Marc Burger: Katalogdaten im Herbstsemester 2018 |
| Name | Herr Prof. Dr. Marc Burger |
| Lehrgebiet | Mathematik |
| Adresse | Dep. Mathematik ETH Zürich, HG G 37.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 49 73 |
| Fax | +41 44 632 10 85 |
| marc.burger@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~burger |
| Departement | Mathematik |
| Beziehung | Ordentlicher Professor |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-3200-64L | Proofs from THE BOOK  Maximale Teilnehmerzahl: 24 | 4 KP | 2S | M. Burger, weitere Referent/innen | |
| Kurzbeschreibung | |||||
| Lernziel | Ziel des Seminares ist zu lernen wie man Mathematik vortraegt. Als Vorlage fuer dieses Seminar dient das Buch von Aigner und Ziegler "Proofs from the BOOK" das aus allen Gebieten der Mathematik fundamentale Saetze und deren "schoensten" Beweise praesentiert. Die Auswahl der Themen ist also gross und es gibt etwas fuer jeden Geschmack. | ||||
| 401-3225-00L | Introduction to Lie Groups  | 8 KP | 4G | M. Burger | |
| Kurzbeschreibung | Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. | ||||
| Lernziel | The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. | ||||
| Literatur | A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A. Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F. Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A. Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press) | ||||
| Voraussetzungen / Besonderes | Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. Course webpage: https://metaphor.ethz.ch/x/2018/hs/401-3225-00L/ | ||||
| 401-5530-00L | Geometry Seminar | 0 KP | 1K | M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, Uni-Dozierende | |
| Kurzbeschreibung | Research colloquium | ||||
| Lernziel | |||||
| 406-2004-AAL | Algebra II Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. | 5 KP | 11R | M. Burger | |
| Kurzbeschreibung | Galois theory and Representations of finite groups, algebras. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||
| Lernziel | Introduction to fundamentals of Galois theory, and representation theory of finite groups and algebras | ||||
| Inhalt | Fundamentals of Galois theory Representation theory of finite groups and algebras | ||||
| Skript | For a summary of the content and exercises with solutions of my lecture course in FS2016 see: https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/ | ||||
| Literatur | S. Lang, Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag I.R. Shafarevich, Basic notions of algebra, Springer verlag G. Mislin: Algebra I, vdf Hochschulverlag U. Stammbach: Algebra, in der Polybuchhandlung erhältlich I. Stewart: Galois Theory, Chapman Hall (2008) G. Wüstholz, Algebra, vieweg-Verlag, 2004 J-P. Serre, Linear representations of finite groups, Springer Verlag | ||||
| Voraussetzungen / Besonderes | Algebra I | ||||
| 406-2005-AAL | Algebra I and II Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. | 12 KP | 26R | M. Burger, E. Kowalski | |
| Kurzbeschreibung | Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||
| Lernziel | |||||
| Inhalt | Basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Group actions and applications Basic notions and examples of rings; Ring Homomorphisms, ideals, and quotient rings, rings of fractions Euclidean domains, Principal ideal domains, Unique factorization domains Basic notions and examples of fields; Field extensions, Algebraic extensions, Classical straight edge and compass constructions Fundamentals of Galois theory Representation theory of finite groups and algebras | ||||
| Skript | For a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see: https://www2.math.ethz.ch/education/bachelor/lectures/hs2015/math/algebra1/index-2.html https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/ | ||||
| Literatur | S. Lang, Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag I.R. Shafarevich, Basic notions of algebra, Springer verlag G. Mislin: Algebra I, vdf Hochschulverlag U. Stammbach: Algebra, in der Polybuchhandlung erhältlich I. Stewart: Galois Theory, Chapman Hall (2008) G. Wüstholz, Algebra, vieweg-Verlag, 2004 J-P. Serre, Linear representations of finite groups, Springer Verlag | ||||