Detailed information can be found in the course descriptions and in the module handbooks (in German only).
Further Chapters in Analysis
Lecturer: Nadine Große
Assistant: Jonah Reuß
Language: in German
Lecture: Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
12.02., 08:30-11:30, GHS Chemie (HS -1028), Flachbau Chemie, Albertstr. 21
Sit-in exam (resit) 09.04., 08:30-11:30, HS II, Albertstr. 23b
\textit{Multiple integration:} Jordan content in \(\mathbb R^n\), Fubini's theorem, transformation theorem, divergence and rotation of vector fields, path and surface integrals in \(\mathbb R^3\), Gauss' theorem, Stokes' theorem.\ \textit{Complex analysis:} Introduction to the theory of holomorphic functions, Cauchy's integral theorem, Cauchy's integral formula and applications.
Required: Analysis~I and II, Linear Algebra~I and II
Further Chapters in Analysis
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Algebraic Number Theory
Lecturer: Abhishek Oswal
Assistant: Andreas Demleitner
Language: in English
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Short description of topics: Number fields, Prime decomposition in Dedekind domains, Ideal class groups, Unit groups, Dirichlet's unit theorem, local fields, valuations, decomposition and inertia groups, introduction to class field theory.
Required: Algebra and Number Theory
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Patrick Dondl
Assistant: Oliver Suchan
Language: in German
Lecture: Mo, 12-14h, HS Rundbau, Albertstr. 21, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
19.02., 10:15-11:45, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 28.04., 10:00-11:30, SR 226, Hermann-Herder-Str. 10
Lebesgue measure and measure theory, Lebesgue integral on measure spaces and Fubini's theorem, Fourier series and Fourier transform, Hilbert spaces. Differential forms, their integration and outer derivative. Stokes' theorem and Gauss' theorem.
Required: Analysis I and II, Linear Algebra I
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: in German
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Differential geometry, especially Riemannian geometry, deals with the geometric properties of curved spaces. Such spaces also occur in other areas of mathematics and physics, for example in geometric analysis, theoretical mechanics and the general theory of relativity.
Required: Analysis~I–III, Lineare Algebra~I and II \ Recommended: Analysis of Curves and Surfaces ("Kurven und Flächen"), Topology
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Guofang Wang
Assistant: Christine Schmidt, Xuwen Zhang
Language: in German
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
A large number of different problems from the natural sciences and geometry lead to partial differential equations. Consequently, there can be no talk of an all-encompassing theory. Nevertheless, there is a clear picture for linear equations, which is based on three prototypes: the potential equation \(-\Delta u = f\), the heat equation \(u_t - \Delta u = f\) and the wave equation \(u_{tt} - \Delta u = f\), which we will examine in the lecture.
Required: Analysis III \ Recommended: Complex Analysis ({\em Funktionentheorie})
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Sören Bartels
Assistant: Vera Jackisch
Language: in English
Lecture: Di, Do, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.
Required: Analysis~I and II, Linear Algebra~I and II as well as knowledge about higher-dimensional integration (e.g. from Analysis~III or Extensions of Analysis) \ Recommended: Numerics for differential equations, Functional analysis
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: David Criens
Assistant: Eric Trébuchon
Language: in German
Lecture: Di, Mi, 16-18h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
24.02., 14:00-16:00, HS II, Albertstr. 23b
Complex analysis deals with functions \(f : \mathbb C \to \mathbb C\) , which map complex numbers to complex numbers. Many concepts of Analysis~I can be directly transferred to this case, e.\,g. the definition of differentiability. One might expect that this would lead to a theory analogous to Analysis~I but much more is true: in many respects you get a more elegant and simpler theory. For example, complex differentiability on an open set implies that a function is even infinitely often differentiable, and this is further consistent with analyticity. For real functions, all these notions are different. However, some new ideas are also necessary: For real numbers \(a\), \(b\) one integrates for \[\int_a^b f(x) \mathrm dx\] over the elements of the interval \([a, b]\) or \([b, a]\). However, if \(a\), \(b\) are complex numbers, it is no longer so clear clear how such an integral is to be calculated. One could, for example, in the complex numbers along the line that connects \(a, b \in \mathbb C\), or along another curve that leads from \(a\) to \(b\). Does this lead to a well-defined integral term or does such a curve integral depend on the choice of the curve?
Required: Analysis I+II, Linear Algebra I
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Set Theory – Independence Proofs
Lecturer: Maxwell Levine
Assistant: Hannes Jakob
Language: in English
Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
How does one prove that something cannot be proved? More precisely, how does one prove that a particular statement does not follow from a particular collection of axioms?
These questions are often asked with respect to the axioms most commonly used by mathematicians: the axioms of Zermelo-Fraenkel set theory, or ZFC for short. In this course, we will develop the conceptual tools needed to understand independence proofs with respect to ZFC. On the way we will develop the theory of ordinal and cardinal numbers, the basics of inner model theory, and the method of forcing. In particular, we will show that Cantor's continuum hypothesis, the statement that \(2^{\aleph_0}=\aleph_1\), is independent of ZFC.
Required: Mathematical Logic
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Annette Huber-Klawitter, Amador Martín Pizarro
Assistant: Christoph Brackenhofer
Language: in German
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Semi-algebraic geometry is about properties of subsets of \(**R**^n\), which are given by inequalities of the form [ f(x1, \dots, xn)\geq 0] for polynomials \(f\in**R**[X_1,\dots,X_n]\).
The theory has many different facets. On the one hand, it can be seen as a version of algebraic geometry over \(\mathbf{R}\) (or even more generally over so-called real closed fields). On the other hand, the properties of these fields are a central tool for the model-theoretic proof of Tarski-Seidenberg's theorem on quantifier elimination in real closed fields. Geometrically, this is interpreted as a projection theorem.
From this theorem, a proof of Hilbert's 17th problem easily follows, which was solved by Artin in 1926.
\textit{Is every real polynomial \(P \in \mathbf{R}[x_1, \dots, x_n]\), which takes a non-negative value for every \(n\)-tuple in \(\mathbf{R}^n\), a sum of squares of rational functions (i.e., quotients of polynomials)?}
In the lecture, we will explore both aspects. Necessary tools from commutative algebra or model theory will be discussed according to the prior knowledge of the audience.
Required: Algebra and Number Theory \ Recommended: Knowledge in commutative algebra and algebraic geometry (cf. Kommutative Algebra und Einführung in die algebraische Geometrie), model theory
Mathematical Concentration
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Reading courses
Lecturer: All professors and 'Privatdozenten' of the Mathematical Institute
Language: Talk/participation possible in German and English
In a reading course, the material of a four-hour lecture is studied in supervised self-study. In rare cases, this may take place as part of a course; however, reading courses are not usually listed in the course catalog. If you are interested, please contact a professor or a private lecturer before the start of the course; typically, this will be the supervisor of your Master's thesis, as the reading course ideally serves as preparation for the Master's thesis (both in the M.Sc. and the M.Ed. programs).
The content of the reading course, the specific details, and the coursework requirements will be determined by the supervisor at the beginning of the lecture period. The workload should be equivalent to that of a four-hour lecture with exercises.
Reading Course
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Eva Lütkebohmert-Holtz
Assistant: Hongyi Shen
Language: in English
Lecture: Mo, 10-12h, HS 3042, KG III
Exercise session: Di, 8-10h, HS 1015, KG I
Sit-in exam (resit) 14.08., 15:00-18:00
This course covers an introduction to financial markets and products. Besides futures and standard put and call options of European and American type we also discuss interest-rate sensitive instruments such as swaps.
For the valuation of financial derivatives we first introduce financial models in discrete time as the Cox--Ross--Rubinstein model and explain basic principles of risk-neutral valuation. Finally, we will discuss the famous Black--Scholes model which represents a continuous time model for option pricing.
Required: Elementary Probability Theory~I
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: David Criens
Assistant: Dario Kieffer
Language: in English
Lecture: Do, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
The class of Markov chains is an important class of (discrete-time) stochastic processes that are used frequently to model for example the spread of infections, queuing systems or switches of economic scenarios. Their main characteristic is the Markov property, which roughly means that the future depends on the past only through the current state. In this lecture we provide the mathematical foundation of the theory of Markov chains. In particular, we learn about path properties, such as recurrence and transience, state classifications and discuss convergence to the equilibrium. We also study extensions to continuous time. On the way we discuss applications to biology, queuing systems and resource management. If the time allows, we also take a look at Markov chains with random transition probabilities, so-called random walks in random environment, which is a prominent model in the field of random media.
Required: Elementary Probability Theory~I \ Recommended: Analysis~III, Probability Theory~I
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Mathematical Physics
Lecturer: Wolfgang Soergel
Language: in German
Lecture: Di, 16-18h, SR 403, Ernst-Zermelo-Str. 1
Introduction to classic mechanics from the point of view of mathematics. We start with the mathematical modelling of space and time. Then we discuss Newton's equations of movement, physical systems with compulsory conditions, the D'Alembert principle, the Hamilton formalism and its derivation from the Newton's equations and applications of Hamilton formalism.
Required: Analysis III
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Students in the B.Sc. Mathematics programme can choose to give a talk, in which case the course counts as a seminar. Usability and requirements as for the seminar ‘Theory of Non-Commutative Algebras’.
Lecturer: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: in English
Lecture: Di, Fr, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Computer exercise: 2 hours, date to be determined
Oral exam 06.12.
This course takes only place in the first half of the semester, until end of November.
The aim of this course is to enable the students to carry out simulations and their mathematical analysis for stochastic models originating from applications such as mathematical finance and physics. For this, the course teaches a decent knowledge on stochastic differential equations (SDEs) and their solutions. Furthermore, different numerical methods for SDEs, their underlying ideas, convergence properties, and implementation issues are studied.
Required: Probability and measure theory, basic numerical analysis and basics of MATLAB programming.
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Moritz Diehl
Assistant: Florian Messerer
Language: in English
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
The aim of the course is to give an introduction to numerical methods for the solution of optimal control problems in science and engineering. The focus is on both discrete time and continuous time optimal control in continuous state spaces. It is intended for a mixed audience of students from mathematics, engineering and computer science.
The course covers the following topics:
The lecture is accompanied by intensive weekly computer exercises offered both in MATLAB and Python (6~ECTS) and an optional project (3~ECTS). The project consists in the formulation and implementation of a self-chosen optimal control problem and numerical solution method, resulting in documented computer code, a project report, and a public presentation.
Required: Analysis~I and II, Linear Algebra~I and II \ Recommended: Numerics I, Ordinary Differential Equations, Numerical Optimization
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Mathematics Education ‒ Functions and Analysis
Lecturer: Katharina Böcherer-Linder
Language: in German
Seminar: Do, 9-12h, SR 404, Ernst-Zermelo-Str. 1
Exemplary implementations of the theoretical concepts of central mathematical thought processes such as concept formation, modeling, problem solving and reasoning for the content areas of functions and analysis. \\ Barriers to understanding, pre-concepts, basic ideas, specific difficulties for the content areas of functions and analysis. \\ Fundamental possibilities and limitations of media, in particular of computer-aided mathematical tools mathematical tools and their application for the content areas of functions and analysis. Analysis of individual mathematical learning processes and errors as well as development individual support measures for the content areas of functions and analysis.
Required: Introduction to Mathematics Education, Knowledge about analysis and numerics
Mathematics Education for Specific Areas of Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Mathematics Education ‒ Probability Theory and Algebra
Lecturer: Anika Dreher
Language: in German
Seminar: Fr, 9-12h, SR 226, Hermann-Herder-Str. 10
Exemplary implementations of the theoretical concepts of central mathematical thought processes such as concept formation, modeling, problem solving and reasoning for the content areas of stochastics and algebra. \\ Barriers to understanding, pre-concepts, basic ideas, specific difficulties for the content areas of stochastics and algebra.\ Basic possibilities and limitations of media, especially computer-based mathematical tools and their mathematical tools and their application for the content areas of stochastics and algebra. and algebra. \\ Analysis of individual mathematical learning processes and errors as well as development individual support measures for the content areas of stochastics and algebra.
Required: Introduction to Mathematics Education, knowledge from stochastics and algebra.
Mathematics Education for Specific Areas of Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Mathematics education seminar: Media Use in Teaching Mathematics
Lecturer: Jürgen Kury
Language: in German
Seminar: Mi, 15-18h, SR 127, Ernst-Zermelo-Str. 1
The use of teaching media in mathematics lessons wins both at the level of lesson planning and lesson realization in importance. Against the background of constructivist learning theories shows that the reflective use of computer programs, among other things mathematical concept formation in the long term. For example experimenting with computer programs allows mathematical structures to be discovered, without this being overshadowed by individual routine operations (such as term transformation) would be covered up. This has far-reaching consequences for mathematics lessons. For this reason, this seminar aims to provide students the necessary decision-making and action skills to prepare future mathematics teachers for their professional activities. Starting from initial considerations about lesson planning, computers and tablets with regard to their respective didactic potential and tested with learners during a classroom visit. The exemplary systems presented are:
The students should develop teaching sequences, which will then be tested and reflected on with pupils (where this will be possible).
Recommended: Basic courses in mathematics
Supplementary Module in Mathematics Education
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Mathematics education seminars at Freiburg University of Education
Lecturer: Lecturers of the University of Education Freiburg
Language: in German
Supplementary Module in Mathematics Education
The requirement for coursework, assessments, and examinations are taken from the regulations of the University of Education Freiburg for the degree programme 'Lehramt Sekundarstufe 1'.
Module "Research in Mathematics Education"
Lecturer: Lecturers of the University of Education Freiburg, Frank Reinhold
Language: in German
Part 1: Seminar 'Development Research in Mathematics Education ‒ Selected Topics': Mo, 14-16h, Raum noch nicht bekannt, PH Freiburg
Part 2: Seminar 'Research Methods in Mathematics Education': Mo, 16-19h, Raum noch nicht bekannt, PH Freiburg
Part 3: Master's thesis seminar: Development and Optimisation of a Research Project in Mathematics Education
Registration: see course descriptions
The three related courses of the module prepare students for an empirical Master thesis in mathematics didactics. The course is jointly designed by all professors at the PH with mathematics didactics research projects at secondary levels 1 and 2 and is carried out by one of these researchers. Afterwards, students have the opportunity to start Master thesis with one of these supervisors - usually integrated into larger ongoing research projects.
The first course of the module provides an introduction to strategies of empirical didactic research (research questions, research status, research designs). Students deepen their skills in scientific research and the evaluation of subject-specific didactic research. In the second course (in the last third of the semester) students are introduced to central qualitative and quantitative research methods through concrete work with existing data (interviews, student products, experimental data), students are introduced to central qualitative and quantitative research methods. The third course is an accompanying seminar for the Master thesis.
The main objectives of the module are the ability to receive mathematics didactic research in order to didactic research to clarify questions of practical relevance and to plan an empirical mathematics didactics Master thesis. It will be held as a mixture of seminar, development of research topics in groups and active work with research data. Recommended literature will be depending on the research topics offered within the respective courses. The parts can also be attended in different semesters, for example part~1 in the second Master semester and part~2 in the compact phase of the third Master semester after the practical semester.
Research in Mathematics Education
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Computer exercises for Introduction to Theory and Numerics of Partial Differential Equations
Lecturer: Sören Bartels
Assistant: Vera Jackisch
Language: in English
The computer tutorial accompanies the lecture with programming exercises.
See the lecture – additionally: programming knowledge.
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Computer exercises in Numerics
Lecturer: Sören Bartels
Assistant: Tatjana Schreiber
Language: in German
In the computer tutorial accompanying the Numerics (first term) lecture the algorithms developed and analyzed in the lecture are put into practice and and tested experimentally. The implementation is carried out in the programming languages Matlab, C++ and Python. Elementary programming knowledge is assumed.
See the lecture {\em Numerics I} (which should be attended in parallel or should already have been completed). \ Additionally: Elementary programming knowledge.
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Please note the registration modalities for the individual seminars published in the comments to the course catalog: As a rule, places are allocated after pre-registration by e-mail at the preliminary meeting at the end of the lecture period of the summer semester. You must then register online for the exam; the registration period runs from August 1, 2024 to October 9, 2024.
Lecturer: Ernst August v. Hammerstein
Language: in German
A knot can be mathematically defined relatively simply as a closed curve in the three-dimensional space \(\mathbb{R}^3\). From everyday life, one is certainly already familiar with different types of knots, e.g, surgeons knot, sailors knots, and many more. The aim of mathematical knot theory is to find characteristic quantities for the description and classification of knots and thus possibly also to be able to decide whether two knots are equivalent, i.e., if they can be transformed into one another through certain operations.
Ropes, cords or wires can be used to illustrate knots as well as interlacings. Prospective teachers can use these not only in this seminar, but perhaps also later in the classroom to display different results in a very practical way.
Required: Basic Mathematics courses. \ Possibly a little knowledge in topology in addition.
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Thorsten Schmidt
Assistant: Moritz Ritter
Language: Talk/participation possible in German and English
Seminar: Fr, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting 18.10.
Preparation meetings for talks: Dates by arrangement
This seminar will focus on theoretical machine learning results, including modern universal approximation theorems, approximation of filtering methods through transformes, application of machine learning methods in financial markets and possibly other related topics. Moreover, we will cover topics in stochastic analysis, like fractional Ito calculus, uncertainty, filtering and optimal transport. You are also invited to suggest related topics.
Required: Basic Probability and either Machine Learning or Probability Theory II (Stochastic Processes).
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Machine-Learning Methods in the Approximation of PDEs
Lecturer: Sören Bartels
Assistant: Tatjana Schreiber
Language: Talk/participation possible in German and English
Machine-learning methods have recently been used to approximate solutions of partial differential equations. While in some cases they lead to advantages over classical approaches, their general superiority is widely open. In the seminar we will review the main concepts and recent developments.
Introduction to Theory and Numerics for PDEs
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Medical Data Science
Lecturer: Harald Binder
Language: Talk/participation possible in German and English
Seminar: Mi, 10-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary Meeting 17.07., HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
To answer complex biomedical questions from large amounts of data, a wide range of analysis tools is often necessary, e.g. deep learning or general machine learning techniques, which is often summarized under the term ``Medical Data Science''. Statistical approaches play an important rôle as the basis for this. A selection of approaches is to be presented in the seminar lectures that are based on recent original work. The exact thematic orientation is still to be determined.
Good knowledge of probability theory and mathematical statistics.
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Guofang Wang
Assistant: Xuwen Zhang
Language: Talk/participation possible in German and English
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 17.07., 16:00
Preparation meetings for talks: Dates by arrangement
Minimal surfaces are surfaces in space with a “minimal” area and can be described using holomorphic functions. They occur, for example in the investigation of soap skins and the construction of stable objects (e.g. in architecture). In the investigation of minimal surfaces elegant methods from various mathematical fields such as function theory, calculus of variations, differential geometry and partial differential equations. are applied.
Required: Analysis III or knowledge about multidimensional integration and complex analysis. \ Recommended: Elementary knowledge about differential geometry.
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: Talk/participation possible in German and English
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 16.07., SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
We will discuss advanced topics in algebraic topology. Depending on the interest of the participants we could work on one of the following topics---if you have other topic suggestions, please contact the lecturer.
Algebraic Topology~I and II
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.
Lecturer: Annette Huber-Klawitter
Assistant: Xier Ren
Language: Talk/participation possible in German and English
Seminar: Fr, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting 15.07., 11:00, SR 318, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
In this seminar, we are going to study finite dimensional (unital, possibly non-commutative) algebras over a (commutative) field \(k\). Prototypes are the rings of square matrices over \(k\), finite field extensions, or the algebra \(k^n\) with diagonal multiplication.
We will concentrate on path algebras of finite quivers (German: Köcher). Modules over them are equivalently described as representations of the quiver. Many algebraic properties can be directly understood from properties of the quiver.
Required: Linear Algebra \ Recommended: Algebra and Number Theory, Commutative Algebra and Introduction to Algebraic Geometry
Supplementary Module in Mathematics
Requirement for coursework, assessments, and examinations are described in the current supplements of the module handbooks.