University of West Bohemia
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for academic year 2024/2025
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Course: Affine and Euclidean Geometry

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Course title Affine and Euclidean Geometry
Course code KMA/G1
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 2
Semester Winter
Number of ECTS credits 4
Language of instruction Czech, English
Status of course Compulsory, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Bizzarri Michal, Doc. RNDr. Ph.D.
  • Výrut Radek, Mgr.
  • Vršek Jan, Doc. RNDr. Ph.D.
Course content
Affine space, affine mappings and affine coordinate system. Affine subspaces and their parametric description. Equations of affine subspaces. Relative position of affine subspaces. Pencils of hyperplanes. Affine combination of points, barycentric coordinates. Vector spaces with scalar product. Euclidean space and Cartesian coordinate system. Orthogonality of Euclidean subspaces. Distances of Euclidean subspaces. Angles of Euclidean subspaces. Volumes of parallelotopes. Möbius extension of Euclidean space. Conics - ellipse, hyperbola, parabola. Intersections of the surface of a cone with a plane. Conic sections - quadratic curves in plane. Quadrics - quadratic surfaces in space. Selkected types of quadrics and their prroperties.

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, E-learning, Cooperative instruction, Discussion, Task-based study method, Students' self-study, Textual studies, Lecture, Practicum
  • Contact hours - 39 hours per semester
  • Preparation for an examination (30-60) - 50 hours per semester
  • Preparation for formative assessments (2-20) - 10 hours per semester
  • Preparation for comprehensive test (10-40) - 10 hours per semester
prerequisite
Knowledge
explain the basic lessons of plane, possibly spatial analytic geometry at the high school level
describe and explain the basic procedures for solving geometric problems
describe and explain the basic principles of linear algebra and vector calculus
describe and explain the basic principles of calculus
Skills
apply the acquired procedures to elementary geometric problems at the secondary school level
calculate vectors, matrices and determinants and solve systems of linear and quadratic equations
use the calculus apparatus for basic and intermediate problems
Competences
N/A
N/A
N/A
N/A
learning outcomes
Knowledge
define an affine space and introduce a suitable system of coordinates, understand the problem of affine subspaces, derive their equations and determine their relative positions
define Euclidean space, introduce the Cartesian coordinate system as a specialization of the general affine coordinate system, construct equations of orthogonal subspaces, determine distances and deviations of Euclidean subspaces
define and classify conics in the Euclidean plane, convert their expressions into canonical forms and recognize them
define and classify quadrics in three-dimensional Euclidean space, convert their expressions into canonical forms, and recognize and actively use them
Skills
actively use the analytical method in solving mathematical and application problems
solve geometric problems with linear and quadratic objects
actively use the analytical method to visualise a variety of mathematical concepts
find and use application possibilities not only in geometry and other mathematical disciplines, but also in natural sciences, computer graphics, etc.
solve geometric problems using the synthetic method
Competences
N/A
N/A
teaching methods
Knowledge
Lecture
Lecture supplemented with a discussion
Practicum
Task-based study method
Self-study of literature
Skills
Lecture
Lecture supplemented with a discussion
Practicum
Task-based study method
Self-study of literature
Competences
Lecture
Lecture supplemented with a discussion
Practicum
Task-based study method
Self-study of literature
assessment methods
Knowledge
Combined exam
Test
Seminar work
Skills
Combined exam
Test
Seminar work
Competences
Combined exam
Test
Seminar work
Recommended literature
  • Audin, Michéle. Geometry. Berlin : Springer, 2003. ISBN 3-540-43498-4.
  • Bican, Ladislav. Lineární algebra a geometrie. Vyd. 1. Praha : Academia, 2000. ISBN 80-200-0843-8.
  • Gallier, Jean. Geometric methods and applications : for computer science and engineering. New York : Springer, 2001. ISBN 0-387-95044-3.
  • Horák, P. a Janyška, J. Analytická geometrie. Brno, 1997.
  • Lávička, M. a Vršek J. Geometrie 1: Úvod do afinních a eukleidovských prostorů. Plzeň, 2020.
  • Mahel a kol. Sbírka úloh z lineární algebry a analytické geometrie. ČVUT, 1980.
  • Sekanina, M. a kol. Geometrie I., Státní pedagogické nakladatelství. Praha, 1986.
  • Tarrida, R. Affine Mapsa, Euclidean Motions and Quadrics. London, 2011.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (19) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (15) Category: Informatics courses 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (17) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (18) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (19) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (18) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (17) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (16) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (16) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (18) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (19) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (17) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (17) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (16) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (14) Category: Chemistry courses 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (15) Category: Pedagogy, teacher training and social care 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (19) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (17) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (17) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (15) Category: Physics courses 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (19) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (18) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (15) Category: Biology courses 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (19) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Music in Education (19) Category: Art and applied art 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (16) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (1) Category: Pedagogy, teacher training and social care 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (18) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): English Language in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
University of West Bohemia, date of update: 26.07.2024 23:53. Data created for academic year 2024/2025