Course detail

Geometrical Algorithms

FSI-0AVAcad. year: 2020/2021

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

Mode of study

Not applicable.

Guarantor

doc. Mgr. Petr Vašík, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

Co-requisites

Not applicable.

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.

Course curriculum

Not applicable.

Work placements

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DORST, Leendert, D.H.F FONTIJNE a Stephen MANN. Geometric algebra for computer science: an object-oriented approach to geometry. Rev. ed. Burlington, Mass.: Morgan Kaufmann Publishers, c2007. Morgan Kaufmann series in computer graphics. ISBN 978-0-12-374942-0. (EN)
GONZÁLEZ CALVET, Ramon. Treatise of plane geometry through geometric algebra. 1. Cerdanyola del Vallés: [nakladatel není známý], 2007. TIMSAC. ISBN 978-84-611-9149-9. (EN)
HILDENBRAND, Dietmar. Foundations of geometric algebra computing. Geometry and computing, 8. ISBN 3642317936. (EN)
HILDENBRAND, Dietmar. Introduction to geometric algebra computing. Boca Raton, 2018. ISBN 978-149-8748-384. (EN)
MOTL, Luboš a Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Karolinum, 2002. ISBN 80-246-0421-3. (CS)
PERWASS, Christian. Geometric algebra with applications in engineering. Berlin: Springer, c2009. ISBN 354089067X. (EN)

Recommended reading

HILDENBRAND, Dietmar. Introduction to geometric algebra computing. Boca Raton, 2018. ISBN 978-149-8748-384. (EN)
MOTL, Luboš a Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Karolinum, 2002. ISBN 80-246-0421-3. (CS)

Classification of course in study plans

  • Programme B-MAI-P Bachelor's 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Mgr. Petr Vašík, Ph.D.

Syllabus

1. Review: vector space, basis, dimension, scalar product, bilinear and quadratic forms.
2. Euclidean transformations of two and three dimensional space.
3. Symplectic form, volume elements, quadratic spaces.
4. Tensor calculus, 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.