Welcome to the Graduate Center's Department of Mathematics. I can serve as your dissertation advisor in Matroid Theory or Graph Theory. Some of the information below is general and applies to all graduate students and some is more specific for students interested in doing a PhD in Combinatorics broadly defined. At the end you'll find some very specific information for students interested in Matroid Theory.

General Information for PhD candidates

The summer before you arrive please review the department's Qualifying Exams page. The department offers the following qualifying exams:

1) Algebra

2) Complex Analysis

3) Differential Geometry

4) Logic

5) Real Analysis

6) Topology 

Take a look at the department's syllabus and sample exams and compare them with the courses you've already done.

To begin with, you have to pass 3 of the 6 qualifying exams to pass what is called "First Examination."  Qualifying exams are given in May and Aug/Sep. You have a second chance to take an exam if you don't pass the first time. Qualifying exams must be completed in the first two years. See the Graduate Student Catalog. 

The exams you decide to take at the end of your first academic year in May should dictate which courses you'll take in the Fall and the Spring of your first year. Not all courses are offered every semester. So, once you decide which exams you'll take, be sure to take the corresponding courses as soon as they are offered because the professors who teach these courses during the academic year also make the qualifying exams at the end of the year.

The following courses are required, and each course is 4.5 credits.

MATH 70100 - Real Analysis

MATH 70300 - Complex Analysis (first of a two-semester course)

MATH 70500 - Algebra

MATH 70700 - Topology (first of a two-semester course)

You also have to demonstrate the ability to read mathematics in one of French, German, Russian, or Chinese. (If one of these languages is your native language, you'll have to select another one.) You can take a language course and pass the required exam.

Once you pass your First Examination, you can explore the electives offered. 

The "Second Examination" is what called the Oral Examination. You'll specializes in an area of advanced mathematics of your choosing and with your dissertation advisor's help you'll create a program of study. When it is completed, you'll take the Oral Exam. After this you will begin your dissertation research formally, but if you know what you want to specialize in then it is better to be engaged in research earlier. If you have done an REU as an undergraduate, then you are familiar with the process of diving deeply into a problem and writing up your results. 

Specific Information for PhD candidates in Combinatorics and Graph Theory

A PhD candidate in Combinatorics should complete the First Examination as soon as possible. Algebra and Topology courses are especially useful for Combinatorics, so it would be a good idea to take those qualifying exams at the end of the academic year in May. 

However, you may choose to do any 3 of the 6 qualifying exams. There are many moving parts and it may be the case that you'll prefer to do a qualifying exam in one of the other topics. 

The important thing is to pass the First Examination in May at the end of your first year and it is best not to get side-tracked from this key accomplishment in your journey toward a PhD. 

However, should you fail the first attempt, don't lose hope. You can try again in August after studying for it intensely over the summer. If you fail an exam in a specific topic twice you cannot repeat it a third time, but you may be able to obtain permission to take an exam in another topic. Hopefully, this will not be an issue, but if it is, do not lose hope. Work with your dissertation advisor to make a plan for success. It does help to seek a dissertation advisor as soon as possible.

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FALL 2025

The Fall 2025 courses are listed at https://www.gc.cuny.edu/mathematics/curriculum-and-degree-information/courses 

(Scroll down to see the Fall 2025 Courses link.) Among the courses offered this Fall, a first-year student interested in doing a PhD in Combinatorics should take three of the following courses. 

MATH 70100: Functions of a Real Variable

Mon & Wed, 9:30 AM - 11:00 AM, Room TBA

MATH 70300: Functions of Complex Variable

Tues & Thurs, 2:00 PM - 3:30 PM, Room TBA

MATH 70700: Topology

Tues & Thurs, 9:30 AM - 11:00 AM, Room TBA

MATH 71100: Logic

Mon & Wed, 6:30 PM - 8:00 PM, Room TBA

Until you select a dissertation advisor, you'll have to take a required 1-credit seminar course. This research seminar is just a weekly seminar where the department's faculty give talks designed for graduate students on their work, so it requires only your presence at that time.

MATH 89901.03: Research Seminar

Monday, 4:15 PM - 6:15 PM, Room TBA

The Combinatorics Research Group has a Combinatorics Learning Seminar on Wednesday 4:15 pm - 6:15 pm. It will be mostly online with a few in-person meetings. Please put this Mon/Wed 4:15 pm - 6:15 pm time slot on your calendar for the Fall and Spring.

Specific Information for PhD candidates in Matroid Theory

Matroids are a kind of synthetic geometry. In fact, Rota wanted to call them "combinatorial geometry" but the original name that Whitney gave stuck. 

For a PhD in matroids, a student must know quite a bit on projective geometries, so if such a special topics course is offered you should take it or learn the material through a learning seminar. 

The new perspective on matroids originating from differential geometry is quite fascinating. See this article "Hodge Theory of Matroids." If this interests you, then you must take the department's Differential Geometry course. It is up to you whether you want to take the Differential Geometry qualifying exam.