406-2005-AAL Algebra I and II
| Semester | Autumn Semester 2018 |
| Lecturers | M. Burger, E. Kowalski |
| Periodicity | every semester recurring course |
| Language of instruction | English |
| Comment | 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. |
Courses
| Number | Title | Hours | Lecturers | |
|---|---|---|---|---|
| 406-2005-AA R | Algebra I and II Self-study course. No presence required. | 360s hrs | M. Burger, E. Kowalski |
Catalogue data
| 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. |
| Learning 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: Link 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 |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 12 credits |
| Examiners | E. Kowalski, M. Burger |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | oral 30 minutes |
| Additional information on mode of examination | The precise content changes with the examiners. Candidates must therefore contact the examiners in person before studying the material. Students who take the oral examination in the examination session Summer 2019 or Winter 2020 are allowed to take part in the optional written examination for Algebra I that will be offered before or at the start of the Spring Semester 2019. If the grade of the written examination exceeds the grade of the final oral examination for Algebra I and II, then the grade of the written examination will be taken into account with a weight of 20%. The written examination is only offered once; for details see the announcements for the course unit 401-2003-00L Algebra I in the Autumn Semester 2018. |
| This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| No public learning materials available. | |
| Only public learning materials are listed. |
Groups
| No information on groups available. |
Restrictions
| There are no additional restrictions for the registration. |
Offered in
| Programme | Section | Type | |
|---|---|---|---|
| Mathematics Master | Course Units for Additional Admission Requirements | E- |  |