# Mathematics, Ph.D.

The Department of Mathematics and Statistics at Saint Louis University offers graduate programs of advanced study and research leading to Master of Arts and Doctor of Philosophy degrees in mathematics. Due to the low student-faculty ratio, graduate students receive extensive individualized instruction.

## Curriculum 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.

## Fieldwork and Research Opportunities

Courses at the advanced graduate level allow students to proceed beyond the standard graduate curriculum into research areas represented by the faculty. To graduate, students must write and successfully defend a dissertation that presents the results of the original and independent mathematical research that they have carried out, with the guidance of a faculty member.

## Careers

SLU's Ph.D. in Mathematics prepares students for research or teaching careers in colleges, universities or industry.

## Admission Requirements

### Continuation Standards

Students must maintain a cumulative grade point average (GPA) of 3.00 in all graduate/professional courses.

Applicants should have a master’s degree or a bachelor’s degree in mathematics that includes a year of coursework in algebra and in analysis or topology.

### Application Requirements

- Application form and fee
- Transcript(s)
- Three letters of recommendation
- Résumé
- Professional goal statement

Requirements for International Students

All admission policies and requirements for domestic students apply to international students. International students must also meet the following additional requirements:

- Demonstrate English Language Proficiency
- Financial documents are required to complete an application for admission and be reviewed for admission and merit scholarships.
- Proof of financial support that must include:
- A letter of financial support from the person(s) or sponsoring agency funding the student's time at Saint Louis University
- A letter from the sponsor's bank verifying that the funds are available and will be so for the duration of the student's study at the University

- Academic records, in English translation, of students who have undertaken postsecondary studies outside the United States must include:
- Courses taken and/or lectures attended
- Practical laboratory work
- The maximum and minimum grades attainable
- The grades earned or the results of all end-of-term examinations
- Any honors or degrees received.

WES and ECE transcripts are accepted.

### Assistantship and Application Deadlines

Students who want to be considered for an assistantship must submit their application by Jan. 1.

U.S. students who want to be considered for the fall semester should apply by July 1 and for the spring semester by Nov. 1.

International students should apply for the fall semester by May 1 and for the spring semester by Oct. 1.

### Review Process

All applications are reviewed by committee with about a six-week wait for decision notification to applicants. All applicants have until April 15 to decide to accept.

## Tuition

Tuition | Cost Per Credit |
---|---|

Graduate Tuition | $1,310 |

Additional charges may apply. Other resources are listed below:

Information on Tuition and Fees

## Scholarships, Assistantships and Financial Aid

For priority consideration for a graduate assistantship, apply by the program admission deadlines listed. Fellowships and assistantships provide a stipend and may include health insurance and a tuition scholarship for the duration of the award.

- Graduates will be able to demonstrate fundamental knowledge in at least three of the areas of algebra, analysis, statistics, and topology.
- Graduates will be able to demonstrate mastery in at least two of the above four areas.
- Graduates will be able to demonstrate ability to identify and solve new research problems in pure or applied mathematics.
- Graduates will be able to demonstrate ability to effectively communicate new research in both a written and oral setting.
- Graduates will be able to demonstrate ability to manage a large research project and prepare a manuscript.

Code | Title | Credits |
---|---|---|

Required Courses | ||

Select at least 3 of 4 core courses | 9 | |

MATH 5110 | Algebraic Structures I | |

Analysis Sequence | ||

MATH 5210 | Measure Theory | |

MATH 5310 | Point Set Topology | |

STAT 5850 | Statistical Inference | |

Select five additional courses in core areas | 15 | |

Dissertation Research | ||

MATH 6990 | Dissertation Research (taken over multiple semesters, 12hrs total) | 0-6 |

Elective Courses | ||

Eight additional MATH or STAT courses at the 5000-level or above. | 24 | |

Total Credits | 60 |

## Non-Course Requirements

### 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 Program 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.

### Dissertation

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. 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. The student must also complete 12 credits hours of MATH 6990 Dissertation Research.

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.

### Continuation Standards

Students must maintain a cumulative grade point average (GPA) of 3.00 in all graduate/professional courses.

Roadmaps are recommended semester-by-semester plans of study for programs and assume full-time enrollment unless otherwise noted.

Courses and milestones designated as critical (marked with !) must be completed in the semester listed to ensure a timely graduation. Transfer credit may change the roadmap.

This roadmap should not be used in the place of regular academic advising appointments. All students are encouraged to meet with their advisor/mentor each semester. Requirements, course availability and sequencing are subject to change.

Year One | ||
---|---|---|

Fall | Credits | |

Participation in first-year mentoring program | ||

MATH 5080 | Probability Theory | 3 |

MATH 5130 | Computational Algebra | 3 |

MATH 5310 | Point Set Topology | 3 |

Credits | 9 | |

Spring | ||

MATH 5110 | Algebraic Structures I | 3 |

MATH 5220 | Complex Analysis | 3 |

MATH 6310 | Algebraic Topology | 3 |

Credits | 9 | |

Year Two | ||

Fall | ||

Algebra core written examination (August) | ||

MATH 5210 | Measure Theory | 3 |

MATH 5360 | Applied Topology and the Shape of Data | 3 |

MATH 6130 | Advanced Group Theory | 3 |

Credits | 9 | |

Spring | ||

Analysis core written examination (January) | ||

MATH 5015 | Number Theory | 3 |

MATH 5140 | Algebraic Combinatorics | 3 |

MATH 6220 | Metric Space Analysis | |

Credits | 6 | |

Year Three | ||

Fall | ||

Algebra specialization written examination (August) | ||

MATH 6990 | Dissertation Research | 3 |

MATH 5XXX or 6XXX | Topics course or Graduate Reading Course | 3 |

Credits | 6 | |

Spring | ||

MATH 6990 | Dissertation Research | 3 |

MATH 5XXX or 6XXX | Topics course or Graduate Reading Course | 3 |

Credits | 6 | |

Year Four | ||

Fall | ||

MATH 6990 | Dissertation Research | 3 |

MATH 5XXX or 6XXX | Topics course or Graduate Reading Course | |

Credits | 3 | |

Spring | ||

MATH 6990 | Dissertation Research | 3 |

MATH 5XXX or 6XXX | Topics course or Graduate Reading Course | |

Credits | 3 | |

Total Credits | 51 |

## Program Notes

This is presented as one example of how a student could complete the PhD in four years, or perhaps an additional two semesters of dissertation research would lead to a five-year Ph.D.

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 MATH 6990 Dissertation Research. 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, andSTAT 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.

For more information about our program, please contact:

Benjamin Hutz, Ph.D.

Graduate Program Coordinator

Department of Mathematics and Statistics

benjamin.hutz@slu.edu