholars.”

The Graduate School Dean’s Scholars program is led by Associate Dean for Inclusion and Student and Faculty Engagement Sara Xayarath Hernández. Many Dean’s Scholars are recipients of competitive fellowships in support of diversity while others are funded via other internal or external sources.

Read the story on the Cornell University Graduate School website .

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/images/cornell/logo35pt_cornell_white.svg" alt="mathematics phd cornell"> Cornell University --> Graduate School

Graduate funding and enrollment, enrollment and student status.

Enrollment is the official recognition of a student’s relationship with the university.  Enrolling is the basic authorization for a student’s access to campus resources including campus labs, assistantships, fellowships, travel grants, etc. each semester.

Doctoral students must be enrolled until they finish their degree unless requesting a non-student status. Further details on enrollment can be found on the Enrollment in Your Program page .

Graduate Funding

Graduate funding is a source of financial aid for enrolled doctoral students. To receive graduate funding, including assistantships, fellowships, stipends, and travel grants, a student must be enrolled for the semester in which they will receive the funds.    

Ph.D. students are fully funded to pursue their degrees through a combination of competitive internal and external fellowships and research and teaching assistantships. Funding packages include tuition, health insurance/health fee, and a living allowance or stipend.

Cornell offers limited financial assistance for research master’s and professional degree programs. The terms of these awards can vary by program. For further details, please reach out to the specific program.

Funding and Non-Enrollment (M or B Exams, Graduation, Leave of Absence, or Withdrawal)

During periods of non-enrollment, such as a leave of absence, withdrawal, an individual does not retain student status; student access is deactivated, and graduate funding is ended. Without enrollment, students are ineligible to receive fellowships, assistantships, travel grants, or other forms of financial aid.

Students are not allowed to enroll or receive funding (such as assistantships, fellowships, travel grants, etc.) for any term following the date they pass their M or B exam. When a student and their committee determine the M or B exam date, it is important to notify all relevant members, including the graduate field administrator and the staff member administering the student’s appointment, so that the student may be well informed for the end day of their current appointment. Funding and enrollment are prohibited in future terms after a passed M or B exam.

Students are not allowed to enroll or receive funding for any term or period following the date of a leave of absence or withdrawal from the program.  

Enrollment and Employment Limitations

All enrolled students are limited to 20 hours of combined assistantship, hourly student appointments, and/or outside employment per week. Further limitations may apply to students based on their funding source. Full employment limits can be found on the Employment policy page .

Funding and Satisfactory Academic Progress

All funding is conditional upon a student remaining in good academic standing, making satisfactory academic progress toward the degree, and performing satisfactorily in all assistantship responsibilities. Advanced doctoral students who require more than the allowed seven years to complete their degree shall not be funded as a TA after the 14 th semester. Academic progress requirements can be found on the Requirements page .

Maxwell Fellows to boost data science research in medicine

A gift establishing the Professor William Maxwell '56 Fellows will financially support research professors and students affiliated with Cornell's Engineering Innovations in Medicine initiative.

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Sylvester Zhang awarded Doctoral Dissertation Fellowship

MINNEAPOLIS / ST. PAUL (6/28/2024) – School of Mathematics PhD student Sylvester Zhang was recently awarded the Doctoral Dissertation Fellowship from the University of Minnesota. The Doctoral Dissertation Fellowship (DDF) gives the University's most accomplished Ph.D. candidates an opportunity to devote full-time effort to an outstanding research project by providing time to finalize and write their dissertation during the fellowship year.

Sylvester Zhang started the University of Minnesota Mathematics PhD program in Fall 2020, after completion of his undergraduate studies in Mathematics and Economics here at UMN. Zhang is interested in algebraic combinatorics. In particular he aims to explore topics like total positivity, cluster algebras, symmetric functions, and the flag manifold. Advised by Pavlo Pylyavskyy, Zhang is currently primarily focused on two distinct research topics: 1) an approach to Schubert polynomials using methods from mathematical physics, and 2) affine symmetric group and combinatorics of the affine flag variety. He says he is looking forward to continuing a career in academia and research after graduation.

The University of Minnesota DDF program aims to give the most accomplished Ph.D. candidates – those who have passed the written and oral preliminary examinations and their program coursework – an opportunity to devote full-time effort to an outstanding research project by providing time to finalize and write their dissertation during the fellowship year. The fellowship grants awardees a $25,000 stipend, academic year tuition, subsidized health insurance through the Graduate Assistant Health Plan for up to one calendar year, and a $1,000 conference grant. 

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