Affine and Projective Geometry

obowiązkowe

Course objectives: Understanding elements of projective (and affine) geometry to the extend necessary to listen to specialized lectures.

Course profile: academic

Form of study: stationary

Course type: obligatory

Academic discipline: science and natural science, field of study in the arts and science: mathematics

Year: 3, semester: 5

Prerequisities: none

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

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.

Knows roles of fundamental configurational axioms: Minor and Major Desargues Axiom, Minor and Major Pappus Axiom.

Knows the structure of subspaces of a projective space: can determine meets of subspaces and subspaces spanned by systems of subspaces.

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.

Knows how collineations act on the family of subspaces; knows the Chow Theorem.

KA6_WK01, KA6_WG01, KA6_WG02, KA6_UK01, KA6_KK01

The overall form of credit for the course: final exam