- 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).
Module MAT-40-20-M-6
Multilinear Algebra (M, 3.0 LP)
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 |
---|---|
Position of the semester | 1 Sem. irreg. |
Level | [6] Master (General) |
Language | [EN] English |
Module Manager | |
Lecturers | |
Area of study | [MAT-AGCA] Algebra, Geometry and Computer Algebra |
Reference course of study | [MAT-88.105-SG] M.Sc. Mathematics |
Livecycle-State | [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")
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
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.
Requirements for attendance (informal)
Modules:
Courses
Requirements for attendance (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 | Pure Mathematics | [WP] Compulsory Elective |
[MAT-88.706-SG] M.Sc. Mathematics International | Pure Mathematics | [WP] Compulsory Elective |
Module-Pool | Name | |
[MAT-GM-MPOOL-5] | General Mathematics (Introductory Modules M.Sc.) |