Affine and Projective Geometry

General data

Course ID:	0600-MS1-3GAR#a
Erasmus code / ISCED:	11.103 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Affine and Projective Geometry
Name in Polish:	Affine and Projective Geometry
Organizational unit:	Faculty of Mathematics and Informatics
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	obligatory courses
Prerequisites:	Algebra I 0600-MS1-2ALG1#a Rudiments of Geometry 0600-MS1-2GEL#a
Short description:	Course objectives: Understanding elements of projective (and affine) geometry to the extend necessary to listen to specialized lectures.
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: 3, semester: 5 Prerequisities: Rudiments of Geometry, Algebra I 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 and understands notions of an affine and of a projective space; via the operations of the projective completion and of the affiine reduction he can transform problems of affine geometry to the framework of projective geometry and vice versa. K_W01, K_W02, K_W06, K_U01, K_K01 Knows roles of fundamental configurational axioms: Minor and Major Desargues Axiom, Minor and Major Pappus Axiom.K_W01, K_W02, K_W06, K_U01, K_K01 Knows the structure of subspaces of a projective space: can determine meets of subspaces and subspaces spanned by systems of subspaces.K_W01, K_W02, K_W06, K_U01, K_K01 Knows analytical characterizations of collineations and correlations of (Pappian) projective spaces; knows the role of Chasles Theorem and the role of cross ratio invariance in this context.K_W01, K_W02, K_W06, K_U01, K_K01 Knows how collineations act on the family of subspaces; knows the Chow Theorem.K_W01, K_W02, K_W06, K_U01, K_K01
Assessment methods and assessment criteria:	The overall form of credit for the course: final exam

This course is not currently offered.

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