- 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).
Multilinear Algebra (M, 3.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-20-M-6||Multilinear Algebra||3.0 CP (90 h)|
|CP, Effort||3.0 CP = 90 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|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")
Evaluation of grades
The grade of the module examination is also the module grade.
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.
- 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.
Requirements for attendance of the module (informal)
Requirements for attendance of the module (formal)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|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|