This entry is from Winter semester 2019/20 and might be obsolete. You can find a current equivalent here.

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

 Level, degree of commitment Basic module, required module Forms of teaching and learning,workload Lecture (4+2 SWS), recitation class (2 SWS), 360 hours (120 h attendance, 200 h preparation and follow-up inklusive Studienleistungen, 40 h Vorbereitung and Ablegen von Prüfungsleistungen) Credit points,formal requirements 12 CP Course requirement(s): 1) Successful completion of at least 50% of the weekly exercises as well as at least 1-3 presentations of the tasks. 2) Two written tests (45-120 min.). Examination type: Oral examination (20-30 min.) Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program LAaG Mathematics. In the event of failure, a total of 4 attempts are available for the examination. 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

Foundations of mathematics:

elementary set theory, number domains, induction, functions, propositional calculus and its use in mathematical proofs

Linear algebra:

• Vector spaces and linear maps
• Matrices and linear systems of equations
• Determinants and eigenvalues
• Euclidean vector spaces and selfadjoint endomorphisms
• geometric aspects of linear algebra

## Qualification Goals

Competences:

The students can

• understand and use the basic principles of linear structures, linearization and coordinate systems and are familiar with the associated basic concepts,
• apply mathematical methods to concrete questions,
• can distinguish between mathematical intuition and formal deduction and can use and relate both components,
• know and understand the principles of strict axiomatic construction of mathematical theories through the comparatively simple structure of a vector space,
• have basic knowledge and linear algebra skills required for the entire degree program, especially for the modules Analysis, Algebra, Complex Analysis, Geometry.

Qualification goals:

The students know and understand the basic principles of linear structures and their conceptualization in linear algebra. They are familiar with basic mathematical methods and the importance of building an axiomatic theory.

None.

## Applicability

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

• LAaG Mathematics

When studying LAaG Mathematics, this module must be completed in the study area Basic Modules.