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Bologna Process. 1998 Sorbonne Declaration1999 Bologna Declaration2001 Prague2003 Berlin2005 Bergen2007 London . Sorbonne 1998. Two cycles, u/g and graduate (Dr or M)Credit transfer and semestersLanguage proficiencyStudents should spend at least one semester abroadSigned by France, Germany,
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1. Mathematics HE in Europe
Bologna and some snapshots
David Salinger
2. Bologna Process 1998 Sorbonne Declaration
1999 Bologna Declaration
2001 Prague
2003 Berlin
2005 Bergen
2007 London
3. 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
4. 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
5. Prague 2001 Not much change, but brought Rectors’ organisation (European Universities’ Association) and student organizations on board.
Added lifelong learning
33 Countries
6. 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)
7. 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
8. 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.
9. Implementation Most European Countries have put in place a Bachelor – Master– Doctorate system.
Still in transition
Grandes Ecoles untouched in France
10. 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.
11. Bologna = no change? 2+3=2+2+1=5 = 3+2 “=“ 3+1
But students get a degree after 3 years.
12. 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)
13. 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.
14. 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.
15. 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.
16. 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)
17. 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.
18. Heidelberg continued Analysis: includes Lebesgue integral, Stokes theorem, Differential geometry, Fourier series
19. 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.