Richard Pink: Catalogue data in Autumn Semester 2020

Name Prof. Dr. Richard Pink
FieldMathematics
Address
Professur für Mathematik
ETH Zürich, HG G 65.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 06 40
E-mailrichard.pink@math.ethz.ch
URLhttp://www.math.ethz.ch/~pink
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-3180-61LCategories and Derived Functors Restricted registration - show details
Mathematics Bachelor or Master programmes with preference for Mathematics Bachelor 5th semester
4 credits2SR. Pink
AbstractCategories, functors, natural transformations, limits, colimits, adjoint functors, additive & abelian categories, exact sequences, diagram lemmas, injectives, projectives, Mitchell's embedding theorem, complexes, homology, derived functors, acyclic resolutions, Tor, Ext, Yoneda-Ext, spectral sequence of filtered or double complexes & composite functors, group cohomology, derived functor of limits
Objective
401-5110-00LNumber Theory Seminar Information 0 credits1KÖ. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz
AbstractResearch colloquium
Objective
406-2004-AALAlgebra II
Enrolment 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 credits11RR. Pink
AbstractGalois theory and related topics.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
ObjectiveIntroduction to fundamentals of field extensions, Galois theory, and related topics.
ContentThe 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.
LiteratureJoseph 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 / NoticeAlgebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4.
406-2005-AALAlgebra I and II
Enrolment 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 credits26RR. Pink
AbstractIntroduction 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
ContentBasic 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
LiteratureJoseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society