406-2005-AAL Algebra I and II
| Semester | Spring Semester 2021 |
| Lecturers | M. Burger, M. Einsiedler |
| 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, M. Einsiedler |
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. |
| 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 |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 12 credits |
| Examiners | M. Einsiedler, 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 content coincides with the content of the course units 401-2003-00L Algebra I and 401-2004-00L Algebra II and changes with the examiners. Candidates must therefore contact the examiner in person before studying the material. Students who take the oral examination in the examination session Summer or Winter are allowed to take part in the learning tasks. |
| 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- |  |