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 or Involve.

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

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


The list of research topics and professors proposing them can be seen below. Contact the professor whose problem you are interested in at the Welcome Party, but read everything carefully below first.


  • Title: Distribution of colors in Gallai colorings

    Description: Click here for the description

    Prerequisites: some graph theory
    Best for: students interested in graph theory and combinatorics
    Professor: dr Andras Gyarfas

    Assignment for the first week: 1. Understand the statements of the results in the paper
    2. Email to me (at gyarfas.andras at renyi dot mta . hu ) solutions for at least two of the three exercises from here, not later than June 12, 2019. If something is not clear, do not hesitate to ask for clarification.

  • Title: Completing Latin rectangles and edge coloring of regular, bipartite graphs

    Description: The aim of this research course is to study the solution space of edge-colorings of regular, bipartite graphs and the possible completions of Latin rectangles. Detailed description: here

    Prerequisites: basic combinatorics, discrete mathematics and graph theory, basic computer science
    Best for: students interested in modern combinatorics and computer science
    Professor: dr István Miklós

    Assignment for the first week: See here

  • Title: Combinatorial problems motivated by coding theory

    Description: Click here

    Prerequisites: basic combinatorics and probability theory
    Best for: students interested in combinatorics, discrete mathematics, computer science or information theory
    Professor:Dr. Miklós Ruszinkó
    Assignment for the first week: read and try to digest the papers below:
    paper1, paper2, paper3

  • Title: Explicit Burgess type estimates for composite moduli

    Description: Click here for the description

    Prerequisites: basics of number theory, characters of finite abelian groups, analytic techniques
    Best for: students interested in number theory
    Professor:Dr. Péter Maga;
    Assignment for the first week: Click here