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: 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 - 1, where n is the number of vertices. There are results when each degree sequence is a tree degree sequence, that is, each degree is positive, and the sum of the degrees is 2n-2. The proposed research project is to give necessary and/or sufficient conditions for sparse degree sequences to have edge disjoint realizations. 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: