Ph.D. in Mathematics with the
the Algebra, Combinatorics, and Geometry Group (ACoG)
The purpose of a Ph.D. in the ACOG program is to produce research oriented mathematicians in pure mathematics. This requires a major transformation in the student, from a consumer of mathematics created by other mathematicians throughout history, to a producer of new mathematical ideas, conjectures, proofs, and theorems. This program guides students through this transformation, from student to mathematician. The most significant moment of the program is the Thesis Defense, at which the student presents original mathematical theorems to members of the thesis committee and other members of the audience.
The skills developed in this research program accompany our graduates throughout life, whether they continue on as research mathematicians in academics or industry, teachers, or some other profession.
Why Algebra, Combinatorics, and Geometry at Pitt?
Algebra, Combinatorics, and Geometry (along with Topology, Number Theory, and Analysis) are at the heart of pure mathematics. The interests of the group are broadly conceived. Each faculty member of this research group is an expert in two or more separate subfields of mathematics, and has found ways to combine them in research. This provides a rich environment for students, who wish to be exposed to a large number of ideas from many areas, while training to become a mathematician.
There are many ongoing research projects that students may participate in.
The group is actively seeking graduate students. We encourage anyone with questions to contact a faculty member in the group.
The Path to a Ph.D.
The math department graduate handbook gives details of the requirements.
The first step is to apply online to the graduate program. The department offers Teaching Assistantships, Fellowships, free tuition and free health insurance.
There will be faculty members and other graduate students to help guide you along the path to a Ph.D. Here is the general outline of the program.
First Year
- Pass the preliminary exams. Here is the syllabus.
- Courses:
- Algebra I, II
- Combinatorics I, II for students with sufficient background to pass the preliminary exams without coursework. If more work is needed on preliminary exams, the combinatorics sequence can be taken in the second year.
Second Year
- Advanced Course Work. By this time, the student has learned the foundational material and is ready to concentrate on advanced course work in pure mathematics. Research in pure mathematics requires a broad understanding of many fields of mathematics and a deep understanding of specialized areas.
- Algebra III, IV
- Another ACOG course each semester, according to course offerings
- An elective course each semester.
- Introductory research. In the second year, students get some exposure to research in mathematics. The research will often be done in collaboration with other students. The research done this year does not need to be on the same topic as the eventual thesis research. The purpose is to learn the steps of a research project. It will result in a research report or publication.
- The comprehensive exams come at the end of the second year.
- By the end of the second year, it is time to pick a research advisor from among the faculty members in the group.
Second Summer
- The second summer can be an opportunity to get involved with research projects in the ACOG group.
Third Year
- Further Advanced Course Work.
- Two ACOG courses each semester, according to course offering.
- In the third year, the primary focus shifts from course work to research. The graduate student settles on a research question with the help of an advisor. The general strategy for a solution to the problem is formulated. Serious research begins.
- The student presents a thesis overview that describes the research proposal in detail.
Third Summer
- The third summer can be the most critical research period of the entire degree program. Students are normally expected to devote their full energy to research during this summer. A thesis defense and job applications are rapidly approaching.
Fourth Year
- Begin the job application process. We will help to guide you through the job search. Academic job applications are generally due in November and December. By then, the research should be substantially complete so that applications can accurately reflect the graduate research accomplishments. Applications generally involve a teaching statement, a research statement, and letters of recommendation.
- Write the thesis.
- Defend the thesis.
Sometimes, the graduate program can extend into a fifth year.
Graduate Courses
Graduate students will normally take two graduate level courses within the Algebra, Combinatorics, and Geometry syllabus each semester. Additional elective courses may be taken as well.
All ACOG students should complete the following sequences
- Algebra 1, 2, 3, 4
- Combinatorics 1, 2
Here is a list of course offerings in the ACOG group.
Resources for Graduate Students
A weekly colloquium exposes students to a broad range of mathematical ideas.
A weekly math research seminar covers recent developments in pure mathematics. The colloquium and math research seminar will occasionally present advanced mathematical concepts that will be difficult for a graduate student to understand. This should not deter students from attending. On the contrary, it is through the repeated exposure to advanced ideas over a long period of time and by thinking deeply about the parts that they are able to understand that graduate students mature as mathematicians.
There is a weekly student research training seminar, in which student give presentations on papers relevant to their research program. It is specifically geared to the current needs of the graduate students in the group.