Rahul Pandharipande: Katalogdaten im Herbstsemester 2019 |
| Name | Herr Prof. Dr. Rahul Pandharipande |
| Lehrgebiet | Mathematik |
| Adresse | Professur für Mathematik ETH Zürich, HG G 55 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 56 89 |
| rahul.pandharipande@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~rahul |
| Departement | Mathematik |
| Beziehung | Ordentlicher Professor |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-5000-00L | Zurich Colloquium in Mathematics  | 0 KP | S. Mishra, P. L. Bühlmann, R. Pandharipande, Uni-Dozierende | ||
| Kurzbeschreibung | The lectures try to give an overview of "what is going on" in important areas of contemporary mathematics, to a wider non-specialised audience of mathematicians. | ||||
| Lernziel | |||||
| 401-5140-11L | Algebraic Geometry and Moduli Seminar | 0 KP | 2K | R. Pandharipande | |
| 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 | R. Pandharipande | |
| 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 | R. Pandharipande | |
| 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 | ||||