401-2004-00L  Algebra II

SemesterSpring Semester 2020
LecturersR. Pink
Periodicityyearly recurring course
Language of instructionGerman



Courses

NumberTitleHoursLecturers
401-2004-00 VAlgebra II2 hrs
Fri08:00-10:00ER SA TZ »
08:15-10:00HG G 3 »
30.04.17:15-19:00HG »
R. Pink
401-2004-00 UAlgebra II2 hrs
Tue15:00-17:00ER SA TZ »
15:15-17:00HG E 1.2 »
15:15-17:00HG E 21 »
15:15-17:00HG E 22 »
15:15-17:00HG E 33.5 »
15:15-17:00HG G 26.3 »
R. Pink

Catalogue data

AbstractThe main topics are field extensions and Galois theory.
ObjectiveIntroduction to fundamentals of field extensions, Galois theory, and related topics.
ContentThe 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.
LiteratureJoseph 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.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a two-semester course together with 401-2003-00L Algebra I
For programme regulations
(Examination block)
Bachelor's Degree Programme in Mathematics 2016; Version 25.02.2020 (Examination Block 2)
Bachelor's Programme in Mathematics 2010; Version 24.02.2016 (Examination Block 2)
ECTS credits12 credits
ExaminersR. Pink
Typesession examination
Language of examinationGerman
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 examinationDie Lernelemente der beiden Semesterkurse gelten auch für den Jahreskurs und werden in dem gleichen Verfahren in einen Notenbonus von maximal 0.25 Notenpunkten umgerechnet.
Performance assessment as a semester course (other programmes)
ECTS credits5 credits
ExaminersR. Pink
Typesession examination
Language of examinationGerman
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Admission requirementIm Bachelor-Studiengang Mathematik wird die Lerneinheit Algebra II zusammen mit Algebra I geprüft (30-minütige mündliche Sessionsprüfung).
Studierenden in einem anderen Studiengang, die Algebra I und Algebra II prüfen lassen wollen, wird empfohlen, sich zur Prüfung des Jahreskurses direkt bei der Prüfungsplanstelle anzumelden (über myStudies nicht möglich).
Mode of examinationoral 20 minutes
Additional information on mode of examinationDie während des Semesters angebotenen Lernelemente messen die aktive Teilnahme am Übungsbetrieb. Dabei werden zu Beginn jeder Übungsstunde 5 Single Choice Aufgaben individuell bearbeitet. Jede richtig beantwortete Aufgabe ergibt 1 Punkt. Die im Semester erreichte Punktzahl m wird in einen Notenbonus von maximal 0.25 Notenpunkten umgerechnet mit der Formel max(0,min(0.25,(m-r)/s mal 0.25)), wobei r und s noch festgelegt werden. Dieser Bonus wird ungerundet zu der vorläufigen Note aus der Prüfung addiert; das Resultat wird zur Endnote gerundet.
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkInformation
Only public learning materials are listed.

Groups

401-2004-00 UAlgebra II
GroupsG-01
Tue15:00-17:00ER SA TZ »
15:15-17:00HG E 1.2 »
G-02
Tue15:15-17:00HG E 21 »
G-03
Tue15:15-17:00HG E 33.5 »
G-04
Tue15:15-17:00HG G 26.3 »
G-05
Tue15:15-17:00HG E 22 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mathematics BachelorExamination Block IIOInformation
Physics BachelorAdditional Courses (from Second Year Mathematics Bachelor)ZInformation