Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-40-20-K-6

Multilinear Algebra (2V, 3.0 LP)

Course Type

SWS	Type	Course Form	CP (Effort)	Presence-Time / Self-Study
2	V	Lecture	3.0 CP	28 h	62 h
(2V)			3.0 CP	28 h	62 h

Basedata

SWS	2V
CP, Effort	3.0 CP = 90 h
Position of the semester	1 Sem. irreg.
Level	[6] Master (General)
Language	[EN] English
Lecturers	Decker, Wolfram, Prof. Dr. (PROF \| DEPT: MAT) Zintl, Jörg, PD Dr. (EXT \| DEPT: MAT) + further Lecturers of the department Mathematics
Area of study	[MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State	[NORM] Active

Contents

multilinear maps (bilinear forms, determinants, duality),
tensors (general properties, tensor algebra),
symmetric and exterior algebra (decomposition theorems, complex algebra, polynomial algebra),
functorial properties (exact sequences, flat modules, derived functors),
Applications (e.g. derivations and differentials, Koszul complex, K-theory).

Literature

W. Greub, Multilinear Algebra,
D. Eisenbud: Commutative Algebra with a view towards algebraic geometry,
S. Lang: Algebra,
S. Mac Lane: Categories for the Working Mathematician.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

Modules:

[MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)

Courses

[MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)

Requirements for attendance (formal)

None

References to Course [MAT-40-20-K-6]

Module	Name	Context
[MAT-40-20-M-6]	Multilinear Algebra	P: Obligatory	2V, 3.0 LP
Course-Pool	Name
[MAT-40-2V-KPOOL-4]	Elective Courses Algebra, Geometry and Computeralgebra (2V, B.Sc.)