Rudiments of Geometry
General data
Course ID: | 0600-MS1-2GEL |
Erasmus code / ISCED: |
11.102
|
Course title: | Rudiments of Geometry |
Name in Polish: | Geometria elementarna |
Organizational unit: | (in Polish) Instytut Matematyki. |
Course groups: | |
ECTS credit allocation (and other scores): |
(not available)
|
Language: | Polish |
Type of course: | obligatory courses |
Prerequisites (description): | (in Polish) Założenia i cele przedmiotu: Student zapozna się z podstawowymi pojęciami geometrii afinicznej i afiniczno metrycznej oraz z własnościami grup przekształceń zachowujących podstawowe relacje w tych geometriach. |
Mode: | (in Polish) w sali |
Short description: |
Course objectives: A student becomes familiar with basic notions of affine and metric affine geometry and with properties of transformations which preserve basic relations of these geometries. |
Full description: |
Course profile: academic Form of study: stationary Course type: obligatory Academic discipline: Mathematics, field of study in the arts and science: mathematics Year: 2, semester: 4 Prerequisities: Linear Algebra II, Elements of Logic and Set Theory lecture 30 h. exercise class 30 h. Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. ECTS credits: 4 Balance of student workload: attending lectures15x2h = 30h attending exercise classes 7x4h + 2h(preliminary teaching) = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 5x2h = 10h the final examination: preparation.and take 15h + 4h = 19h Quantitative description Direct interaction with the teacher: 74 h., 2 ECTS Practical exercises: 75 h., 3 ECTS |
Learning outcomes: |
Learning outcomes: Knows basic techniques of the analytical affine geometry; in particular: he can determine equations of a line, a plane, and of an arbitrary subspace characterized in terms of their geometrical position, can solve problems where the affine cross ratio is involved, can apply the Ceva and the Menelaos Theorem.K_W04, K_U17, K_U18 Knows fundamental types of affine transformations and their analytical characterization, can characterize affine transformations determined by means of simple invariants.K_W04, K_W05, K_U20 Knows fundamental systems of notions used to characterize Euclidean Geometry (orthogonality, equidistance); can characterize mutual position of spheres and subspaces. Can use inversion to translate problems of inversive ((Moebius) geoemetry into the language of Euclidean Geometry and vice versa.K_W04, K_U17, K_U18 Knows and can use (in simple cases) principles of classification of isometries of Euclidean Spaces.K_W04, K_U17, K_U18 After completing the course student gets backgrounds enabling him to learn and develop classical geometry.K_W06, K_K01, K_K02 |
Assessment methods and assessment criteria: |
The overall form of credit for the course: final exam |
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