cornell math phd program

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Application and Admissions Process

Please note:   Consideration of COVID-19 Disruptions The deadline to apply for admission into the CAM PhD program is January 7 . Applications are only accepted for the fall semester. Begin the application process by creating an account on the Graduate School's  application page . The online application is secure and can be immediately viewed by the CAM admissions committee upon submission. You can learn more about the application process and review additional guidelines on the  Graduate School website .

Materials needed for application process:

• You will be asked to enter typical application information such as nationality, GPA, schools attended, etc.
• You will be required to upload an accurate unofficial transcript for each school you have attended. Please do not send official copies to the CAM office. Please note that there are only up to three fields for listing schools attended. If you attended more than three, you must upload those transcripts in the writing sample portion of the application.
• If you have appropriate supplemental documents such as an undergraduate research paper, awards, etc., upload them in the writing sample portion of the application.
• A statement of purpose is required and can be uploaded directly into the application.
• At least three letters of recommendation are required. Additional letters are allowed. Recommenders may submit their letters online. Once an application is submitted, recommenders receive an automated email soliciting their letter (you will be prompted to provide their contact information before you submit your application). 
• Neither GRE General nor GRE subject scores are accepted.
• The Graduate School requires an application fee of $105. A fee waiver request will be considered if this fee presents a financial hardship. See Application Fees  for instructions on how to submit a waiver request.
• Applicants who are non-US citizens may be contacted via email 1-3 weeks after the application submission deadline to participate in a brief, conversational English video interview (no specialized knowledge necessary). Though not all non-US-citizen applicants will be required to participate in this interview, definite exceptions include citizens of Australia, Canada (except Quebec), Ireland, New Zealand and the United Kingdom.
• 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 & IELTS Scores 

• Submit official TOEFL iBT or IELTS Academic scores that meet or exceed Cornell's minimum requirements
• Request a standing Exemption by attesting that you meet one of the standing exemptions outlined below. Provide documentation if required. 
• Request a Special Examination (see guidelines below)

How to Send Your Scores to Cornell

IELTS Academic

• When you register for the exam, you may select up to 5 institutions to which you would like to have your scores sent. Cornell University has multiple IELTS accounts so please be sure to select  Cornell University Graduate Admissions  when registering for your IELTS test date.
• You may also ask your test center to send additional score reports to institutions not originally listed on your test registration form. Scores must be sent electronically (e-delivery) to the  Cornell University Graduate Admissions, Caldwell Hall  e-download account. E-delivery may also be referred to as an e-TRF by your test center. Paper TRFs (Test Report Form) are not accepted.
• Your IELTS Academic scores must be valid as of your program’s application deadline (scores are valid for 2 years after your test date).
• Have scores delivered electronically to  Cornell University Graduate School, Institution code 2098.  Department codes are not needed;  if ETS requires you to select a department code, you may choose code 99 “undecided.”
• Your TOEFL scores must be valid as of your program’s application deadline (scores are valid for 2 years after your test date).
• If you have taken the TOEFL iBT more than once within the last 2 years, have ETS send us your most recent score report. ETS will automatically include your  MyBest  scores  along with the traditional scores from your selected test date. If your most recent scores do not meet the Graduate School’s minimum sub-score requirements, but your  MyBest  scores do, let the Graduate School and your proposed field of study know that you would like us to consider your  MyBest  scores. Please note: while the Graduate School accepts  MyBest  scores, individual graduate fields may not accept them.

Standing Exemptions

For admissions purposes, Cornell University Graduate School does not require IELTS or TOEFL scores from applicants who meet one of the following standing exemptions.  However, applicants admitted to research degrees may still need to complete the  English Language Assessment  before being a TA.  If you meet the criteria for one of the following standing exemptions, you will indicate this in your application for admission. There is no need to contact the Graduate Admissions Office in advance.

• Speak English as a first language  and  are a citizen or permanent resident of a country where  English is an official language . Research degree applicants who meet this exemption are automatically approved to serve as a TA without an individual English Language Assessment.
• At the time of enrollment at Cornell, will have earned a bachelor’s degree from an accredited U.S. college or university located in the U.S. (Please note that you must have been physically present in the U.S. for the majority of your enrollment.) Research degree applicants who meet this exemption will need to complete the English Language Assessment and may be offered an individual support plan. 
• At the time of enrollment at Cornell, will have earned the  international equivalent of a U.S. bachelor’s degree  from a college or university located in a country where  English is an official language ,  and  where English is the language of instruction. The medium of instruction must be indicated on the transcript or easily verified on the institution’s website. (Please note that you must have been physically present in the exempt country for the majority of your enrollment.) Research degree applicants who meet this exemption will need to complete the English Language Assessment and may be offered an individual support plan. 
• At the time of enrollment at Cornell, will have studied and/or worked full-time for at least 2 consecutive years* within the last 10 years in a country where  English is an official and widely spoken language . This experience must be noted on a transcript and/or described on a resume or CV. We will accept a combination of study and work—e.g., an applicant who completed a 1-year master’s degree in the U.S. followed by 1 year of OPT. If you are or were a student, the full-time study must have been for at least 2 consecutive academic years (potentially slightly less than 24 months) AND English must have been the language of instruction for your studies. (Please note that you must have been physically present in the exempt country for the majority of your enrollment.) Research degree applicants who meet this exemption will need to complete the English Language Assessment and may be offered an individual support plan. 

Special Exemptions

Applicants who speak English as a first language, but do not otherwise qualify for a standing exemption, may be considered for a special exemption under the following circumstances: 

• Speak English as a first or native language, but citizenship does not meet the Standing Exemption criteria.
• Full-time study or work in a primary English country was for less than 2 years, was not consecutive, or occurred more than 10 years ago.

Contact the  Graduate Admissions Office  if you think you qualify for a  special  exemption. Note: Research degree applicants with special exemptions admitted to research degrees may still need to complete the  English Language Assessment  prior to being a TA.

Any questions, material, or correspondence may to be sent to  [email protected] .   Center for Applied Mathematics 657 Frank H.T. Rhodes Hall Cornell University Ithaca, NY 14583 USA

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Ph.D. Program Content

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 . In addition to the usual areas of algebra, analysis and geometry, the department has outstanding groups in the areas of algebraic geometry, combinatorics, dynamical systems, logic, Lie groups, and partial differential equations, including their numerical treatment. The field also maintains close ties with distinguished graduate programs in the fields of applied mathematics , computer science , operations research , and statistics .

Special Committee

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. An entering student is assigned a special committee, but over time the committee changes its membership to reflect the student's interests, and is finally chaired by the student's thesis adviser.

First-Year Courses

A normal course load for a beginning graduate student is three courses per term. A typical first-year program includes four of the following six basic courses:

• MATH 6110, Real Analysis ( syllabus )
• MATH 6120, Complex Analysis ( syllabus ) At the level of Rudin, Real and Complex Analysis. -->
• MATH 6310, Algebra ( syllabus )
• MATH 6320, Algebra ( syllabus ) At the level of Lang, Algebra, or Jacobson, Lectures in Abstract Algebra. -->
• MATH 6510, Introductory Algebraic Topology ( syllabus ) At a level similar to that of Massey, Algebraic Topology, and Eilenberg-Steenrod, Foundations of Algebraic Topology. -->
• MATH 6520, Differentiable Manifolds I ( syllabus ) At the level of Lee, Introduction to Smooth Manifolds , or Conlon, Differentiable Manifolds -->

There are no qualifying exams, but the program requires that all students take four basic courses to be selected from the above six core courses by the time they are ready to take the A exam. They are to be distributed among three main areas: analysis, algebra and topology/geometry. A student must take 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. Students who are not ready to take some of these courses may take MATH 4130-4140, Introduction to Analysis , and/or MATH 4330-4340, Introduction to Algebra , which are the honors versions of our basic undergraduate courses. A first-year student is also able to explore other areas, such as differential equations, mathematical logic, and probability theory, in filling out the normal course load.

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. At this stage the committee is formed of faculty who are experts in the proposed area of research, and the chair is also the thesis advisor. 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 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 standard first-year graduate courses. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.

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.

Language Requirement

Every doctoral student must pass a test of mathematical reading ability in a foreign language at the time of their A exam. The allowed languages are French, German, Russian, Chinese, Japanese, Spanish, and Portuguese. The choice of language must be approved by the student’s special committee chair.

More about the language requirement

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 .

Master's Degree in the Minor Field

Ph.D. students in the field of mathematics may earn a master's degree in certain minor fields. The available options are Master of Science in Education, Master of Arts in Teaching in Education, and Master of Science in Computer Science. More options may be made available in the future. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for one of these degrees, 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 laid down here .

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 Minor in Mathematics

In order to get a minor in mathematics, any graduate student in any field must request a member of the field of mathematics to serve on his/her special committee representing mathematics. This committee member, after consulting with the graduate student, will set course requirements. The number of courses required will typically be four or more, but can be less in special circumstances. The committee member will attend (and ask questions on) the student's qualifying, admission to the Ph.D. candidacy and final exams. In addition, he/she will read at least the mathematical aspects of the student's thesis and be responsible (together with the other committee members) for giving final approval to the thesis.

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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

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, 2005: 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.

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 $21,400 for 10–15 hours per week in 2009–2010. 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.

Last modified: October 20, 2011

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

Applied mathematics ph.d. (ithaca), field of study.

Applied Mathematics

Program Description

The graduate program in applied mathematics is based on a solid foundation in pure mathematics, which includes the fundamentals of algebra and analysis. It involves a grounding in the methods of applied mathematics and studies of scientific areas in which significant applications of mathematics are made. The field has a broadly based interdepartmental faculty that can direct student programs in a large number of areas of the mathematical sciences.

Many specialized or interdisciplinary programs can be designed for individual students, including, for example, a variety of possibilities in biomathematics.

The dissertation is normally a mathematical contribution toward the solution of a problem arising outside mathematics.

Contact Information

614 Frank H. T. Rhodes Hall Cornell University Ithaca, NY 14853-3801

Concentrations by Subject

• applied mathematics

Visit the Graduate School's Tuition Rates page.

Application Requirements and Deadlines

Fall, Jan. 7; no spring admission

Requirements Summary:

Applicants must have an undergraduate background that contains a substantial mathematical component.

• all Graduate School Requirements , including the English Language Proficiency Requirement  for all applicants
• three recommendations
• Please note:  applicants who are non-US citizens may be contacted via email 1-3 weeks after the application submission deadline to participate in a brief, conversational English video interview (no specialized knowledge necessary). Though not all non-US-citizen applicants will be required to participate in this interview, definite exceptions include citizens of Australia, Canada (except Quebec), Ireland, New Zealand and the United Kingdom.

Learning Outcomes

A graduate student in Applied Mathematics is expected to demonstrate both mastery of knowledge in mathematics and its applications, and ability to create new mathematical knowledge and innovative ways to apply mathematical tools to important problems in science, industry and society. Each student is expected to demonstrate the following proficiencies.

• Make substantial original contributions to applied mathematics. This includes ability to identify new important and promising research problems; ability to think independently, critically and creatively; ability to complete research work by bringing it to the stage where it can be published and be used by the others.
• Maintain ability to acquire new knowledge by keeping up with the new developments in the field through professional publications and professional meetings.
• Ability to communicate effectively research findings and plans. This includes ability to present results in the format of technical papers and have them published in professional journals and conference proceedings; ability to explain complex ideas to peers in technical presentations; being aware of funding opportunities and ability to write effective research proposals and obtain research funding.
• Dedication to advancing science through effective teaching, advising, mentoring and service to professional community.
• Awareness of the ethical standards in the field, and ability to maintain and advance these standards.

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