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  Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


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 nonhomogeneous 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

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  or  UMB/551 and UMB/CV585  or  UMB/585 and UMB/CV584  or  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 

Study plans that include the course 
Faculty  Study plan (Version)  Category of Branch/Specialization  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 