406-2004-AAL Algebra II
Semester | Spring Semester 2020 |
Lecturers | R. Pink |
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. Pink |
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. Pink |
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. Students who take the oral examination in the examination session Summer 2020 or Winter 2021 are allowed to take part in the learning tasks described in Link |
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- |