The spring semester 2021 will certainly take place online until Easter. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers.

Richard Pink: Catalogue data in Autumn Semester 2016

Name Prof. Dr. Richard Pink
FieldMathematik
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
401-3132-00LCommutative Algebra Information 10 credits4V + 1UR. Pink
AbstractThis course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry. The material in this course will be assumed in the lecture course "Algebraic Geometry" in the spring semester 2017.
ObjectiveWe shall cover approximately the material from
--- most of the textbook by Atiyah-MacDonald, or
--- the first half of the textbook by Bosch.
Topics include:
* Basics about rings, ideals and modules
* Localization
* Primary decomposition
* Integral dependence and valuations
* Noetherian rings
* Completions
* Basic dimension theory
LiteraturePrimary Reference:
1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)
Secondary Reference:
2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)
Tertiary References:
3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)
Prerequisites / NoticePrerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).
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 Representations of finite groups, algebras.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
ObjectiveIntroduction to fundamentals of Galois theory, and representation theory of finite groups and algebras
ContentFundamentals of Galois theory
Representation theory of finite groups and algebras
Lecture notesFor 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/
LiteratureS. 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
Prerequisites / NoticeAlgebra I
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
Lecture notesFor 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/
LiteratureS. 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