Mathematics, Ph.D.

Program Overview

The Saint Louis University Ph.D. in Mathematics emphasizes individualized instruction and equips students with fundamental mathematical knowledge, problem-solving abilities, and communication and project management skills. Through coursework, written exams, and dissertation research, the program prepares graduates for research or teaching careers in academia or industry.

Program Outline

Degree Overview:

The Department of Mathematics and Statistics at Saint Louis University offers a Doctor of Philosophy (Ph.D.) degree in Mathematics. The program emphasizes individualized instruction due to a low student-faculty ratio.

Objectives:

The Ph.D. program aims to equip students with:

• Fundamental knowledge in algebra, analysis, statistics, and topology.
• The ability to identify and solve new research problems in pure or applied mathematics.
• Effective communication skills for presenting new research in written and oral formats.
• Project management skills for handling large research projects and preparing manuscripts.

Outline:

Program Structure:

• The Ph.D. program consists of coursework, written preliminary examinations, and dissertation research.
• Students must demonstrate mastery in at least two of the four core subject areas: algebra, analysis, statistics, and topology.
• Students must complete a dissertation that presents original and independent mathematical research under the guidance of a faculty member.

Coursework:

• Required Courses:
• Select at least 3 of 4 core courses:
• MATH 5110 Algebraic Structures I
• MATH 5210 Measure Theory
• MATH 5310 Point Set Topology
• STAT 5850 Statistical Inference
• Select five additional courses in core areas.
• Dissertation Research:
• MATH 6990 Dissertation Research (taken over multiple semesters, 12 hours total)
• Elective Courses:
• Eight additional MATH or STAT courses at the 5000-level or above.

Total Credits:

60

Non-Course Requirements:

• Written Examinations:
• Three written examinations are required.
• Two exams cover core subject areas (algebra, analysis, topology, and statistics).
• The third exam covers advanced topics in the student's dissertation area.
• Exams are given twice a year (January and August).
• All exams must be completed before the student's seventh semester.
• Oral Examination:
• After completing written exams and choosing a dissertation advisor, students must pass an oral examination.
• The exam involves a presentation on the student's research area followed by questions from a committee of five faculty members.
• Dissertation:
• After passing written and oral exams, students advance to candidacy.
• They must write a dissertation prospectus and identify three faculty members to serve as readers.
• The dissertation must present original and independent mathematical research.

Course Schedule:

• The program roadmap suggests a four-year completion timeline, with the possibility of an additional two semesters for dissertation research.
• Students typically take three courses per semester, including reading courses and dissertation research.

Assessment:

• Written Examinations:
• Students must pass three written examinations covering core subject areas and their dissertation area.
• Oral Examination:
• Students must pass an oral examination on their research area.
• Dissertation:
• Students must write and defend a dissertation that presents original and independent mathematical research.

Teaching:

• The program emphasizes individualized instruction due to a low student-faculty ratio.
• Faculty members provide guidance and mentorship throughout the program.

Careers:

• The Ph.D. in Mathematics prepares students for research or teaching careers in colleges, universities, or industry.

Other:

• Students who enter the program with a bachelor's degree in mathematics must complete 48 credit hours of coursework at the 4000 level or higher, in addition to 12 hours of dissertation research.
• Students who enter with a master's degree in mathematics must complete 24 hours of coursework at the 5000 or 6000-level plus 12 hours of dissertation research.
• All Ph.D. students must complete eight core subject area courses at the 5000-level or higher.
• The department offers a variety of electives and advanced topics courses on a rotating basis.