Instructor: Dr. Péter JUHÁSZ
Course Prerequisits: none
The aim of the course is two-fold.
On one hand, you will learn elements of a very special "Hungarian style" method of nurturing mathematical talent developed for age groups 12-18. The method is discovery based and is fondly called by many mathematicians "the Pósa method", after the developer, Lajos Pósa.
Here is what a former BSM student says about Lajos Pósa:
"For me, it was very amazing to learn that he had been such a gifted mathematician as a young lad, and in spite of his strengths (or maybe because of them) he instead dedicated himself to giving other kids and students the same taste of discovery. There's a saying that 'there's no golden road to the truth' but I think that the Posa method of teaching is a one of the most pleasant journey's one can take to get there."
You can also read an account of Paul Erdôs' recollection about the young Pósa here.
This method, which is a culmination of Hungarian traditions in mathematics education,
has been applied at more than 250 special weekend and summer math camps since 1992. Its long term effects
participants earning 27 Gold, 42 Silver and 26 Bronze Medals at various International Mathematical Olympiads. Many of
the first generation students, such as
Benedek Valkó or
are established academics by now.
On the other hand, you will have the opportunity of experiencing mathematics as a subject of this method, since during the course oftentimes you will take the role of participants of the math camps.
Thus classes will be very similar to a problem solving seminar. The choice of mathematical areas we develop will depend on students' preference and background. Special emphasis will be put on pursuing paths laid out by student's questions.
You will meet problems given to gifted kids, in the form of group work, individual work, team play, quick questions, etc. always keeping the philosophy of the Pósa method in mind: " mathematics is not the private affair of a selected few, but the fun of discovering and autonomous thinking is everyone's right."
NOTE: If you are thinking about pursuing a career in academics, this course may be very useful for you
in both as developing your teaching and (math) communication techniques (TA and further) as well as
improving your problem solving skills.
You can read previous students' opinions about the method and course here. (Students' opinions were asked during the Semester.)
Course ObjectivesThe aim of this course is to introduce students to the "Pósa method" i.e. basics of making gifted kids discover mathematics.
In particular, after finishing this course, participants
- will be able to solve problems which have been designed for gifted high school students;
- will have a detailed conception what a "thread of problems" means and how to create one's own;
- will learn how to create a web of ideas inside the kids' head, often placing the methods or ideas required to solve the problem unnoticed, so that in the deciding moment everything should come together to make the discovery possible;
- will learn to give appropriate hints if the discovery is not happening;
- will know what to do if despite of all efforts the discovery is simply not happening;
- as well as what to do if some kids find the problems that are just right for the others too easy;
- will learn to ask sensible and interesting questions after solving a problem and how to make this an internal ability and ambition;
- will learn how to come up with good problems.
I am planning to discuss the following topics: proofs of impossibility, mathematical induction, interesting constructions, two-player-games, special real functions, etc.
As was mentioned above: actual mathematics topics to be discussed will be decided together — it is part of the method that we adapt to the abilities, interests and possibilities defined by the group.
AssessmentsMid-term exam. This exam will contain problems we discuss during the previous lessons. Students do not need their own ideas in problem solving, they have to show that they understood the problems and their solutions, and they can write down the solutions correctlzy. 40 points.
Final exam. This exam contains new problems, but these are similar to those we discuss during the lessons. Students do need new ideas in problem solving, they have to show that they can write down the solutions of unknown problems correctly. 60 points.
Homeworks One homework problem will be assigned every week. Students will have seven days to complete their solutions and submit them in writing. There will be 12 such assignments, each worth 4 points. Because the first two will be only for practice, the available total is 40 points.