Course detail
Geometrical Algorithms
FSI-0AV Acad. year: 2021/2022 Summer semester
A survey on advanced structures om multi-linear algebra and, consequently, their application in Euclidean space transformation. Introduction to the theory of geometric algebras and algorithms for elementary tasks of analytic geometry. Simple geometric algorithms for the rigid body motion using Euclidean transformations.
Language of instruction
Czech
Number of ECTS credits
3
Supervisor
Department
Learning outcomes of the course unit
Enhancement of skills that are necessary for applying advanced mathematical structures.
Prerequisites
Elementary notions of algebra and linear algebra.
Planned learning activities and teaching methods
The course is taught in lectures explaining the basic principles and theory of the discipline. Calculations in an appropriate software will be presented.
Assesment methods and criteria linked to learning outcomes
Graded assessment: semester project, oral exm.
Aims
Introduction of advanced mathematical structures and their applications in engineering.
Specification of controlled education, way of implementation and compensation for absences
Lectures, non-compulsory attendance.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Review: vector space, basis, dimension, scalar product, bilinear and quadratic forms.
2. Euclidean transformations of two and three dimensional space.
3. Inner and outer product, exterior algebra.
4. Clifford algebra.
5.-6. Introduction to geometric algebras, special cases of CRA (G3,1) and CGA (G4,1).
7.-8. Computation in geometric algebras.
9. Fundamental tasks of analytic geometry in geometric algebras.
10. Software for symbolic calculations and visualisation in geometric algebras (Python, CLUCalc).
11.-12. Euclidean transformations in geometric algebra, rigid body motion.
13. Consultations to semester project.