Linear Algebra 2 and Discrete Structures
Module MA0005
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2019
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
available module versions | ||
---|---|---|
WS 2021/2 | SS 2020 | SS 2019 |
Basic Information
MA0005 is a semester module in German language at Bachelor’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
- Further Modules from Other Disciplines
Total workload | Contact hours | Credits (ECTS) |
---|---|---|
300 h | 135 h | 10 CP |
Content, Learning Outcome and Preconditions
Content
- Eigenwerte (charakteristisches Polynom, Spur, Diagonalisierbarkeit),
- Euklidische und unitäre Vektorräume (Skalarprodukt, orthogonale Basen, symmetrische u. Hermitesche Matrizen, Hauptachsentransformation),
- Analytische Geometrie (Transformationen, Rotationen, Spiegelungen, Orthogonalprojektionen, affine Teilräume),
- Symmetrische Bilinearformen (definit, semidefinit, indefinit, Trägheitssatz),
- Matrizengruppen (GL, SL, O, SO, U, SU),
- Normalformen (Ähnlichkeit, Jordansche Normalform (Beweis *nicht* verpflichtend), Singulärwertzerlegung)
Diskrete Strukturen:
- Grundlagen Graphentheorie (Wege, Kreise, Zusammenhang, Eulersche Graphen, Matchings)
- Matroide (Unabhängigkeitssysteme, Matroide, Basen, Greedy-Algorithmus)
- Effizienz von Algorithmen (Laufzeit, O-Notation, Kodierungslängen)
- Grundlegende effiziente Algorithmen (Euklidischer Algorithmus, Gauß-Elimination, Breitensuche)
- Dynamische Algorithmen (Bellman-Ford, Dijkstra)
- Netzwerke (Maximale Flüsse, Minimale Schnitte, Bipartites Matching)
- Ausblick Komplexitätstheorie
Learning Outcome
Ihre Fähigkeit, zu abstrahieren und exakt zu argumentieren sowie die Verbindung von Strukturen und Anschauungen herzustellen, wurde weiter geschärft.
Die Studierenden erkennen, wann Methoden der Linearen Algebra und der Diskreten Mathematik angewandt werden können. Ferner sind die Studierenden in der Lage, Konzepte der Linearen Algebra und Diskreten Strukturen zur Modellierung geeigneter Praxisprobleme einzusetzen.
Preconditions
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type | SWS | Title | Lecturer(s) | Dates | Links |
---|---|---|---|---|---|
VO | 2 | Linear Algebra 2 and Discrete Structures - DS [MA0005/0006] | Seidel, I. Weltge, S. |
Thu, 08:30–10:00, Interims I 102 and singular or moved dates |
|
VO | 3 | Linear Algebra 2 and Discrete Structures - LA 2 [MA0005/0006] | Hoffmann, T. Lange, C. Steinmeier, J. |
Wed, 11:30–12:15, MI HS1 Thu, 12:00–13:30, MW 1801 and singular or moved dates |
|
UE | 1 | Linear Algebra 2 and Discrete Structures - DS (Exercise Session) [MA0005/0006] | Seidel, I. Weltge, S. | dates in groups | |
UE | 1 | Linear Algebra 2 and Discrete Structures - LA2 (Exercise Session) [MA0005/MA0006] | Hoffmann, T. Lange, C. Steinmeier, J. | dates in groups | |
UE | 1 | Linear Algebra 2 and Discrete Structures - DS (Central Exercise Session) [MA0005/0006] | Seidel, I. Weltge, S. |
Mon, 16:00–18:00, Interims I 102 |
|
UE | 1 | Linear Algebra 2 and Discrete Structures (Central Exercise Session)[ MA0005/0006] | Hoffmann, T. Steinmeier, J. |
Mon, 16:00–18:00, Interims I 102 |
Learning and Teaching Methods
Media
Literature
Stefan Hougardy, Jens Vygen: Algorithmische Mathematik
Module Exam
Description of exams and course work
Exam Repetition
The exam may be repeated at the end of the semester.
Current exam dates
Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.
Title | |||
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Time | Location | Info | Registration |
Linear Algebra 2 and Discrete Structures | |||
0001 1350 2050 |
|||
2001 |