Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-40-20-M-6

Module Identification

Module Number Module Name CP (Effort)
MAT-40-20-M-6 Multilinear Algebra 3.0 CP (90 h)

Basedata

CP, Effort 3.0 CP = 90 h 1 Sem. irreg. [6] Master (General) [EN] English Decker, Wolfram, Prof. Dr. (PROF | DEPT: MAT) Decker, Wolfram, Prof. Dr. (PROF | DEPT: MAT) Zintl, Jörg, PD Dr. (EXT | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-40-20-K-6
Multilinear Algebra
P 28 h 62 h - - PL1 3.0 irreg.
• About [MAT-40-20-K-6]: Title: "Multilinear Algebra"; Presence-Time: 28 h; Self-Study: 62 h

Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: irregular (by arrangement)
• Examination number: 84153 ("Multilinear Algebra")

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).

Competencies / intended learning achievements

Upon completion of this module, the students have acquired an in-depth knowledge in mathematical foundations. Based on their knowledge of Linear Algebra, they have learnt how to understand abstract algebraic structures and they are able to work with them confidently. They understand the proofs presented in the lecture and are able to comprehend and explain them.

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.

None

References to Module / Module Number [MAT-40-20-M-6]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Pure Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Pure Mathematics [WP] Compulsory Elective
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)