## Richard Pink: Catalogue data in Spring Semester 2020 |

Name | Prof. Dr. Richard Pink |

Field | Mathematik |

Address | Professur für Mathematik ETH Zürich, HG G 65.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 06 40 |

richard.pink@math.ethz.ch | |

URL | http://www.math.ethz.ch/~pink |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-2004-00L | Algebra II | 5 credits | 2V + 2U | R. Pink | |

Abstract | The main topics are field extensions and Galois theory. | ||||

Objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. | ||||

Content | 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. | ||||

Literature | 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. | ||||

401-2200-13L | Representation Theory of Finite Groups Primarily for students Bachelor Mathematics 4th semester (or 6th semester if not fully booked). Number of participants limited to 12. | 4 credits | 2S | R. Pink | |

Abstract | -Grundlegende Begriffe aus der Darstellungstheorie -Zerlegung in irreduzible Darstellungen -Charaktertheorie -Berechnung von Charaktertabellen -Anwendungen zur Gruppentheorie, insbesondere Satz von Burnside | ||||

Objective | Methoden und Resultate der Darstellungstheorie. Vortragstechnik. | ||||

Literature | Representations and Characters of Groups, Gordon James & Martin Liebeck, Cambridge Verlag. | ||||

Prerequisites / Notice | Das Seminar richtet sich primär an Studierende im 4. Semester, die die Vorlesung Algebra I bei mir besucht haben. Am Donnerstag den 6. Januar um 15:00 im Raum HG G43 findet eine Vorbesprechung statt, an der Sie unbedingt teilnehmen sollten. | ||||

401-5110-00L | Number Theory Seminar | 0 credits | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |

Abstract | Research colloquium | ||||

Objective | Talks on various topics of current research. | ||||

Content | Research seminar in algebra, number theory and geometry. This seminar is aimed in particular to members of the research groups in these areas and their graduate students. | ||||

406-2004-AAL | Algebra IIEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 5 credits | 11R | R. Pink | |

Abstract | Galois theory and related topics. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||

Objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. | ||||

Content | 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. | ||||

Literature | 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. | ||||

Prerequisites / Notice | Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4. | ||||

406-2005-AAL | Algebra I and IIEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 12 credits | 26R | R. Pink | |

Abstract | 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. | ||||

Objective | |||||

Content | 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 | ||||

Literature | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society |