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: When the Yule-Simpson paradox can be avoided

    Description: In contingency table analysis (containing joint responses for categorical, mainly binary variables) Yule (1903) and Simpson (1951)detected an effect reversal between marginal and conditional tables in some examples. To illustrate this effect, consider the paper of Range, The New York Times Magazine (1979). Their 2x2x2 table describes the sentences (death or other) in murder cases in Florida (1973-78). The color of the skin both of the murderer and the victim was registered. The marginal table (when the color of the victim is ignored) shows a greater proportion of white murderers receiving death sentence than black; whereas the conditional tables for given color of victim show a different picture: both for black and white victims, there is a much higher proportion of black murderers receiving death sentences. In particular, none of the white murderers, killing black victims, were sentenced to death.

    Later on, in the possession of log-linear models, statisticians were rather interested in conditions of avoiding this effect reversal. Cox and Wermuth, J. R. Statist. Soc. B (2003) gave conditions based on conditional independences in the Gaussian case, and anticipate that similar conditions can be proven in the discrete case. The research task is to formulate such conditions, while understanding the notion of conditional independence and log-linear models, at least for three variables.

    Prerequisites:basic probability and graph theory
    Best for:students who are interested in statistics
    Professor: Dr. Marianna Bolla

    Assignment for the first week: read the two cited papers and and solve the exercise

  • Title:Packing caterpillars without common leaves

    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 degree sequences are tree degree sequences, that is, all degrees are positive and their sum is twice the number of vertices minus 2. Those degree sequences can always be realized by trees and also by some special trees called caterpillars (a tree is called a caterpillar if the vertices with degree more than one form a path.). Although we achieved significant progress in this topic, there are still several open questions. The proposed research project is to prove or disprove that tree degree sequences without common leaves always have edge disjoint caterpillar 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: see

  • Title: The rate of locally thin families

    Description:A family of subsets of an n-set is r-locally thin, if for every r of its member sets the ground set has at least one element contained in exactly one of them. Alon, Fachini and Körner proved fairly tight bounds for the maximum f(n,r) of such a family in case r is even. It is annoying, that for r odd, the gap between the upper and lower bounds is huge. It would be desirable to narrow the gap in this case, which is an open problem in the last almost 20 years.

    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 following papers