Mathematics PhD Program Requirements & Milestones

• Residence

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 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.

• Registration

See section "V. Registration” of the Code of Legislation of the Graduate Faculty for most up to date details.  

Sections for Fully-Time Study and Summer Registration below as highlights. 

• Full-Time Study

An individual is considered a full-time student if registered (including In Absentia) see In Absentia Registration in Code of Legislation), enrolled in courses, or engaged in thesis or dissertation work, and in conformity with limitations on assistantships, hourly student appointments, and/or outside employment specified in this Code (see Assistantships, Hourly Student Appointments, Outside Employment, and Registration Requirements in Code of Legislation).

• Summer Registration

Graduate students must register (by self- enrolling) with the Graduate School for the summer if (1) they are receiving financial aid during the summer—e.g. fellowships, summer loans, assistantships, travel grants, or tuition awards, (2) they wish to use campus facilities, or (3) they are off campus but need to be registered for summer study. 

Employment limitations specified in this Code also apply to summer registration. 

Graduate students funded by assistantships should refer to the CGSU-UEcollective bargaining agreement for employment limitations that apply to summer registration. The summer term does not count toward minimum registration requirements, except by petition.

The Graduate School Requires a minimum cumulative GPA of 2.25 or higher. 

Cornell's Satisfactory Academic Progress policy stipulates that students in research degrees must maintain a minimum GPA of 2.25 to be in good academic standing or to be eligible for Title IV Aid, it is required that a MINIMUM GPA of 2.25 be set. A GPA below this threshold triggers a formal academic warning, requiring a remediation plan. If GPA is not raised within 2 semesters, the student faces loss of funding or dismissal, following Graduate School and CGSU‑UE due process procedures.

The Math PhD Program core curriculum consists of six courses. These core courses are distributed among three main areas: analysis, algebra, topology/geometry. 

There are no qualifying exams. A normal course load for a beginning graduate student is three courses per term. 

Course Descriptions & Tentative Syllabi

i. Core Course Requirement 

1st year: students must pass three of the required core courses by the end of their 2nd semester. 

2nd year: students must pass four (cumulative) core courses by the end of the 4th semester. The program requires that all students must pass at least one course from each area/group; analysis, algebra and topology/geometry. 

Passing requires either a minimum passing grade for the core courses of B-, or placing out.

The Math Field requires Core Courses to have in-person, invigilated assessments that comprise at least 50% of the final course grade. 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 S/U graded core courses will not satisfy the core course requirement. 

ii. Placing out of Core Course Requirement

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, in beginning of the semester, and that faculty member will make a decision. 

No grade is assigned for placing out of a core course. Placing-out of a core course will successfully satisfy the core course requirement but will not generate course credit. The course won't show on the student's transcript

iii. Petition to Extend Core Course Deadline

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, please use the extension request form. 

Consequences for Missed Core Course Requirement

Students who do not meet this course requirement may not advance to the next academic milestone and will no longer be in good academic standing. If a student does not pass 3 core courses by the end of their 2nd semester, they should meet with the GFC & DGS & Advisor (or advising committee member) to discuss and make plans to take or retake relevant core courses in 3rd semester, or if necessary 4th semester. 

If unable to complete 4 core courses by the end of the 4th semester any exceptions or substitutions to course requirements require approval by the special committee and must be submitted before the semester begins. Failure to meet course requirements will trigger an academic review, the results of which can affect eligibility for exams or continued funding.
 

The Teaching Development and Training is part of the Math PhD program's professional development goals for students to become more effective teachers, learners, and communicators. Consisting of several required parts, the details for each specific requirement explained in detail below:

i. Teaching Development Training 

Math PhD Students in their first year are expected to take the week prior to the start of the spring semester. If there is a conflict they can choose to take it earlier, prior to the fall semester, it is a pre-requisite to the spring MATH 6080 course. 

Current sessions include Principles of Grading, Sample Recitations, Creating an Inclusive Classroom, Being Professional, and Roles and Responsibilities of an Instructor. In the final Micro-Teaching Workshop, TAs give a 10-15 minute representative sample of their first day recitation or lecture, and get feedback from their peers and an experienced TA or instructor. 

If there is a conflict expected in the spring semester the training can be completed prior to the fall semester. If this requirement is not satisfied attendance will be expected for the next offered session until the DTAP confirms completion. 

This is a mandatory training for all students (regardless off home program) who will be TAing for Mathematics. The Training is offered within the TA assistantship appointment dates for those who are required to take the training as part of an assistantship appointment. 

ii. Teaching and Learning Mathematics Course (MATH 6080)

Math PhD grads are required to take Teaching and Learning Mathematics (MATH 6080) in their first spring semester. This is a Satisfactory/unsatisfactory class.

Consequences for missed milestone: 

An unsatisfactorily completed Math 6080 training, the student will be required to take it each year until receiving satisfactory grade.

iii. ELPR & ITAP assessment and Courses 

This is a requirement as needed to meet the English Language Proficiency Requitement to TA  (ELPR). 

TA’s must demonstrate a higher level of English proficiency. Incoming students who do not meet the ELRP to TA are required to be assessed by ITAP prior to the start of their 1^st semester, and enroll in any necessary ITAP courses as determined by the assessment results. 

Consequences for missed milestone: 

An unsatisfactory ELPR & ITAP requirement will be for student to continue to enroll and participate in ITAP courses until requirement is met. Missing the requirement may cause funding issues as TAing is the most common funding type in the Math PhD Program.  If refusal to enroll or participate in ITAP courses continues students may be withdrawn from the PhD program. 

iv. Is Teaching a requirement of the Math PhD Program?

Although teaching is not a Program Milestone in itself, Teaching Assistantships (TA) are expected, Math grad students should plan on TA as the usual funding type available.  see Mathematics TA for more details

Students should plan on summer TA appointments at least 1 summer, for planning purposes, this is most often the  2nd or 3rd  summer.

Advisor selection Milestone

In our field, students are required to identify an advisor (also the special committee chair) before beginning their 2^nd year.  This advisor must be recorded in Student Center no later than the start of instruction of the 3^rd semester. Upon matriculation the Director of Graduate Studies (DGS)  is in the grad school system as their temporary advisor, the DGS also assigns each student to a member of the Math Advising Committee who will help guide them through their first semesters. Students experiencing difficulty identifying an advisor should contact the DGS as early as possible

Consequences for missing this milestone: 

This is a Math PhD Program Deadline; if missed, you will need to meet with GFC &  DGS before the start of the 3^rd semester to submit a Request Milestone Extension and plan for completing the requirement. If this newly designated deadline is also missed and an advisor is not selected by the end of the 3^rd semester the graduate school consequences will take effect.  Failure to secure an advisor by the end of their 3^rd semester will impact academic standing and funding, & may result in withdrawal from the program.

Doctoral Students must form a complete special committee of at least three graduate faculty members by the end of their 3^rd semester. Committee members must meet Graduate School requirements and reflect relevant areas of expertise. Entering students in the Math PhD Program are not assigned special committees. 

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 their special committee, which consists of three faculty members, a chair and two minor members. Minor members may be chosen from outside the field of Math as long as they are CU Graduate Faculty. 

Math Grads considering a Special Masters in Computer Science (CS) are required to have a CS field faculty in their committee. 

Consequences for missing this milestone: 

If the special committee requirement is not met by the end of the 3^rd semester the graduate school consequences will take effect, there is an opportunity for a petition to the graduate school, but it is not guaranteed and missing this requirement may result in the student being withdrawn from the program. 

Changes to Special Committee

Doctoral students may make changes to their special committee at any time prior to the A exam. Updates must be submitted through Student Center. Committee changes after an A exam require the dean’s approval.

If a chair or committee member steps down, students must find a replacement within expected timeframes outlined in the Code of Legislation of the Graduate Faculty to remain in good standing. Students may not remain registered in the Graduate School if they fail to reconstitute a committee. If a student is unable to find a new chair within the required timeframes, they will be withdrawn from the Graduate School.

Student Progress Reviews (SPR) are a Graduate school annual requirement beginning in 2nd year. The Math Field deadline for the student section of SPR to be submitted is March 25th. SPRs are an interactive process intended to support the regular exchange of constructive, written feedback between advisees and advisors. It codifies a process for research degree students and their special committees to have at least one formal conversation per year about academic progress and future plans. 

Consequences for missed SPR deadline:

The graduate school deadline is April 1^st. Extension of deadline is not an option. If your student section of the SPR has not been submitted after April 1^st, the graduate school will put a hold on the student account. This means that Student Status is removed (this can affect immigration status), enrollment is blocked - student is ineligible for student funding, If this requirement continues to go neglected, the student is withdrawn from the program.

The admission to candidacy examination (A Exam) is given to determine if the student is “ready to begin work on a Dissertation.”  to meet this Field Milestone the A exam will need to take place before beginning the 3rd year of the program, (prior to 5th semester).
 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 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 third year. Upon passing the A exam, the student will be awarded an M.S. degree without thesis. There is an opportunity for Math Grads to receive a Special Masters in Computer Science instead of a Math Masters. 

 A-Exam Process 

1. Determine the time and date of your A exam with your special committee. Your GFC can assist you with this if you need help or want to consider the availability of Malott 310D in your planning. 
2. Once the date and time is determined let your GFC know and request a room reserved for it. 
3. You need to schedule you’re a-Exam with the graduate school, using the form “Schedule A Examination and Research Compliance Form”, listed under the “Exams and Research” section of this link: https://gradschool.cornell.edu/forms/.  
4. Submit the scheduling form at least one week in advance or you risk your exam will not be approved by the grad school. You do not need to wait to schedule your exam if you know when it will be, schedule the earlier the better, two weeks minimum recommended by your GFC.  
5. Two weeks in advance of your scheduled A-Exam, send the following information to your GFC;  
   • Title 
   • Abstract,  
   • List of committee members starting with the Chair 
   • Date, time and place of your Exam. 
6. You should send a reminder via email to your entire committee a week, and again half an hour, before you are scheduled to take your exam. The Graduate School does not do this for you. 
7. After the exam, you will need to submit the results to the grad school within 3 business days using the Grad school Form “Results for Admission to Candidacy (A Exam)”. If your exam has been canceled or rescheduled, please contact the Graduate Student Services Office immediately, and let your GFC know asap. See Masters of Science in Math section for further details on en route MS degree conferral. 
8. If you are aiming for a CS special masters, here are the requirements which need to be fulfilled within 1 year of you’re A-Exam. (There are a couple other specific changes with CS Masters, please let GFC) know asap if this is something you are aiming for). 

9. Specifically you will need to do the following Before taking you’re A-Exam; 

   1. CS Field member on your special committee (milestone in your 3rd semester) 
   2. Submit a formal application for this degree to the Computer Science Department 
   3. See the CS webpage linked above for further details on requirements and timing. You can only receive one master’s degree at  Cornell, if you opt for the math master’s you cannot acquire the CS master’s later on. At you’re A-Exam, you will be granted a “conditional pass” until you complete the CS degree requirements. The Graduate School will confer your degree when the final completion record is submitted with CS. 

    

Extension Requests

The deadline for the A exam to take place before the start of the 5^th semester is a Math Field deadline. Students may request an extension of the deadline prior to the 5^th semester, by submitting the Milestone Extension Request and setting up a meeting with the GFC and DGS to discuss the need for the extension. 
 

Consequences of Missed A Exam milestone

The Math PhD Program deadline of prior to 3rd year, is before the Grad School's deadline; if this deadline is missed the student will need to meet with GFC & DGS before the start of their 5t^th semester to request an extension and plan for completing the requirement. If this new designated deadline is also missed, meeting with the GFC & DGS, and usually the advisor should be scheduled promptly and the student should prepare for the possibility of not passing the A exam and being withdrawn from the program.  If the A exam is not taken by the end of their 7^th semester the graduate school policy and consequences will take effect, which may result in the student being withdrawn from the program. 

The Post A Exam Paper is an annual program requirement of ten typed pages, comprising an expository explanation of the math that the student has been working on (towards their dissertation) during the year and what their ideas are. Much of this writing would ultimately go into the student's dissertation. 

The requirement is satisfied if the student submits a paper or puts a paper on ArXiv during the year, even if there are coauthors; the paper must be directly related to their thesis research. Students  who are stuck in their research should still write ten pages on what they have been reading and how it relates to their research. 

This requirement is for the student, to advance their research and keep them accountable. This is done before the SPR, so that advisors can communicate clearly about where the student stands; the advisor can determine the first due date based on the A exam date (that is, if the student takes the A exam in the spring, then the advisor could decide to start the milestone either the same year or next year). 

Math PhD Grads are expected to defend their dissertation by the end of their 5th year, the programs' expected time to degree. 

Process and Requirements of B Examinations

Make sure you understand the Deadlines, Requirements, and relevant dates of the whole process: GS Dissertation Page  - note the information for Dissertation not Thesis 

Doctoral candidates in our field are required to complete a dissertation that demonstrates original research contributing new knowledge to the discipline. The dissertation should address significant theoretical questions and may take the form of a traditional monograph or a set of publishable articles. Projects may develop new theoretical frameworks, or introduce innovative methods.

The dissertation must include an abstract and adhere to a recognized academic style guide as approved by the special committee chair. It must also meet the the Graduate School’s formatting requirements for doctoral dissertations.

A complete draft of the dissertation must be given to each committee member at least six weeks before the B exam is scheduled and submitted to the Graduate School within 60 days of passing the final exam. 

Taking B Exam

The B exam must be scheduled through the Graduate School and attempted before the end of the 5th year (10th semester).

Enrollment in future semesters is not permitted after passing the final exam, even if the 60-day submission window extends into a subsequent semester.

Planning Timeline 

Meet with GFC to plan your specific timeline at the beginning of your last year, (at least 1 full semester prior to your goal conferral date).  Consider the date carefully, if you take your B exam outside of a semester you are ineligible to enroll for the following semester, thus no longer in student status, and ineligible for student funding & other benefits and may affects immigration status. note you are required to submit your draft dissertation six weeks prior to your final examination to all members of your Special Committee.

Using the GS planning Timeline. The Check list is particularly helpful in guiding your process.  You will find a general quick summary of steps, Conferral dates and a checklist - USE the checklist to guide your process:

• Complete your research. 
• Learn about GS dissertation formatting guidelines.
• Develop a detailed outline for your approach to writing your dissertation.
• Write the body of text for the dissertation.
• Complete and submit your draft dissertation six weeks prior to your final examination to all members of your Special Committee.
• Meet with GFC to reserve room to schedule your defense.  
  • GFC will need the following information at least 1 week in advance
    • title, abstract, special committee members, date/time/place of exam  
  • GS requires you submit a Schedule B Exam form at least 1 week in advance.
  • Submit a final draft of your dissertation to each special committee member. 
• Six to eight weeks before conferral date, take your final exam (“B” exam), oral dissertation defense.
• Make changes as specified by the special committee.
• Submit the final electronic version of dissertation (ETD) to Graduate School using ProQuest. 
• See Dissertation Submission Process for instructions.
• Attend commencement and celebrate!

Results of B Examination 

Students must submit their results to the GS within 3 business days of the exam. The last section of the GS Taking Exams page goes into detail of the possible results (Passing, Conditional Passing, Failing, Unanimously Failing). 

Consequence for missed B exam milestone deadline

Math PhD Program Deadline of before the end of 5^th year; if missed, student will need to submit a Request Milestone Extension, and meet with GFC, DGS, & their Advisor within a month of the deadline to plan for degree completion. extended deadlines must be at least one month before the end of the semester it falls within and cannot be a date between semesters. 

 If this new designated deadline is also missed, an additional meeting with the GFC, DGS, & Advisor should be scheduled promptly and the student should prepare for the possibility of not passing the B exam and being withdrawn from the program.  

In extreme cases if the B exam is not taken by the end of their 14^th semester the graduate school consequences will take effect, which may result in the student being withdrawn from the program. 

Submitting Dissertation via Pro-Quest

Submission of the final dissertation must be within 60 days of the B exam.  

Make sure you have your submission in by the degree conferral date deadline if this is something that is necessary for you – such as for a new position that wants you to have your degree by a certain date. 

Commencement

There is no requirement for Commencement. However if you do plan on participating you will need to meet the deadlines sent to you by the GS and GFC for planning purposes (GFC will reach out to confirm your plan to attend, guests, and other information in April).  

Department of Mathematics Commencement Ceremony: https://math.cornell.edu/commencement-ceremony

Graduate School Commencement: https://gradschool.cornell.edu/academic-progress/enrollment-status-progress/commencement/

Office of Commencement Events: https://commencement-dec.cornell.edu/  for more details on planning. The Student Information(https://commencement-dec.cornell.edu/students/ ) Tab includes information on Cap & Gowns, Graduate Guest Registration, Ceremony Arrival & Bag Screening, & Diplomas!