Summer School in Mathematics at the Eötvös Loránd University (ELTE Budapest)

The Institute of Mathematics of the Eötvös University is organizing a
one week long summer school in mathematics entitled Higher mathematics through problem solving”.

Although mathematics is much more than just going through a series of drill problems — posing new questions, building new theories, applying the existing tools to other areas of science are just as important –, problem solving remains one of the most important parts of mathematics education.

A new definition, a theorem or even whole theories are best understood when we are guided to discover these results through our own efforts. Carefully chosen problems will lead us to understand these results without feeling the difficulties of reading a “dry theorem”, and we will also better appreciate the conditions which give the proper setting of a mathematical statement. By getting trained in problem solving, we will also get a training for doing research.

Problem solving competitions have a long tradition in Hungary. The first high school competitions were established more than 120 years ago and they served as a model to many nowadays existing competitions throughout the world. And the problem solving tradition was extended to university education, too. Most math courses taught at universities come together with a practical class where individual problem solving skills are developed, parallel to the theory, explored in the lectures. Perhaps one of the most challenging math competitions in the world is the Miklós Schweitzer Memorial competition, held annually: in this open book competition students have ten days to solve 10 to 12 problems, some of which are of research level difficulty.

During the summer school there will be problem solving sessions in algebra, number theory, combinatorics, geometry, analysis and probability theory, each of them concentrating on one or two special topics. Participants will get a brief introduction into the necessary notions and results and then individual work will follow, with the guidance of the lecturers and their assistants.

Lecturers and lecture titles:

  • Márton Elekes: The Banach-Tarski paradox
  • Péter Frenkel: Shannon capacity of graphs
  • Róbert Freud: Complete disorder is impossible, The power of powers, Matchmakers
  • Balázs Gerencsér: Random walks and ergodicity
  • Bence Csajbók, Tamás Héger: Algebraic methods for finite geometric problems
  • Dávid Kunszenti-Kovács: What is typical behaviour? Examples and counter-examples in analysis

The school will be held between June 6th – June 10th, 2017, at the
Institute of Mathematics, Budapest (Hungary).

Deadline for applications is May 31st 2017. Information for how to
apply can be found at

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