714-0441/01 – Geometry (G)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits6
Subject guarantorRNDr. Jana Volná, Ph.D.Subject version guarantorRNDr. Jana Volná, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semesterwinter
Study languageCzech
Year of introduction2003/2004Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

In this course the students can acquaint with properties of affine and euclidean spaces, with affine, isometric and similar tranformations in this spaces.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Vector spaces. Orientation, spaces with scalar multiplication. Vector multiplication, orthogonal transformations. Affine spaces. Affine coordinates, relations between linear subspaces. Linear systems of hyperplanes. Affine transformations, classification of affine transformations in spaces of dimension 2 and 3. Euclidean spaces. Cartesian coordinates, Euclidean metrics, orthogonality. Isometric transformations. Classification of isometries in spaces of dimension 1 and 2. Similarities.

Compulsory literature:

Holme, A.: Geometry. Springer – Verlag, Berlin, Heidelberg, New York, 2002, ISBN 3-540-41949-7.

Recommended literature:

Jennings, G.A.: Modern Geometry with Applications, Springer-Verlag, New York, 1994, ISBN 0-387-94222-X.

Way of continuous check of knowledge in the course of semester

Conditions for credits of the seminar in Geometry Necessary conditions: 1. At least 80% presence in seminar. 2. Processing of two projects: I. Examples of partially parallel spaces of the affine space (dimension n≥4 ). II. Examples of the distance of partially parallel, nonparallel and nonintersecting spaces (dimension n≥4 ). 3. If all necessary conditions are fulfilled – 9 points. Supplementary condition: 4. Three tests, each 0 – 7 points. It is necessary to obtain at least 10 points from possible 30 points. Conditions for exam in Geometry 1. At least 10 points in seminar. 2. The exam consists of written (0- 40 points ) and oral (0 – 30 points ) examination. The minimum of written part is 15 points, in oral part is 10 points. 3. The result consists of sum of the points from seminar and from exam. 4. Evaluation is based on VSB-TUO statue. Set of questions: 1. Definition of affine space, affine coordinates, arithmetic affine space, linear independent points, transformation of affine coordinates. 2. Subspaces of affine space, analytical expressions of subspaces, symbolic equations, parametric and general equations of affine subspaces. 3. Mutual position of subspaces, collinearity of linear systems of hyperplanes. 4. Affine transformations of affine space, determinateness of analytical expression, module, invariant points, composition of transformations. 5. Classification of transformation classes. 6. Classification for line and plane. 7. Definition of Euclidean space, Cartesian coordinates, distance of points, transformation of coordinates. 8. Orthogonality and distances in Euclidean spaces. 9. Angles in Euclidean spaces for lines, for line and hyperplane and for subspace and hyperplane. 10. Isometries in Euclidean space, analytical expression, group of isometries. 11. Symmetries, classifications of symmetries, particularly in the plane. 12. Similarity in Euclidean space.

E-learning

Další požadavky na studenta

Extra requirements are not.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1.Affine spaces, affine coordinates. 2.Subspaces of the affine space, analytical formulation of the subspaces. 3.Mutual position of the subspaces. 4.Collinearity, linear systems of hyperplanes. 5.Affine transformations, affine transformaton of the affine space. 6.Classification of the affine transformations. 7.Classification for the line and the plane. 8.Vector spaces vith scalar multiplication, Euclidean space. 9.Cartesian coordinates, orthogonality. 10.Distances, perturbations. 11.Isometries. 12.Classification of isometries in spaces of dimension 1 and 2. 13.Similarities. 14.Reserve.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2008/2009 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 20 (20) 0
                Written exam Written test 15  5
                Other task type Other task type 5  5
        Examination Examination 80 (80) 0
                Written examination Written examination 60  0
                Oral Oral examination 20  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

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