Budapest University of Technology and EconomicsCo-Host of ICEE 2008 July 28-31, 2008

Specialities of Bologna type Education in Hungary Peter MOSONDeputy DirectorInstitute of Mathematicswww.bme.hu , www.math.bme.hu(joint paper with Akos JOBBAGY)

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter MosonSUMMARY

European Union, BSc, MSc Hungary, Higher Education, Engineering programs Mathematics

Budapest University of Technology and Economics (BME) Leaflet about ICEE 2008 (Photos, anniversaries)

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter MosonEuropean Union, BSc, MSc.

EU: 15 + 10 (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: specialty of each country, tradition, special objectives etc.

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter Moson2. 1. Hungary, Higher Education, Engineering programs

Hungary, Central Europe, 100.000 Km,Population 10.000.000, capital Budapest, 2.000.000.

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). 2006 BSc, MSc. Change: German, Russian Anglo-Saxon.

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter Moson2. 2. Hungary, Higher Education, Engineering programs

Engineering programs. BSc level (accredited). Double objective :

prepare for MSc studies, 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).

BSc Programs at the BME

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 TrainingFaculty of Civil EngineeringFaculty of Mechanical Engineering

Faculty of ArchitectureFaculty of Chemical Engineering

Faculty of Electrical Engineering and InformaticsFaculty of Transportation Engineering

Faculty of Natural Sciences

Faculty of Economic and Social Sciences

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter Moson3. 1. Mathematics General principlesTraditional 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) 4 semesters (22/24)

Mathematics in BSc engineering training (Hours/Credits)MathA1 (6/6), MathA2 (6/6), MathA3 (4/4) 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

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter Moson3. 2. 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

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter Moson3. 3. Mathematics MethodologyStrong 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.

Budapest University of Technology and Economics (BME)

1782 Institutum Geometricum -Hydrotechnicum2000- Budapest University of Technology and Economics

8 Faculties, 90 Departments

24 000 Students, incl. 834 PhD students18 BSc and a large number of Master Programs, 15 Doctorate SchoolsAcademic Staff: 1314, with scientific qualification: 680Faculties: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)

Nobel laureates of BMEDnes GBOR (1900 - 1979) holography, in 1971Jen WIGNER (1902 - 1995)theoretical physics, in 1963

Gyrgy OLH (b:1927)carbonic chemistry, in 1994Research @ higher education

Former students of BMETdor (Theodore) von KRMNAeronautical Engineer & Mathematician(1881-1963)

Leo SZILRD Physicist (1898-1964) Ern RUBIK " cube " (1944-)

ICEE 2006, San Juan, Puerto Rico, USASpecialities of Bologna type Education in Hungary , Peter Moson5. Leaflet about ICEE 2008

Photos (3+2)Budapest, Danube, BME, Gellrt Hill.2-4. Central building.5. Informatics building.

Anniversaries (2006-2007)Central building (100 years)1956 50 years225 years of BME final event: ICEE 2008

Technical University of Budapestwww.bme.hu - tel.: (36-1) 463-1111 fax: (36-1) 463-2220Technical University of BudapestThe surroundings of the Budapest University of Technology and Economicswww.bme.hu - tel.: (36-1) 463-1111 fax: (36-1) 463-2220Technical University of BudapestOpening Ceremony of the Academic year 2004/2005www.bme.hu - tel.: (36-1) 463-1111 fax: (36-1) 463-2220Technical University of BudapestCentral Building of the University (designed by A. Hauszmann, 1909)www.bme.hu - tel.: (36-1) 463-1111 fax: (36-1) 463-2220Technical University of BudapestBuilding of Informaticawww.bme.hu - tel.: (36-1) 463-1111 fax: (36-1) 463-2220