This course is designed in the style of the Hungarian "TDK" system, allowing advanced undergraduates to become acquainted with research methods and means in detail and acquire additional knowledge beyond their obligatory curriculum. (For a brief English description of the TDK system see a relevant ELTE University homepage.)

In this course, a student can choose from the topics/problems listed below and work with other students and the professor to solve the given problem. All work is summarized in a paper and during the semester there will be opportunities to present your work as well.

This may contribute to the successful beginning of a scientific career: depending on level, the results obtained can be presented at school, statewide or national undergraduate meetings ranging from a local Undergradute Seminar at your home school to MAA's MathFest. Papers may also be published in undergraduate research journals. such as The Rose-Hulman Undergraduate Mathematics Journal, Involve or many others.

In some PhD programs, fruitful undergraduate reserach activity is a prerequisite for admission.

Student research is supervised by professors. Research topics are offered by them, but students can also propose topics of their own interest.

You can view articles that were written under the auspices of the BSM program


The list of research topics and professors proposing them can be seen below. Contact the professor whose problem you are interested in.


  1. Title: Graph parameters of degree sequences

    Description: click here

    Prerequisites: basic combinatorics and graph theory
    Best for: students who intend to do research in graph theory or combinatorics
    Professor: Dr. Zoltán Király
    Assignment for the first week: Work on the exercises given in the description.

  2. Title: Minimal Spanning Forests on infinite graphs

    Description: click here

    Prerequisites: basic probability, but we can go over the necessary background if needed.
    Best for: student with interest in probability, graph theory, statistical physics.
    Professor: dr Adam Timar
    Assignment for the first week: Work on the exercises given in the description.

  3. Title: Packing sparse degree sequences

    Description: The edge packing or graph factorization problem asks the question if an ensemble of edge disjoint graphs exists with prescribed degrees. The problem in general is a hard computational problem, however, it is easy for special cases. One special case is when the graph is very sparse, the sum of the degrees is less than or equal to 2n -2, where n is the number of vertices. Above the existance problem, we are also interested in the connectivity problem: what are the necessary and sufficient transformations to transform solutions into each other? More detailed description can be found here:

    Prerequisites: basic combinatorics and graph theory.
    Best for: students interested in combinatorics, discrete mathematics and computer science
    Professor: Dr. István Miklós
    Assignment for the first week: see in

  4. Title: What is unavoidable - Forbidden Configurations

    Description: Click here
    Professor: Dr. Attila Sali