Doctoral Program (PhD)

complex equations.

UB's doctoral program in mathematics aims toward generating career options for our students. Additionally, the program guides students toward being prepared for research by the end of 3rd third year of coursework.

As reported by the American Mathematical Society, mathematician was the #1 rated career in CareerCast’s Job Rated 2014 report. Individual who have demonstrated a high level of mathematical acumen by obtaining a PhD in mathematics are highly prized in both the academic and private sector job markets.

The requirements below are for students admitted in Fall 2016 and later. The main steps in completing a PhD are:

(A) First Year's Coursework and Evaluation exams—Successfully completing the first year's 6 core courses and passing at least 4 out of 6 evaluation exams attached to these courses. For students interested in pursuing research in pure mathematics the 6 core courses are in algebra, analysis and geometry/topology. For students interested in pursuing research in applied mathematics the 6 core courses are in analysis, numerical analysis and methods in applied mathematics.

(B) Oral Examination and Advancing to Candidacy—An oral examination covering material in advanced topics and research ideas in the student's chosen area of research. This oral examination is also the final requirement for advancement to candidacy and should be taken before the end of the student's third year.

(C) PhD Thesis and Final Oral Examination—Writing a dissertation and passing an oral defense.The dissertation must consist of original research of sufficient quality for publishing in a respectable mathematics journal.

After the 1st year's course work, the student will take more advanced courses at the 600 level and 700/800 level topics course. Entering their 3rd year, students will focus on their preferred area of research. Advancement to candidacy and dissertation work requires passing an oral exam. Students should pass their oral examination prior to the end of the 3rd year of the program.

In addition to these primary steps, the program offers a 1st year mentoring seminar meant to help students in their career development and management. Topics covered include: study mathematics; using LaTex; media in research mathematics; documenting your achievements; writing, editing and publishing mathematics; seminars, conferences and workshops; and, job options for PhD's in mathematics.  

This mentoring seminar will also include faculty talks directed at graduate students, presenting their area of research.

Both the MA and the PhD degrees have residency requirements: one year for the MA and two years for the PhD.

On this page

PhD Program Requirements

The main steps in obtaining a PhD in mathematics are: (A) Satisfactory completion of first year's coursework and evaluation exams; (B) Passing oral exam in intended area of research and advancing to candidacy; and, (C) Writing the dissertation and successfully defending it in a final oral exam. The aspects of each step are more fully discussed on this page.

(A) First Year's Coursework and Evaluation exams

The course schedule outlined below is for students in the PhD program who are supported by a teaching assistantship and tuition fellowship. It is 9-credits per semester. For students who do not have support an additional 3-credit course is require so as to be a full time student. See the listing of course descriptions.

Learning mathematics is a shared enterprise. Thus, all members of an entering doctoral class advance through the first year coursework as a cohort.

Fall semester:

  1. Pure Track.
    1. Analysis--measure theory (MTH 534).
    2. Algebra--groups and rings (MTH 519).
    3. Geometry/Topology--point set topology (MTH 527).
       
  2.  Applied Track.
    1. Analysis--measure theory (MTH 534)..
    2. Methods of applied mathematics I (MTH 539)
    3. Numerical analysis I (MTH 537).

Spring semester offering:

  1. Pure Track.
    1. Analysis--complex analysis (MTH 625).
    2. Algebra--module and galois theory (MTH 520).
    3. Geometry/Topology--homotopy theory (MTH 528).
       
  2. Applied Track.
    1. Analysis--complex analysis (MTH 625).
    2. Methods of applied mathematics II (MTH 540).
    3. Numerical analysis II (MTH 538).

Evaluation Exams: Attached to each first year course is an evaluation exam. This exam will be given during the regularly scheduled final exam time.  All first year evaluation exams are pass/fail.  To continue in the PhD program a student needs to achieve at least 4-out-of-6 exam passes. To continue in the MA program a student needs to achieve at least a 3-out-of-6 exam passes. To be in good standing in any graduate program a student needs a GPA of B or above

Deficiency: Students who are marginally below the mark (e.g., pass 2 out of 4 exams or better at PhD level) and/or are marginally below the required B-GPA level, so that they can still advance with their cohort, have an opportunity to retake the relevant exams which will be offered in August before the Fall Semester. If the student passes these “make ups’’, then the student will be allowed to advance through the program along with their entering cohort. If the student performance on this exam is still below the mark, then the student will retake the appropriate exam during the subsequent semester’s finals week.  If the student’s performance is still insufficient, then the student will be dismissed from the program. Students whose performance at the end of their 1st year is judged to be significantly insufficient by the Graduate Director will be dismissed from the program before the beginning of their 2nd year.

(B) Oral Examination and Advancing to Candidacy

After the first year's course work, the student will take more advanced courses at the 600 level and 700/800 level topics course. Students also typically arrange individual reading courses with professors and participate in area seminars.

Entering their third year, students will be focusing on their preferred area of research and the faculty with whom they would like to work. Students will be required to form an oral examination committee of two or three faculty members chaired by a potential thesis advisor.

Students will work with their committee to prepare a syllabus outlining topics to be covered in the oral examination including a bibliography of books and/or articles. Typically the topics to be covered in the oral examination should be at the level of 600 to 800 level courses and include material that the student learned individually.

The syllabus must be approved by the Graduate Director’s office and the student’s committee members. Students should pass their oral examination prior to the end of the third year of the program.

(C) PhD Thesis and Final Oral Examination

The final departmental steps in attaining the degree is completion of a dissertation that must consist of original research of sufficient quality for publishing in a respectable mathematics journal. It is not unusual for the mathematics in a single dissertation to generate two or three published manuscripts.