Marc Burger: Katalogdaten im Herbstsemester 2021 |
| Name | Herr Prof. em. 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 | Professor emeritus |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-0213-16L | Analysis II  | 5 KP | 2V + 2U | M. Burger | |
| Kurzbeschreibung | Differential- und Integralrechnung in mehreren Variablen, Vektoranalysis. | ||||
| Lernziel | |||||
| Literatur | Für allgemeine Informationen, sehen Sie bitte die Webseite der Vorlesung | ||||
| 401-2000-00L | Scientific Works in Mathematics Zielpublikum: Bachelor-Studierende im dritten Jahr; Master-Studierende, welche noch keine entsprechende Ausbildung vorweisen können. | 0 KP | M. Burger | ||
| Kurzbeschreibung | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | ||||
| Lernziel | Learn the basic standards of scientific works in mathematics. | ||||
| Inhalt | - Types of mathematical works - Publication standards in pure and applied mathematics - Data handling - Ethical issues - Citation guidelines | ||||
| Voraussetzungen / Besonderes | Weisung https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-de/wiss-arbeiten-eigenst%C3%A4ndigkeitserklaerung.pdf | ||||
| 401-5530-00L | Geometry Seminar | 0 KP | 1K | M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, 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 anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. | 5 KP | 11R | M. Burger | |
| Kurzbeschreibung | Galois theory and related topics. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||
| Lernziel | Introduction to fundamentals of field extensions, Galois theory, and related topics. | ||||
| Inhalt | The main topic is Galois Theory. Starting point is the problem of solvability of algebraic equations by radicals. Galois theory solves this problem by making a connection between field extensions and group theory. Galois theory will enable us to prove the theorem of Abel-Ruffini, that there are polynomials of degree 5 that are not solvable by radicals, as well as Galois' theorem characterizing those polynomials which are solvable by radicals. | ||||
| Literatur | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society Galois Theory is the topic treated in Chapter A5. | ||||
| Voraussetzungen / Besonderes | Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4. | ||||
| 406-2005-AAL | Algebra I and II Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. | 12 KP | 26R | M. Burger, M. Einsiedler | |
| 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 | ||||
| Literatur | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society | ||||