Mathematics HE in Europe Bologna and some snapshots David Salinger

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

Sorbonne Two cycles, u/g and graduate (Dr or M) 2.Credit transfer and semesters 3.Language proficiency 4.Students should spend at least one semester abroad Signed by France, Germany, Italy, UK

Bologna 1999 Creation of a European HE Area by Common 2 cycle system 2.Credit transfer 3.Mobility of Staff and Students 4.Quality assurance 5.European dimension 29 European Countries

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 1.Added the third, doctoral cycle. 2.All countries should ratify the Lisbon Convention (recognition of qualifications) 3.From 2005 all students should receive a diploma supplement, free of charge 4.Overarching Qualifications Framework desired, but primary responsibility lies with the institution 40 Countries (incl.Russia)

Bergen Partnership with HE Institutions 2.Specifications for Cycles 1 and 2 3.(Part of) Salzburg declaration approved for Cycle 3 4.Descriptors for the European Higher Education Area Qualifications Framework agreed 45 Countries

Not 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 Most European Countries have put in place a Bachelor – Master– Doctorate system. Still in transition Grandes Ecoles untouched in France

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? 2+3=2+2+1=5 = 3+2 “=“ 3+1 But students get a degree after 3 years.

Maths Many different traditions of teaching maths but 3 generalities 1.Greater proportion of (possibly directed) examples classes, maybe more than lectures 2.Greater proportion allowed to fail 3.‘Maths’ often means ‘Pure Maths’, at least to begin with (e.g. Spain)

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

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 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 1 st two years at university. Measure and Probability is a standard component.

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

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.