Inhalt

[ 521THEOALGV13 ] VL Algebra

Versionsauswahl
(*) Unfortunately this information is not available in english.
Workload Education level Study areas Responsible person Hours per week Coordinating university
3 ECTS B1 - Bachelor's programme 1. year Mathematics Erhard Aichinger 2 hpw Johannes Kepler University Linz
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 gcd-algorithm 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, Karl-Heinz 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)
On-site course
Maximum number of participants -
Assignment procedure Direct assignment