Button to scroll to the top of the page.

Coursework Policy "3+2+2" Requirement

The department offers two-semester “Prelim” course sequences in six core areas, making twelve Prelim segments in total:  Algebra; Analysis (Real and Complex); Applied Mathematics (principally functional analysis); Numerical Analysis; Probability; and Topology (Algebraic and Differential).  The course syllabi can be found here.

2-hour examinations (“prelim exams”) covering the twelve areas are administered twice per academic year: in August before the start of the Fall semester, and in January before the start of the Spring semester.

Whenever possible, exams covering different areas are administered on different days.  The two exams covering a single area (for instance, the two Algebra exams) are administered sequentially on the same day, with a brief rest break in between.  

Of the 12 Prelim segments, students must pass at least 7, in distinct areas, of which at least 3 must be by exam.  A passing grade in a Prelim course is a “B”, while the passing standard for a Prelim exam is determined by the faculty committee administering that exam.

Students are expected to meet the following milestones:

  • By the beginning of their 2nd Semester: Pass 1 Prelim exam.

  • “3+2”: By the beginning of their 4th Semester: pass 5 Prelim segments, all distinct, at least 3 by exam. Note that you become eligible to take a candidacy oral exam once the above requirements are completed.

  • “3+2+2”: By the beginning of their 8th semester (or before the beginning of the semester of their Ph.D. thesis defense, whichever comes first): pass two additional prelim courses or exams, distinct from the “3+2”.

While this schedule is not rigidly enforced, students are expected to make steady progress towards the completion of their prelim requirements. Students falling distinctly behind this schedule risk losing their good academic standing within the program, and should consult the Graduate Advisor.

Students are welcome to take both a prelim course and the corresponding exam, though they cannot both be counted towards the prelim requirements.   There is no penalty for failing a prelim exam; they can be retaken on subsequent occasions. There are no waivers for prelim exam requirements.

There are three ways in which students may be allowed to skip some or all of required prelim courses:

  • As implied by the above rules, they may pass more exams instead of taking the courses.

  • Students with prior graduate coursework may appeal to the Graduate Advisor for waivers of one or more prelim course requirements.

  • Interdisciplinary students, with the advice of an academic supervisor and permission of the ASGSC (Administrative Subcommittee of the Graduate Studies Committee) may be allowed to substitute courses in their specialty for some of the four required prelim courses.


    january 2024 Exam SchedulE

  • Wednesday, January 10, 2024
    9:00am-11:00am – Numerical Analysis I
    11:30am-1:30pm – Numerical Analysis II & Topology II
    2:00pm-4:00pm –   Probability II

  • Thursday, January 11, 2024
    9:00am-11:00am  - Topology I
    11:30am-1:30pm – Analysis I
    2:00pm-4:00pm – Analysis II

  • Friday, January 12, 2024
    9:00am-11:00am – Probability I
    11:30am-1:30pm – Algebra I
    2:00pm-4:00pm – Algebra II

  • Saturday, January 13, 2024
    9:00am-11:00am – Applied I
    11:30am-1:30pm – Applied II

    January 2024 Exam Procedure

Signup deadline: Friday, December 15

Exam room: PMA 12.166
Exams are in-person
Exams are 2 hours.

You can sign up for exams here.

A listing of historical exams can be found here.