Graduate students in the Saint Louis University Department of Mathematics and Statistics must fulfill certain academic requirements.

## Master’s Degree Coursework

Saint Louis University’s Master of Arts in Math requires 10 courses in mathematics at the 4000-level or higher. At least seven of the courses must be at the 5000-level or higher. All master’s students must complete at least two 5000-level sequences chosen from algebra, analysis and topology.

Many students build their program around a number of year-long sequences from areas including algebra, analysis and topology. The department typically offers year-long sequences in algebra, analysis, complex variables and probability and statistics at the 4000-level; algebra, analysis and topology at the 5000-level; and differential geometry at the 6000-level. The department also routinely offers a variety of electives determined by student and faculty interest. Full-time students typically take three courses a semester and complete the degree in two years.

A first year master’s student usually takes two or three year-long sequences. If you have not had courses in algebra or analysis at the undergraduate level, we recommend taking the 4000-level algebra and analysis sequences. This prepares you to take the 5000-level sequences in algebra, analysis and topology your second year. For students who have had substantial coursework in algebra or analysis at the undergraduate level, some of the 5000-level sequences could be completed in the first year.

### Additional Requirements

In addition to the 10 courses in mathematics, master’s students must take a comprehensive oral exam in the final semester of their program. This exam is administered by three faculty members. The exam consists of three parts, one for each of three assessment areas.

Assessment areas are chosen by the director of graduate studies in consultation with the student. In each part, the student gives a 10-minute talk on a mathematical topic in that area. Each talk will be followed by a question-and-answer period. The duration of each of the three parts is about 30 minutes.

Master’s students have the option of writing a master’s thesis. In that case, two of the courses in the second year would be devoted to research for the thesis, and the master’s oral exam is replaced by an oral defense of the thesis.

### Financial Support

A master’s student can receive up to two years of support as a teaching assistant. Renewal of the assistantship for the second year is not guaranteed as the student needs to demonstrate sufficient progress towards the degree.

A master’s student must obtain at least a 3.0 GPA overall. If after the first year the GPA is lower than a 3.0, the teaching assistantship cannot be renewed for the second year.

Furthermore, a B or better must be obtained in each course comprising the two required 5000-level sequences. A master’s student who plans to pursue a Ph.D. in mathematics should maintain a GPA above a 3.0 and should include some As.

## Ph.D. Coursework

The requirements for SLU’s Ph.D. in mathematics include written examinations, a language examination, an oral examination, and writing and defending a dissertation. In addition, there is an important procedural step called “advancement to candidacy.”

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 12 hours of dissertation research as part of MATH 6990: Dissertation Research. At most, nine of these 48 hours can be at the 4000-level with the remaining 39 hours at the 5000- or 6000-level. For those who enter with a master’s degree in mathematics, the requirement is 24 hours (eight courses) of coursework at the 5000 or 6000-level plus 12 hours of dissertation research.

All Ph.D. students must complete the 5000-level sequences in algebra, analysis, and topology, as well as the 6000-level sequence in differential geometry. Beyond that, 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 routinely offers a variety of electives determined by student and faculty interest. Full-time students typically take three courses each semester, including reading courses and dissertation research.

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.

Ph.D. students must pass three-hour written examinations in three of the four areas covered by the 5000-level and 6000-level sequences: algebra, analysis, topology, and differential geometry. These examinations are given three times each year – at the beginning of each semester, and at the end of the spring semester. Students should take these examinations as soon as possible after completing the relevant coursework and must, in any case, attempt them within 10 months of completing the relevant coursework. However, if the sequence was completed before entering our Ph.D. program the exam must be taken within 10 months of entering the Ph.D. program. A student who fails any written examination twice ordinarily cannot continue in the Ph.D. program.

Ph.D. students must pass a written examination in one of the following languages: French, German or Russian. The examination consists of translating a mathematical journal article that is written in one of those languages.

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.

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 fellowships must have advanced to candidacy.

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.

### Financial Support

A graduate student can receive total of up to five 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, as the student needs to demonstrate sufficient progress towards the degree.

Students who are awarded teaching assistantships normally teach one course per semester. This allows graduate students maximum freedom to pursue graduate study while perfecting their teaching skills. The nine-month stipend amount is approximately $19,000, including full tuition remission and medical benefits. In addition, each year the department can nominate outstanding candidates for Minority Fellowships and Presidential Fellowships.