1 Budapest University of Technology and Economics Co-Host of ICEE 2008 – July 28-31, 2008

Specialities of Bologna type Education in Hungary Peter MOSON Deputy Director Institute of Mathematics (joint paper with Akos JOBBAGY)

3 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson SUMMARY 1. European Union, BSc, MSc 2. Hungary, Higher Education, Engineering programs 3. Mathematics 4. Budapest University of Technology and Economics (BME) 5. Leaflet about ICEE 2008 (Photos, anniversaries)

4 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson 1.European Union, BSc, MSc. EU: (Hungary) +2 (2007) = 27 countries EU Higher Education, Bologna Declaration (1999) – 10 years Common European elements: Easily readable and comparable degrees, Two main cycles (BSc, MSc, undergraduate, graduate), System of Credits (ECTS – European Credit Transfer system). Mobility (for students, teachers, researchers). Realization: s pecialty of each country, tradition, special objectives etc.

5 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson Hungary, Higher Education, Engineering programs Hungary, Central Europe, Km², Population , capital Budapest, Higher education. Ca. 25 institutions (state run). Autonomy – Ministry – Hungarian Accreditation Board. Increase of the number of students (1990 – 15% ⇒ 2006 – 50% of the corresponding generation) Credit system – ECTS has been introduced. Dual HE: colleges min. 180, universities min. 300 credits (other: high level professional education ⇒ doctorate schools, 120) – BSc, MSc. Change: German, Russian ⇒ Anglo-Saxon.

6 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson Hungary, Higher Education, Engineering programs Engineering programs. BSc level (accredited). Double objective : (i)prepare for MSc studies, (ii) give competencies which can be directly used in the economy. The length of the training is variable : bac+3 (180 credits, e.g. mathematics); bac+3,5 (210 credits, e.g. mechanics); bac+4 (e.g. civil engineering). The total (BSc+MSc) length is ≦ 5.5 years(330 credits).

7 Civil Engineering Mechanical Engineering Energy Engineering Industrial Design Engineering Mechatronics Architecture Chemical Engineering Bioengineering Environmental Engineering Electrical Engineering Computer Science and Engineering Transportation Engineering Management in Engineering Mathematics Physics Applied Economics Business and Management Technology Teacher Training BSc Programs at the BME Faculty of Civil Engineering Faculty of Mechanical Engineering Faculty of Architecture Faculty of Chemical Engineering Faculty of Electrical Engineering and Informatics Faculty of Transportation Engineering Faculty of Natural Sciences Faculty of Economic and Social Sciences

8 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson Mathematics –General principles Traditional strength of Hungarian HE – strong theoretical knowledge – preserve – double objective Mathematics in ‘5 year’ engineering training (Hours/Credits) Math1 (6/7), Math2 (6/7), Math3 (6/6), Math4 (4/4) Σ 4 semesters (22/24) Mathematics in ‘BSc’ engineering training (Hours/Credits) MathA1 (6/6), MathA2 (6/6), MathA3 (4/4) Σ 3 semesters (16/16) The total number of credit points of mathematics in the BSc, MSc courses cannot be less than it used to be in the corresponding 5 year training

9 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson Mathematics – Contents (BSc) Mathematics A1 – Calculus: Algebra of planar, spatial vectors. Complex numbers. Infinite sequences. Real functions. Continuity. Derivation. Mean value theorems, l'Hospital's rule, Taylor theorem. Maximum, minimum. Graphs. Riemann integral, Newton-Leibniz theorem. Applications. Mathematics A2 – Vector functions: Matrices, determinant. Systems of linear equations. Linear space, basis. Linear transformations, eigenvalues, eigenvectors. Infinite series. Sequences and series of functions. Taylor, Fourier series. Functions of several variables. Vector-vector functions. Derivation, integration. Mathematics A3 depends on the engineering program. It may contain: complex functions; Laplace transformation; more vector analysis, optimization, ordinary and partial differential equations, probability theory, statistics etc. - RISK

10 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson Mathematics – Methodology Strong knowledge of basic definitions, theorems, methods. Common learning material for all (Hungarian and foreign language) training. Book: Thomas' Calculus, 11th ed. Addison Wesley 2004 (Hungarian translation). Less theoretical, more application oriented lectures. More personal contact with the students (less than 30 students at practical lectures; regular homework; system of permanent consultations etc.). Wide use of mathematical software, modern ICT.

11 Budapest University of Technology and Economics (BME) 1782 Institutum Geometricum -Hydrotechnicum Budapest University of Technology and Economics  8 Faculties, 90 Departments Students, incl. 834 PhD students 18 BSc and a large number of Master Programs, 15 Doctorate Schools Academic Staff: 1314, with scientific qualification: 680 Faculties:  Civil Engineering (1782)  Mechanical Engineering (1871)  Architecture (1873)  Chemical Engineering (1873)  Electrical Engineering and Informatics (1949)  Transportation Engineering (1951)  Natural Sciences (1998)  Economic and Social Sciences (1998)

12 Nobel laureates of BME Dénes GÁBOR ( ) holography, in 1971 Jenő WIGNER ( ) theoretical physics, in 1963 György OLÁH (b:1927) carbonic chemistry, in 1994 higher education

13 Former students of BME Tódor (Theodore) von KÁRMÁN Aeronautical Engineer & Mathematician ( ) Leo SZILÁRD Physicist ( ) Ernő RUBIK " cube " (1944-)

14 ICEE 2006, San Juan, Puerto Rico, USA Specialities of Bologna type Education in Hungary, Peter Moson 5. Leaflet about ICEE 2008 Photos (3+2) 1.Budapest, Danube, BME, Gellért Hill Central building. 5. Informatics building. Anniversaries ( ) 1.Central building (100 years) – 50 years years of BME – final event: ICEE 2008

15

16

17

18

19