Course: Geometry I.

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Course title Geometry I.
Course code UMB/584
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the summer semester.
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Zalabová Lenka, doc. Mgr. Ph.D.
Course content
The content of the course is the coordinated geometry, mainly the studying of linear objects in affine and Euclidean spaces. The main goal of the course is to explain the theory, which generalizes the knowledge of students on geometry in plane and space from high schools. In the course, we focus on solution intersection and distance problems. Summary: 1. Affine spaces. 2. Affine frames and coordinates. 3. Affine subspaces and their description. 4. Intersection problems for affine subspaces. 5. Sheaves of hyperplanes. 6. Distinguished subsets; half-spaces, angles, convex sets, simplices. 7. Euklidean spaces. 8. Orthonormal frames and coordinates. 9. Perpendicular subspaces, normal line of hyperplane. 10. Cross product, Gramm determinant, volume of parallelepiped. 11. Distance and angle between subspaces. 12. Affine mappings and affine transformations. Content of practicals: Solving of concrete problems demonstrating the theory.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
  • Preparation for classes - 56 hours per semester
  • Preparation for exam - 56 hours per semester
  • Class attendance - 56 hours per semester
Learning outcomes
The goal of the course is the coordinated geometry of linear objects (affine, Euclidean).
Student will acquire knowledge of affine geometry.
Prerequisites
The knowledge of linear algebra on the level of the courses UMB551 Linear algebra a UMB585 Linear algebra II.
UMB/CV551
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UMB/551 and UMB/CV585
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UMB/585

Assessment methods and criteria
Combined exam

Active participation in the course and understanding of the theory, passing both written and oral part of the exam (50%).
Recommended literature
  • Budínský B., Analytická a diferenciální geometrie, Praha, SNTL, 1983, 296 stran..
  • Horák P., Janyška J., Analytická geometrie, Brno, Masarykova univerzita, 1997, 151 stran..
  • Leischner P., Geometrická zobrazení, Č. Budějovice, Jihočeská univerzita, 2010, 120. stran..
  • Pech P., Afinní bodový prostor, Č. Budějovice, Pedagogická fakulta, Jihočeská univerzita, 1996, 46 stran..
  • Pech P., Analytická geometrie lineárních útvarů, Č. Budějovice, Jihočeská univerzita, 2004, 162 stran..
  • Pech P., Euklidovský prostor, Č. Budějovice, Pedagogická fakulta, Jihočeská univerzita, 1997, 51 stran..
  • Pech P., Strobl J., Analytická geometrie lineárních útvarů, Pedagogická fakulta, Jihočeská univerzita, Č. Budějovice, 1994, 158 stran..
  • Sekanina M. a kol., Geometrie I, Praha, SPN, 1986, 197 stran..
  • Sekanina M. a kol., Geometrie II, Praha, SPN, 1988, 307 stran..


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer