Welcome to the USC Math Department. We have two Ph.D. programs:

The two programs have different requirements, so it is important to know the requirements for your program. This guide is intended as a brief outline of major points; for full details, see the USC Catalog for your program.

Program Milestones

  • We suggest students complete the fundamental courses in their first year of study to provide a firm foundation for our advanced courses and for their foray into mathematical research.

    Each of our 500-level courses are offered in Fall or Spring, so students should plan accordingly to ensure sequenced courses are taken in the correct order.

    Three of the courses associated with a written screening exam (exam courses) are offered in the fall with two more in the spring. These courses are:

    • Math 505a – Applied Probability
    • Math 510a – Algebra
    • Math 525a – Real Analysis
    • Math 540 – Topology
    • Math 555a – Partial Differential Equations

    Incoming students should choose three of these courses (AMAT students should take 505a + 525a + 555a), with a few exceptions.

    1. Any incoming student who passes the corresponding written exam for an exam course is exempt from that course.
    2. Incoming students who opt to be a TA instead in their first semester may take two courses instead of three.

    At the end of the Fall semester, first year students are assigned a temporary advisor in their field of interest. With guidance from their temporary advisor, for the Spring semester, students may begin to explore our elective options, many of which have the exam courses as prerequisites. Common choices for Spring include:

    • Math 505a students may continue in 505b (Applied Probability) or 541a (Statistics)
    • Math 510a students may continue in 510b (Algebra) or 533 (Algebraic Combinatorics)
    • Math 525a students may continue in 520 (Complex Analysis) or  525b (Real Analysis)
    • Math 540 students may continue in 535a (Differential Geometry)
    • Math 555a students may continue in 555b (PDE) or 565 (ODE)

  • Our written screening examinations test mastery of fundamental domains of mathematics. Passing the associated course is necessary but not sufficient preparation for the exams.

    Topics covered and copies of past exams are on our website, at https://dornsife.usc.edu/mathematics/graduate-exams/. We strongly encourage student to focus on writing solutions to past exams clearly and completely.

    All PhD students
    • must pass THREE of the following exams:
      • Algebra, based on Math 510a and Math 510b
      • Analysis, based on Math 525a
      • PDE, based on Math 555a
      • Topology, based on Math 540a
      • Probability, based on Math 505a
    • should pass ONE of Algebra or Analysis by August of their 2nd year;
    • AMAT students must opt for Analysis, PDE, and Probability;
    • should pass ALL THREE written exams after 4 semesters.

    Students may be given additional time to complete exams if they are making steady progress and if the student’s (temporary) advisor recommends it.

  • You should try to choose an advisor in your 2nd year, and certainly by early into your 3rd year.

    There is no one way to find an advisor. We suggest you:

    • go to classes taught by various faculty;
    • attend the area seminars;
    • discuss advisors with older students;
    • speak with faculty in office hours or at tea;
    • request a reading course (Math 590) on a special topic.

    The student-advisor relationship is much like an apprenticeship, so good fit between student and advisor is important. We recommend you keep an open mind about your research area in order to find the best advisor for you.

  • After completing a minimum of 24 units of study, selecting an advisor, and obtaining partial results towards a thesis, students should complete the Oral Qualifying Examination, which includes both a written and oral component.

    Expectations for what constitutes partial results varies by area and advisor. It’s up to the advisor (not the student) to establish the bar the student is expected to meet. Students talk with their advisor to ensure they understand what is expected.

    The 10-page written proposal must include background on the research problem(s) and references to prior work . Students should include precise statements and proof sketches but not rigorous proofs. The proposal must be typeset in LaTeX, and the writing should be of the quality we expect of papers submitted to area journals.

    The 1.5 hour oral exam begins with a presentation by the student during which the committee will ask clarifying questions to assess the student’s domain knowledge. The student should prepare a 45 minute presentation so that the exam plus questions is 75-90 minutes.

    Students should take their oral exam within 2-3 semesters after finishing their written exams. The oral exam must be taken by the end of the 3rd year at the latest.

    The oral exam committee consists of five USC faculty members:

    • Committee chair (this person must be the advisor)
    • 3 additional tenured or tenure-track faculty in Mathematics
    • 1 tenured or tenure-track faculty member at USC outside of Mathematics

    Students must submit the Appointment or Change of Qualifying Exam Committee form to the Mathematics Graduate Advisor at least 2 weeks prior to taking the exam. For more details about this process, please consult the Ph.D. Handbook.

  • The student must give a public lecture (thesis defense) on their research, to be approved by their dissertation committee.

    The Dissertation Committee consists of three USC faculty members:

    • Committee chair must be the advisor
    • 1 additional tenured or tenure-track faculty in Mathematics
    • 1 faculty member at USC outside of Mathematics

    This defense should take place at least two months before the end of the semester in which they intend to receive their degree, so that they can complete all of the graduate school Thesis and Submission Deadlines on time.

Mathematics Ph.D. Handbook