Mathematics HE in Europe

Mathematics HE in Europe : Mathematics HE in Europe Bologna and some snapshots David Salinger

Bologna Process : Bologna Process 1998 Sorbonne Declaration 1999 Bologna Declaration 2001 Prague 2003 Berlin 2005 Bergen 2007 London

Sorbonne 1998 : Sorbonne 1998 Two cycles, u/g and graduate (Dr or M) Credit transfer and semesters Language proficiency Students should spend at least one semester abroad Signed by France, Germany, Italy, UK

Bologna 1999 : Bologna 1999 Creation of a European HE Area by 2010 Common 2 cycle system Credit transfer Mobility of Staff and Students Quality assurance European dimension 29 European Countries

Prague 2001 : Prague 2001 Not much change, but brought Rectors’ organisation (European Universities’ Association) and student organizations on board. Added lifelong learning 33 Countries

Berlin: the process gathers pace : Berlin: the process gathers pace Added the third, doctoral cycle. All countries should ratify the Lisbon Convention (recognition of qualifications) From 2005 all students should receive a diploma supplement, free of charge Overarching Qualifications Framework desired, but primary responsibility lies with the institution 40 Countries (incl.Russia)

Bergen 2005 : Bergen 2005 Partnership with HE Institutions Specifications for Cycles 1 and 2 (Part of) Salzburg declaration approved for Cycle 3 Descriptors for the European Higher Education Area Qualifications Framework agreed 45 Countries

Not 3+2+3 : Not 3+2+3 The cycles are specified in terms of ECTS credits which themselves are defined a little vaguely in terms of time and learning outcomes. In practice this means the first cycle can last 3 to 4 years, the second 1 to 2 and the third 3 to 4.

Implementation : Implementation Most European Countries have put in place a Bachelor – Master– Doctorate system. Still in transition Grandes Ecoles untouched in France

Transition : Transition Each country has its own traditions, so I can only caricature. I shall stick to Western Europe. Broadly the old systems were for a nominal 4 or 5 years for the first degree, but students would take longer: in Germany much longer.

Bologna = no change? : Bologna = no change? 2+3=2+2+1=5 = 3+2 “=“ 3+1 But students get a degree after 3 years.

Maths : Maths Many different traditions of teaching maths but 3 generalities Greater proportion of (possibly directed) examples classes, maybe more than lectures Greater proportion allowed to fail ‘Maths’ often means ‘Pure Maths’, at least to begin with (e.g. Spain)

France : France Students taught at school in ‘preparatory’ classes for stiff entry competition. Bac + 2 2 Maths + 1 Physics Syllabus: Linear algebra, including dual spaces, bilinear maps; reduction of matrices; Cayley-Hamilton Theorem but not Jordan Canonical form.

Syllabus (cont) : Syllabus (cont) Euclidean and affine geometry; conics; inner-product spaces (both real and complex) as far as Bessel’s inequality; reduction of quadratic forms. Analysis and Differential Geometry going as far as Fréchet derivative in normed spaces. Completeness, compactness. Regulated integral. Power series, Fourier series. Linear and non-linear differential equations. Curves and surfaces.

Consequences : Consequences Students from Grandes Ecoles attend university courses. Hence some syllabuses from year 3 take account of the classes preparatoires syllabus. Year 3 can be tough for students who spend 1st two years at university. Measure and Probability is a standard component.

L(MD) at Paris-Sud : L(MD) at Paris-Sud 6 routes: Economics-Maths, Maths Pure and Applied, Maths and Applications, Algebra-Analysis-Geometry(for teachers), Biomath & Biostats, Maths-Informatics High proportion of pure maths to other. Measure and Probability in year 3 in 1 path only Language tuition is compulsory (5 ECTS)

Germany : Germany Vor-Diplom + Diplom Now Bachelor + Master Heidelberg: vor-diplom year 1 basic study: Analysis 1-2, Linear Algebra 1-2 (4 hrs lecture + 3 hours class each per week), Programming course (4 hours); Semester 3 Analysis 3, Practical Maths, Proseminar (2 hrs) . Oral exams.

Heidelberg continued : Heidelberg continued Analysis: includes Lebesgue integral, Stokes theorem, Differential geometry, Fourier series

Is Germany Bologna compliant? : Is Germany Bologna compliant? In principle but not in practice? These are but examples: with 45 Bologna signatories, there’s far more than can be said in 30 minutes.