 |
| Detailed information |
| Original study plan |
Bachelor's programme Computer Science 2025W |
| Learning Outcomes |
Competences |
| 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.
|
|
| Skills |
Knowledge |
- Perform vector and matrix operations K3, K4
- Model geometric problems with vectors K3, K4
- Solve systems of linear equations K3, K4
- Know the basic concepts of vector space theory K3
- Represent linear mappings by matrices K3
- Calculate the greatest common divisor in Euclidean domains K3
- Construct finite fields and calculate in them K3
|
- Vectors and matrices for the description of geometric questions.
- Projective geometry and homogeneous coordinates.
- Scalar product, cross product, matrix multiplication, inversion of matrices
- Determinants
- Intersection of lines and planes in space.
- Gauss algorithm
- Basis, linear independence, linear span
- Linear mappings
- representation matrices of linear mappings, in particular of reflections and rotations
- Extended Euclidean algorithm
- Finite fields
|
|
| 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.
- Aichinger, E. Algebra (Bachelorstudium Informatik), Vorlesungsskriptum, 2008
http://www.algebra.uni-linz.ac.at/Students/MathInf/vlss08/sommer08-0.pdf
|
| 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)
|
| Earlier variants |
They also cover the requirements of the curriculum (from - to)
521THEOALGV13: VL Algebra (2013W-2023S)
|
|
