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Affine and Projective Geometry

General data

Course ID: 0600-MS1-3GAR#a Erasmus code / ISCED: 11.103 / (0541) Mathematics
Course title: Affine and Projective Geometry Name in Polish: Affine and Projective Geometry
Department: Faculty of Mathematics and Informatics
Course groups: (in Polish) 3L stac. I st. studia matematyki - przedmioty obowiązkowe
ECTS credit allocation (and other scores): 4.00
view allocation of credits
Language: English
Type of course:

obligatory courses


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

Classes in period "Academic year 2018/2019" (in progress)

Time span: 2018-10-01 - 2019-06-30
Choosen plan division:

see course schedule
Type of class: Class, 30 hours more information
Lecture, 30 hours more information
Coordinators: Jarosław Kotowicz
Group instructors: (unknown)
Students list: (inaccessible to you)
Examination: Examination
Course descriptions are protected by copyright.
Copyright by University of Bialystok.