Richard Pink: Catalogue data in Autumn Semester 2016
| 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 | |
|---|---|---|---|---|---|
| 401-3132-00L | Commutative Algebra  | 10 credits | 4V + 1U | R. Pink | |
| Abstract | This 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. | ||||
| Objective | We 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 | ||||
| Literature | Primary 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 / Notice | Prerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory). | ||||
| 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 | |||||
| 406-2004-AAL | Algebra 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 credits | 11R | R. Pink | |
| Abstract | Galois 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. | ||||
| Objective | Introduction to fundamentals of Galois theory, and representation theory of finite groups and algebras | ||||
| Content | Fundamentals of Galois theory Representation theory of finite groups and algebras | ||||
| Lecture notes | For 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/ | ||||
| Literature | S. 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 / Notice | Algebra I | ||||
| 406-2005-AAL | Algebra 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 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 | ||||
| Lecture notes | For 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/ | ||||
| Literature | S. 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 | ||||