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Functional Analysis
Lecturer: Guofang Wang
Language: in English
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
Attention: Change of time and room!
Linear functional analysis, which is the subject of the lecture, uses concepts of linear algebra such as vector space, linear operator, dual space, scalar product, adjoint map, eigenvalue, spectrum to solve equations in infinite-dimensional function spaces, especially linear differential equations. The algebraic concepts have to be extended by topological concepts such as convergence, completeness and compactness.
This approach was developed at the beginning of the 20th century by Hilbert, among others, and is now part of the methodological foundation of analysis, numerics and mathematical physics, in particular quantum mechanics, and is also indispensable in other mathematical areas.
Linear Algebra I+II, Analysis I–III
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematical Logic
Lecturer: Markus Junker
Language: in German
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
This introductory course in mathematical logic consists of several parts. It the basics of predicate logic and a brief introduction to model theory and the axiom system as well as the axiom system of set theory. The aim of the lecture is to explain the recursion-theoretical content of the predicate calculus, in particular the so-called Peano-arithmetic and Gödel's incompleteness theorems.
Basic knowledge of mathematics from first semester lectures
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Probability Theory
Lecturer: Thorsten Schmidt
Language: in English
Lecture: Fr, 8-10h, HS II, Albertstr. 23b, Do, 12-14h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
The problem of axiomatising probability theory was solved by Kolmogorov in 1933: a probability is a measure of the set of all possible outcomes of a random experiment. From this starting point, the entire modern theory of probability develops with numerous references to current applications.
The lecture is a systematic introduction to this area based on measure theory and includes, among other things, the central limit theorem in the Lindeberg-Feller version, conditional expectations and regular versions, martingales and martingale convergence theorems, the strong law of large numbers and the ergodic theorem as well as Brownian motion.
necessary: Analysis I+II, Linear Algebra I, Elementary Probability Theory I
useful: Analysis III
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Topology
Lecturer: Heike Mildenberger
Assistant: Simon Klemm
Language: in German
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
A topological space consists of a basic set \(X\) and a family of open subsets of the basic set, which is called topology on \(X\). Examples over the basic sets \(\mathbb R\) and \({\mathbb R}^n\) are given in the analysis lectures. The mathematical subject \glqq{}Topology\grqq\ is the study of topological spaces and the investigation of topological spaces. Our lecture is an introduction to set-theoretic and algebraic topology.
Analysis I and II, Linear Algebra I
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.