german mathematics curricula
TRANSCRIPT
Tempus
German Mathematics Curricula
Saarland University
11.09.2014
Michael Bildhauer
Partial Differential Equations
Calculus of Variations
Geometric Analysis
Fluid Mechanics
Image Analysis
Personal Fields of Interest
Higher Mathematics for Engineers
Special courses in geometry and mathematical physics
Seminars for forthcoming teachers
Main Teaching Obligations
Long time guests at our chair (Martin Fuchs)
(DAAD, Humboldt Awards …)
Prof. Ladyshenskaya (St.Petersburg)
Prof. Osmolovskii (St. Petersburg)
Prof. Repin (St.Petersburg)
Prof. Seregin (St. Petersburg)
Prof. Shilkin (St. Petersburg)
Prof.Uraltseva (St. Petersburg)
Contact to Russia
Members of our group (Martin Fuchs)
P.D. Dr. Apushkinskaya (St.Petersburg)
Dr. Kinderknecht (Moskow)
Several visits in St. Petersburg
Contact to Russia
UdS Mathematics
Teaching:
Top rankings CHE
“Landespreis für Hochschullehre”
Research:
Two european research awards, Leibniz award
Two ICM-invited talks
Several further awards and projects
Strong representation of students
Exams in Mathematics
Staatsexamen46
Master14
Bachelor19
Promotio
n
7
„Bridges“ Math-Comp. Sci.
Matthias Hein
•Machine learning
•ERC Starting Grant
Joachim Weickert
• Image Analysis
•DFG Leibniz Pries
Frank-Olaf Schreyer
• Algebraic geometry, geometry and Computeralgebra
•Invited Speaker, ICM 2010
School: 12 years instead of formerly 13
No more obligations concerning military
Possibility for excellent pupils: Juniorstudium in school class 11 and 12
University: Bologna Process (Bachelor/Master instead of Diploma, Magister, Staatsexamen)
German Education, Main Changes
30 CP each semester (40 h per week)
1 CP: 30 hours of working
Beginners course: 9 CP (270 h per semester)
60 h lecture
30 h exercises
about 180 h homework
Bologna Process – Credit Points
4 h lectures per week
2 h exercises (small groups up to 20 students)
Homework (exercises) is corrected and discussed by students with some experience
Examinations (lecture + modul)
Standard Course
Analysis 1-3 (Calculus)
Lineare Algebra 1,2 (Linear Algebra)
Modellierung/Progammierung (Numerics)
Praktische Mathematik (Numerics)
Theorie und Numerik gewöhnlicher Differentialgleichungen (Ordinary Differential Equations)
Special Courses (leading to a thesis)
BSc Mathematics
Mathematics in Computer Sciences (3 x 4)
Mathematics in Engineering (4 x 4)
Mathematics in Sciences (2 x 4)
Mathematics in Biology (1 x 4)
MINT – STEM: Mathematical Beginners Courses
Foundations
Limits, uniform convergence ...
Power series
exp & … (question: definition of e^\sqrt{2} ?)
R^n (vector), complex numbers
Mathematical Beginners Coursesfor Engineers I
Matrices (definition, calculus, det …)
Linear mappings (representation by matrices, tensor …)
Continuity
Differentiability
Integrability
Numerical aspects
Taylor, Fourier series
Mathematical Beginners Coursesfor Engineers II
Linear ordinary differential equations -systems
Eigenvalues, Jordan …
Continuity in R^n
Curves
Differentiability in several variables
Integrability in several variables
Vectoranalysis: Theorems of Gauß and Stokes
Mathematical Beginners Coursesfor Engineers III
Part 1: Fourier/Laplace transform, Complex analysis
Part 2: Ordinary differential equation (existence, uniqueness …), numerical methods
Mathematical Beginners Coursesfor Engineers IV
Approx. 1000 pages of manuscript (including exercises and hints for solutions)
Maple etc.
Mathematical Beginners Coursesfor Engineers: Support
Computational Electromagnetics I Structure of Maxwell’s equations: de Rham complex.
Spatial discretization: cell / finite integration method.
Computational Electromagnetics II Finite element methods: Whitney forms.
Modelling techniques: time and frequency-domain.
Methods of Model-Order Reduction Balanced truncation.
Moment-matching.
Mathematical Courses – Chair of Electromagnetic Theory (Prof. Edlinger)
Systems Theory and Control Eng. I - III o.d.e., linear algebra, polynomial matrices.
Systems Theory and Control Eng. IV p.d.e., operational calculus, special functions, power
series, method of characteristics.
Systems Theory and Control Eng. V differential geometry, nonlinear dynamics, calculus of
variations, module theory …
Courses – Chair of Systems Theory and Control Engineering (Prof. Rudolph)
BSc+ MINT (STEM) (4 years)
Idea: Close the “gap” between school and university
Main point: How to start research by myself (structures of learning, understanding …)
Avoid failures in studying MINT (STEM).
New Developments inBologna Process
Universal knowledge in MINT (STEM) topics
Beginners courses in physical, chemical, engineering and computer sciences in the first year
Central course: Mathematics
Particular Bachelor courses after the first year
New Developments inBologna Process
Additional excercises (“Präsenzübungen”) during the first year (including additional CP)
Supported by “Stifterverband für die Deutsche Wissenschaft” and “Heinz Nixdorf Stifung”
New Developments inBologna Process