406-2005-AAL  Algebra I and II

SemesterAutumn Semester 2016
LecturersR. Pink
Periodicityevery semester recurring course
Language of instructionEnglish
CommentEnrolment 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

NumberTitleHoursLecturers
406-2005-AA RAlgebra I and II
Self-study course. No presence required.
360s hrsR. Pink

Catalogue data

AbstractIntroduction 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
ContentBasic 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 notesFor a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see:
Link
Link
LiteratureS. 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 credits12 credits
ExaminersR. Pink
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
Additional information on mode of examinationThe precise content 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 2016 or Winter 2017 were allowed to take part in the optional written examination for Algebra I that was offered before the start of the Spring Semester 2016. ---

Students who take the oral examination in the examination session Summer 2017 or Winter 2018 are allowed to take part in the optional written examination for Algebra I that will be offered before the start of the Spring Semester 2017. 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 2016.
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

ProgrammeSectionType
Mathematics MasterCourse Units for Additional Admission RequirementsE-Information