Course: Geometry II

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Course title Geometry II
Course code UMB/586
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Frequency of the course In academic years starting with an odd year (e.g. 2017/2018), in the summer semester.
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory-optional
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
Content of lectures: The goal of the course is the studying of analytic theory of conic sections and quadrics. Firstly we explain complex and projective extension of affine space, which are natural constructions useful for the theory. The main object then is to formulate the definition of conic sections and quadrics, and study projective, affine and metric properties. On examples we demonstrate, how is the theory related with the usual facts that students know from high school and other courses. We present projective, affine and metric classifications of conic sections and quadrics, together with method for recognising of the type of conic section or quadric. Summary: 1. The complex extension of vector and affine spaces. 2. Projective spaces, arithmetical and geometric basis. 3. Restriction of projective space to affine space, projective extension of an affine space, homogeneous and non-homogeneous coordinates. 4. Conic sections of projective plane - definition, regular and singular conic sections, pole and polar line, tangent line, the projective classification. 5. Affine properties of conic sections - centres, diameters, asymptotic lines, the affine classification. 6. Metric properties of conic section - principal numbers and directions, axes, vertices, metric classifications. 7. Conic sections as sets of points with suitable properties - connections with high school concepts.

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 geometry of conic sections (projective, affine, Euclidean).
Student will acquire knowledge od analytic theory of conic sections.
Prerequisites
The konwlege of linear algebra and geometry on the level of courses UMB584 Geometry I a UMB585 Linear algebra II.
UMB/CV551
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UMB/551 and UMB/CV585
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UMB/585 and UMB/CV584
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UMB/584

Assessment methods and criteria
Combined exam, Seminar work

Active participation in the course and understanding of the presented theory, passing both theoretical and practipal part of the exam (50%).
Recommended literature
  • Budínský, B., Analytická a diferenciální geometrie, Praha, SNTL, 1983, 296 stran.
  • Janyška , J., Sekaninová, A, Analytická teorie kuželoseček a kvadrik, Brno, Masarykova univerzita, 1996, 178 stran.
  • Pech, P., Kuželosečky, Č. Budějovice, Jihočeská univerzita, 2004, 150 stran.
  • Pech, P., Kuželosečky, Č. Budějovice, Pedagogická fakulta, Jihočeská univerzita, 1998, 90 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): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer