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
At this point professors evaluate progress and final enrollment decisions are made, based on the written summary, oral presentation and work done during the first 2.5 weeks.
Please, note that some research groups may die out or be discontinued after the 3rd week, so plan accordingly. Also, the research class is the oly class where a student wishing to take the course may not be able due, since it is at the discretion of the professor to let students become members of their research group.
Week 7 - Milestone 2: at week 7 (just like at week 3), each student is required to submit a (relatively short) report on the work in progress, to their professor. (Thus the report should include a eg description of the problem, as well as the methods used in tackling the it and a write-up of results, if any.)
Based on all work up to that point and the written report, students receive "midterm evaluation grades".
Week 13 - Milestone 3:: Work continues throughout the semester. At the 13th week each group should present their results at a "Preliminary report session" organized for all RES participants, their professors and everyone else interested.
Grading is done on an A-F scale.
Write up of results is continuous and oftentimes streches to after the semester is over.Description: The subject is a new, fast developing area of extremal graph theory. There are two types of basic problems:
The various constructions of extremal graphs make the subject particularly interesting. An interesting direction is the combination of these basic type problems: what is the maximum number of copies of H in an n vertex planar graph not containing F as a subgraph.
The starting point of this subject was the classical result that the maximum number of edges in a planar graph of n vertices is 3n-6 if n> 3. Many years later, Dowden proved that the maximum number of edges in a planar graph not containing any 4-cycle is at most 12(n-2)/7 and it is sharp for infinitely many values of n. (For details, see C. Dowden, Extremal C_4-free/C_5-free planar graphs, J. Graph Theory 83 (2016), 213– 230.) We plan to consider problems of this type when the graphs F and H are small.
Prerequisites: graph theory and combinatoricsDescription: Click here.
Prerequisites:We shall mostly use graph theoretic and combinatorial methods but
geometric intuition is also useful. Since some of the
rigidity properties are defined by the ranks of certain
matrices, linear algebra tools may also be needed.
Professor:Tibor Jordan
Contact:tibor.jordan@ttk.elte.hu
Qualifying problems:Solve at least four out of the
five exercises at the end of this document.