406-2004-AAL Algebra II
| Semester | Autumn Semester 2019 |
| Lecturers | R. Pandharipande |
| 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 | |
|---|---|---|---|---|
| 406-2004-AA R | Algebra II Self-study course. No presence required. | 150s hrs | R. Pandharipande |
Catalogue data
| Abstract | Galois theory and related topics. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |
| Objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. |
| Content | The 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. |
| Literature | Joseph 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 / Notice | Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 5 credits |
| Examiners | R. Pandharipande |
| 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 20 minutes |
| Additional information on mode of examination | The content coincides with the content of the course unit 401-2004-00L Algebra II and changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |
| 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- |  |