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# Linear Algebra and Discrete Structures 1

## Module MA1101

This Module is offered by TUM Department of Mathematics.

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 WS 2012/3

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
SS 2021WS 2020/1SS 2013WS 2012/3

### Basic Information

MA1101 is a semester module in German language at Bachelor’s level which is offered in winter semester.

This module description is valid from WS 2012/3 to SS 2021.

300 h 105 h 10 CP

### Content, Learning Outcome and Preconditions

#### Content

Basic structures (sets, maps, relations, graphs, groups, fields, permutations),
Vector spaces (subspaces, quotient spaces, basis, dimension, direct sum, independence systems and matroids)
Linear Maps (isomorphisms, kernel, range, dual spaces),
Matrix calculus (System of linear equations, inverse, rank, basis transformations, incidence matrices)

#### Learning Outcome

After successful completion of this module students are able to handle basic axiomatic structures, to understand and to use the corresponding terminology and to connect the structures with graphical depiction.
Students will have obtained first experience in abstract formalization and gained basic skills in exact reasoning. They will have learned the basic structures of linear algebra and discrete mathematics and know how to handle them. They have the ability to translate between algebra and matrix calculus.

#### Preconditions

Mathematikkenntnisse im Umfang der allgemeinen Hochschulreife

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 5 Linear Algebra 1 [MA0004] Liedtke, C. Wed, 08:30–10:00, PH HS1
Thu, 14:15–15:45, MI HS1
Fri, 12:15–13:00, MI HS1
and singular or moved dates
eLearning
UE 2 Linear Algebra 1 (Exercise Session) [MA0004] Liedtke, C. Mundelius, D. dates in groups
UE 2 Linear Algebra 1 (Central Exercise Session) [MA0004] Liedtke, C. Mundelius, D. Fri, 14:15–15:45, Interims I 101
and singular or moved dates

#### Learning and Teaching Methods

lecture, tutorial, supplement lecture

#### Media

blackboard, exercise sheets

#### Literature

Fischer Gerd (2005): Lineare Algebra, Vieweg, 15. Auflage.

### Module Exam

#### Description of exams and course work

The module examination is based on a written exam (90 minutes). Students have to deal with basic structures of linear algebra and discrete mathematics and calculate them. They are able to abstract and argue precisely under time pressure.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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