This entry is from Winter semester 2016/17 and might be obsolete. No current equivalent could be found.

# Linear Algebra I (incl. Foundations of Mathematics) (dt. Lineare Algebra I mit Grundlagen der Mathematik)

 Level, degree of commitment Basic module, compulsory elective module Forms of teaching and learning,workload Lecture Grundlagen der Mathematics (2 SWS) lecture Lineare Algebra 1 (4 SWS) central recitation class (2 SWS) recitation class (2 SWS), 450 hours (150 h attendance, 300 h private study) Credit points,formal requirements 15 CP Course requirement(s): Written examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Duration,frequency One semester, each winter semester Person in charge of the module's outline Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker

## Contents

Fundamentals of Mathematics:

• elementary set theory
• natural and whole numbers, complete induction, rational numbers
• mappings, functions, relations
• elementary propositional logic and its application in mathematical proofs
• real numbers, inequalities (Bernoulli etc.), complex numbers
• groups, solids.

Linear algebra:

• Vector spaces and linear mappings
• Matrices and linear systems of equations
• determinants and eigenvalues
• Euclidean vector spaces and self-adjoint endomorphisms
• Geometric aspects of linear algebra

## Qualification Goals

Technical: Students should

• Learn fundamentals of mathematical reasoning and argumentation,
• master basic principles of linear and algebraic structures and be able to apply them to simple mathematical problems,
• acquire the basic mathematical knowledge that is the foundation for the entire course of study.

Soft skills: The students should

• practice mathematical working methods (developing mathematical intuition and its formal justification, training the ability to abstract, understanding the strict axiomatic structure of mathematical areas on a (comparatively) simple structure),
• improve their oral communication skills in the exercises by practicing free speech in front of an audience and in discussion.

None

## Applicability

The module can be attended at FB12 in study program(s)

• B.Sc. Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Basic Modules in Mathematics.

The module can also be used in other study programs (export module).

• Jänich, K.: Lineare Algebra, Springer, Berlin-Heidelberg 1996
• Brieskorn, E.: Lineare Algebra und Analytische Geometrie I und II, Vieweg, Braunschweig-Wiesbaden 1983/1985
• Bröcker, T.: Lineare Algebra und Analytische Geometrie, Birkhäuser, Basel-Boston-Berlin 2003
• Fischer, G.: Lineare Algebra, Vieweg, Braunschweig-Wiesbaden 1995

This page describes a module according to the latest valid module guide in Winter semester 2016/17. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

• Winter 2016/17
• Summer 2018 (no corresponding element)
• Winter 2018/19 (no corresponding element)
• Winter 2019/20 (no corresponding element)
• Winter 2020/21 (no corresponding element)
• Summer 2021 (no corresponding element)
• Winter 2021/22 (no corresponding element)
• Winter 2022/23 (no corresponding element)
• Winter 2023/24 (no corresponding element)

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.