Education

Currently, the Bolyai Institute is undergoing major changes in the educational system: the former 10 semester programmes are gradually replaced by the 3-level system of the Bologna Process. As a first step in this direction, the Mathematics Bachelor programme was started in the Bolyai Institute in September 2006.

Study programmes in the Bologna System

Bachelor of Mathematics: The purpose of this 6 semester programme is to give a firm background in the mathematical sciences with special emphasis on areas necessary to pursue studies in applied mathematics and the teaching of mathematics. Students completing the programme receive a Bachelor degree in Mathematics. Traditionally, a mathematics degree is valued highly by a large variety of employers and thus its holder has a good chance of finding employment soon after graduation. Those who wish to study further may enter a Master’s programme or enroll in a special training programme in banking, finance, accounting or small business management.

After the first 2 semesters of the Bachelor programme, students may choose from three specializations: Pure Mathematics, Applied Mathematics and Teaching of Mathematics. These special directions of study prepare students for the entrance to the Mathematics MSc programmes. Choosing a specialization is not compulsory, however, it increases the chance of admittance to the Master programme. To help gifted students, some of the Bachelor programme courses are also available at the honours level.

Master Programmes in Mathematics: The Bolyai Institute is currently planning to start three Master programmes from September 2009: Applied Mathematics, Pure Mathematics and High School Teacher of Mathematics. These programmes will give a degree equivalent to the former 10 semester programmes continuing the long tradition of high quality instruction of advanced mathematics in the Bolyai Institute.

Study programmes in the 10 semester system

The former 10 semester programmes currently co-exist with the Mathematics Bachelor programme; they are being phased out gradually.

High School Teacher of Mathematics: The purpose of this 10 semester progamme is to train mathematics teachers who are well-prepared to explain and demonstrate the basic mathematical ideas and laws that appear in nature, engeneering, and society. Furthermore, they acquire a solid high quality knowledge of mathematics, and undergo a comprehensive theoretical and practical training in the teaching of mathematics.

Mathematics major: The purpose of this 10 semester programme is to train mathematicians who, on the one hand posess high quality theoretical knowledge of mathematics and thus are capable of working in the mathematical sciences, on the other hand are able to apply their knowledge in engineering, business, and statistics.

Applied Mathematics major: The purpose of this 10 semester programme is to train applied mathematicians who are capable of working efficiently in industry or in an interdisciplinary environment. During this program students gather knowledge in engineering mathematics, business, economics and in operations research. They become well-acquainted with the applications of modern mathematical methods and learn to recognize new problems in their fields of work. Furthermore, they become proficient in using computers, and learn to collaborate with engineers, economists, and scientists in solving economical and engineering problems.

Doctoral Programme in Mathematics: The doctoral (PhD) programme was started in 1993 at the Bolyai Institute among the first ones in Hungary. The purpose of this programme is to provide students deep and up-to-date knowledge of a mathematical discipline and enable them to pursue independent research in the mathematical sciences. The programme is based on a three year study period when students are required both to take advanced level graduate courses in mathematics and pursue research in their chosen special area. Doctoral students may choose from four major directions of study: Algebra, Analysis, Dinamical Systems and Stochastics, and Geometry and Combinatorics. At the end of the programme, students are required to take a final oral examination and write and defend a doctoral dissertation which contains original research.

Research Topics in The Bolyai Institute

Department of Algebra:
Universal algebra (Béla Csákány, Lajos Klukovits, László Szabó, Ágnes Szendrei), lattice theory (Gábor Czédli), theory of semigroups (Mária Szendrei, László Megyesi), theory of ordered sets (László Zádori), history of mathematics (Lajos Klukovits)

Department of Analysis:
Fourier analysis, orthogonal series, inequalities, approximation theory (László Leindler, József Németh, Zoltán Németh), functional analysis, linear operators in Hilbert spaces (László Kérchy), qualitative theory and applications of ordinary and functional differential equations, stability, oscillation, periodicity (László Hatvani, Géza Makay, József Terjéki, Mária Bartha, Róbert Vajda), Navier-Stokes equations (Mónika Van Leeuwen-Pollner), modern methods of the teaching of mathematics (József Kosztolányi, Zoltán Kovács)

Department of Geometry:
Harmonic analysis (Árpád Kurusa, Tibor Ódor), integral geometry (Árpád Kurusa), convex geometry (Ferenc Fodor, János Kincses, Tibor Ódor), discrete, combinatorial and computational geometry (János Kincses, Ferenc Fodor), polytopes (Gábor Gévay), finite geometries, nets (Gábor Nagy, György Kiss)

Department of Numerical and Applied Mathematics:
approximation theory, orthogonal polynomials and orthogonal systems of functions, special functions (Ferenc Móricz), complex analysis, Banach spaces, Jordan theory, numerical methods in quantum chemistry (László Stachó), infinite dimensional dynamical systems generated by functional differential equations, periodicity, bifurcation (Tibor Krisztin)

Department of Set Theory and Logic:
Combinatorics (Péter Hajnal, János Barát), complexity theory (Péter Hajnal), approximation theory, potential theory, harmonic analysis, orthogonal polynomials (Vilmos Totik), ergodic theory, fractals (László Szabó), history of mathematics (Antal Varga)

Department of Stochastics:
Asymptotic distributions in probability and statistics (Sándor Csörgõ, László Viharos), ergodic theory, statistical physics (András Krámli), boundary value problems of partial differential equations (Jenõ Hegedûs)

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