COURSE DESCRIPTION

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

COURSE LOGISTICS

• Who can participate? The list of research topics and professors proposing them is posted below. In addition to the problem description, each professor gives introductory problems for interested students to solve under "Qualifying problems". If you are considering participating, submit your solutions to the qualifying problems of the research problem that you would like to work on August 27th, Sunday, the latest directly to the professor whose problem you are interested in.
  
  Enrollment will be based on solutions submitted to qualifying problems to professors and your transcript and reference letter submitted as your application materials to the American office. Decisions on admittance to the research group will be made by September 1st.
• Which topics will actually be offered ("stay alive")? Of the initially offered research problems those will be offered eventually, for which a group of students sign up and are admitted to the program. Ideally, a group would consist of 3-5 students.
• Course work: weekly meetings & presentation. The research groups will meet at least 2 times weekly, two hours each. (At least) one meeting is devoted to group work, without the professor, when you discuss the problem and possible solutions with your student group. Another (one) meeting of the week is spent with your professor who will monitor your group's progress. (Depending on progress and other factors, you may have more than one meeting with the professor, on a given week.)
  
  Week 3 - Milestone 1: The first 2.5 weeks of the course are spent discussing, gathering and studying necessary background information for your problem. On teh 3rd week, during colloquium, each research group will have to present the problem they are working on in a 20-minute talk, at a "mini workshop" organized for all research participants, their professors and everyone else interested.
  In addition, each student wishing to participate in a research group may have to write a summary of the status of the research project — on their own, at the professor's request. The summary should consist of stating the problem/aims of the research group, plans on tackling the problem, as well as an outline of work done during the first 2.5 weeks with a write up of results (if any) achieved by that time.
  

  Professors evaluate progress and final enrollment decisions are made, based on the written summary (if available), 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 only class where a student wishing to take the course may not be able to, since it is at the discretion of the professor to let students become members of their research group.

  Week 7 - Milestone 2: students receive "midterm evaluation grades" (MAG) and continuance is determined. Grading is done on an A-F scale.

  The MAG depends on all work up to that point as well as a self/group evaluation sent out to all group members (individually). If necessary, each student may be 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.)

  Note that only students meeting each of the following criteria may continue working on research after week 7 (all other students will have to drop research or will receive an "Audit" for the course):
  

  • the midterm assessment grade for the research course is at least A-
  • their grades in all of their other mathematics courses is at least B
  • their GPA in all math courses is at least 3.5 (using the A+ 4.3, A 4 pont, A- 3.7, B+ 3.3, B 3, pont conversion).

  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.
• Course work: writing a paper. Depending on results obtained all work will be summarized in a paper/research report.

RESEARCH PROBLEMS PROPOSED — FALL 2023.