
Detailed information 
Original study plan 
Bachelor's programme Computer Science 2021S 
Objectives 
Students master the operations of vector algebra, linear algebra and matrix calculations and can use these operations to model and solve geometric problems. They are able to compute the greatest common divisor in polynomial rings over fields and in the ring of integers, and they can perform the fundamental operations of some algebraic structures used in coding theory and cryptology, such as finite fields.

Subject 
Linear Algebra
 Vectors and Matrices in modelling geometric problems
 Systems of linear equations
 Projective geometry and homogeneous coordinates
 Vector spaces
 Linear mappings and their matrix representations
 Determinants
Abstract algebra
 Extended Euclidean gcdalgorithm in the integers and in univariate polynomial rings over fields.
 Finite fields, construction from polynomial rings, arithmetic, properties.
 Linear Codes

Criteria for evaluation 
General: Understanding and mastery of the presented solution methods. Acquaintance with the underlying theory and its logical structure. Knowledge and presentation of the proofs contained in the lecture. Correct derivation of methods for solving related problems.
Specifically: Written exam.

Methods 
Lecture

Language 
German 
Study material 
 Kiyek, KarlHeinz and Schwarz, Friedrich, Lineare Algebra, Teubner, Stuttgart, 1999.
 Lidl, R. and Pilz, G. F., Applied abstract algebra, Springer, New York, 1998.
 Robinson, D. J. S., An Introduction to Abstract Algebra, Walter de Gruyter, Berlin, 2003.

Changing subject? 
No 
Corresponding lecture 
^{(*)}ist gemeinsam mit 521THEOALGU13: UE Algebra (1,5 ECTS) und einer LVA aus dem Studienfach Vertiefung (1,5 ECTS) im Bachelor Informatik äquivalent zu INBIPVOALGE: VO Algebra (4,5 ECTS) + INBIPUEALGE: UE Algebra (3 ECTS)

