## Overview

The Ph.D. program at Saint Louis University consists of coursework highlighted by required core subject area courses and three written preliminary examinations. Students will gain fundamental knowledge in the areas of algebra, analysis, statistics, and topology. After demonstrating mastery in these areas, they will develop original mathematics under the direction of a faculty member.

## Coursework

Students who enter the Ph.D. program with a bachelor’s degree in mathematics must complete 48 credit hours (16 courses) in mathematics at the 4000 level or higher, in addition to twelve hours of dissertation research (MATH 6990). At most 6 of these 48 hours can be at the 4000-level with the remaining 42 hours at the 5000 or 6000-level. For those who enter with a master’s degree in mathematics, the requirement is 24 hours (8 courses) of coursework at the 5000 or 6000-level plus twelve hours of dissertation research. All Ph.D. students must complete eight core subject area courses at the 5000-level or higher in algebra, analysis, statistics, or topology. These eight courses can be distributed in two different ways

- Three courses from two subject areas and two courses from a third area (3-3-2). These must include three courses from among MATH 5110 (Algebraic Structures I), MATH 5210 (Measure Theory), MATH 5310 (Point Set Topology), and STAT 5850 (Statistical Inference).
- Two courses from each of the four subject areas (2-2-2-2). These courses must include the courses MATH 5110 (Algebraic Structures I), MATH 5210 (Measure Theory), MATH 5310 (Point Set Topology), and STAT 5850 (Statistical Inference).

Beyond these required courses, students choose a set of courses that provide them with a broad knowledge of mathematics and a deep understanding of their intended research area. The department offers a variety of electives and advanced topics courses on a rotating basis. Full time students typically take three courses each semester, including reading courses and dissertation research.All master’s students must complete at least two courses in two of the subject areas from algebra, analysis, statistics, and topology. At least two of these four required courses must be from MATH 5110 Algebraic Structures I, MATH 5210 Measure Theory, MATH 5310 Point Set Topology, and STAT 5850 Statistical Inference. The department offers the four core courses on a rotating basis as well as a variety of electives and advanced topics each year. Full time students typically take three courses each semester, including reading courses and dissertation research.

## Written examinations

Ph.D. students must pass three written examinations. Two of these examinations are from the core subject areas: algebra, analysis, topology, and statistics. The exams cover the topics from the associated core subject area course: MATH 5110 (Algebraic Structures I), MATH 5210 (Measure Theory), MATH 5310 (Point Set Topology), or STAT 5850 (Statistical Inference) and must be taken at the next exam opportunity following completion of the associated course. The third exam covers advanced topics from one area of specialization from among algebra, analysis, statistics, and topology. The area of specialization is the student’s expected dissertation area and the topics are chosen from two advanced courses taken by the student in that subject area. The specific topics are chosen by the Graduate Coordinator in consultation with the student. These examinations are given twice each year – January and August. All exams must be completed prior to the student’s seventh semester in the program. A student who fails three written examinations cannot continue in the Ph.D. program.

## Oral examination

After a Ph.D. student has completed the written examinations and chosen a dissertation advisor and an area of research, she or he must pass an oral examination administered by a committee of five faculty members. This oral examination involves a presentation on the student’s area of intended research, followed by questions from the examiners.

## Advancement to candidacy

After passing the written and oral Ph.D. examinations, the student is eligible to “advance to candidacy.” This step involves writing a prospectus for the dissertation and identifying the three faculty members who will serve as readers of the student’s dissertation. Students who want to apply for certain Graduate School fellowships, such as Dissertation Fellowships, must have advanced to candidacy.

## Dissertation

The culminating requirement for the Ph.D. degree is writing and successfully defending a dissertation that presents the results of the original and independent mathematical research that the student has carried out, with the guidance of a faculty member.

## Additional requirements

A Ph.D. student must obtain at least a 3.0 GPA overall. If the GPA is lower than a 3.0, then the teaching assistantship cannot be renewed for the next year.

## Financial Support

A graduate student can receive total of up to 5 years of support from Saint Louis University as a teaching assistant, including support received while in the master’s and the doctoral program. Renewal of the assistantship from year to year is not guaranteed, but is typically given when student demonstrates sufficient progress towards the degree.