This document provides an overview of mathematics curricula and courses at Saarland University in Germany. It describes the university's main fields of interest including partial differential equations, calculus of variations, and geometric analysis. It also outlines the university's teaching obligations, contact with universities in Russia, and awards and achievements of the mathematics department. Standard course structures are explained, including courses for bachelor's and master's degrees in mathematics as well as courses in mathematics for other STEM fields.

1. Tempus
German Mathematics Curricula
Saarland University
11.09.2014
Michael Bildhauer

2.  Partial Differential Equations
 Calculus of Variations
 Geometric Analysis
 Fluid Mechanics
 Image Analysis
Personal Fields of Interest

3. Higher Mathematics for Engineers
Special courses in geometry and mathematical
physics
Seminars for forthcoming teachers
Main Teaching Obligations

4. 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

5. Members of our group (Martin Fuchs)
P.D. Dr. Apushkinskaya (St.Petersburg)
Dr. Kinderknecht (Moskow)
Several visits in St. Petersburg
Contact to Russia

6. 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

7. Exams in Mathematics
Staatsexamen
46
Master
14
Bachelor
19
Promotio
n
7

8. „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

9.  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

10.  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

11.  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

12. 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

13.  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

14.  Foundations
 Limits, uniform convergence ...
 Power series
 exp & … (question: definition of e^sqrt{2} ?)
 R^n (vector), complex numbers
Mathematical Beginners Courses
for Engineers I

15.  Matrices (definition, calculus, det …)
 Linear mappings (representation by matrices,
tensor …)
 Continuity
 Differentiability
 Integrability
 Numerical aspects
 Taylor, Fourier series
Mathematical Beginners Courses
for Engineers II

16.  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 Courses
for Engineers III

17.  Part 1: Fourier/Laplace transform, Complex
analysis
 Part 2: Ordinary differential equation
(existence, uniqueness …), numerical
methods
Mathematical Beginners Courses
for Engineers IV

18.  Approx. 1000 pages of manuscript (including
exercises and hints for solutions)
 Maple etc.
Mathematical Beginners Courses
for Engineers: Support

19.  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)

20.  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)

21.  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 in
Bologna Process

22.  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 in
Bologna Process

23.  Additional excercises (“Präsenzübungen”)
during the first year (including additional CP)
 Supported by “Stifterverband für die
Deutsche Wissenschaft” and “Heinz Nixdorf
Stifung”
New Developments in
Bologna Process