This course is designed in the style of
the Hungarian "TDK" system, allowing advanced undergraduates to
become acquainted with research methods 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 two individual reports (as explained below) and
ideally a research paper, however that is not expected to achieve given the time constraints.
In addition, during the semester there will be opportunities
to present your work as well.
Participating in the research course 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 and
several 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
Description: The subject is a new, very fast developing area of extremal graph
theory. The basic problem is to determine/estimate the maximum number
ex(n,H,F) of copies of H in a graph of n vertices not containing F as a subgraph.
(If H is just one edge then we get classical extremal graph theory problems.)
There are cases that are particularly interesting:
Description: click here
Prerequisites:
Although some background in convex geometry and combinatorics is helpful, we will start the semester with learning all the necessary tools.
Thus, it is going to be an excellent opportunity to study convexity, apply combinatorial ideas, and possibly use analytical and probabilistic tools.
Professor: dr Gergely Ambrus
Contact:
Qualifying problems:: See the Qualifying Problems 1, 2 and 3
in the description
Description: Click here
Prerequisites: basic combinatorics (elementary graph theory,
combinatorics) and algebra (elementary linear algebra, finite fields)
Best suitable for students who are interested in computer science and
combinatroics and are comfortable with using algebraic methods to
solve combinatorial and computer science problems.
Professor: dr Istvan Miklos
Contact:
Qualifying problems::
Click here
Description: Click here
Prerequisites: basic graph theory, linear algebra
Professor: dr Attila Sali
Contact:
Qualifying problems:: see within the
description
Description: We will go over background material, then turn to open problems. Here is the plan:
We will be using handouts and notes. Reference for the first few lectures can be found in http://web.cs.elte.hu/summerschool/2019/egyeb/ssm2019.pdf (pages 62-78). In addition, some chapters of Grid homology for knots and links (Ozsvath-Stipsicz-Szabo) (AMS Mathematical Surveys and Monographs, Volume 208) will be used.