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Course Title

Geometry   

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Year of study,

speciality 

1, speciality  “Computer mathematics and systems analysis”

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Semester of study

2

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Credit points

3

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Name of the lecturer, scientific degree, occupation

Professor Sergei M. Ageev,

PhD in Mathematics, Department of Geometry, Topology and Methods of Teaching Mathematics

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Goals of studying

Mastering the basic method of research in geometry – the method of coordinates. Mastering of multidimensional Euclidean, affine, projective spaces and first and second order figures in them. Acquisition of knowledge, skills and abilities in the field of geometry for their use in the study of other mathematical disciplines.
     As a result of the study, the student should be able to:
 -use vector algebra methods; apply and use the method of coordinates; apply and use methods of multidimensional affine, Euclidean, projective spaces; use the properties of figures of the first and second orders

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Prerequisites

Analytic geometry, algebra, mathematical analysis

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Contents

Vectors and operations over them. Affine transformations and Euclidean motions. Affine spaces. Affine maps. Isomorphism of affine spaces. Affine transformations.
Quadrics in the real affine space. Affine classification of quadrics. Euclidean spaces. Euclidean motions  and Euclidean geometry. Quadrics in Euclidean space

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Recommended literature

1. Кононов С.Г.Аналитическая геометрия: учебное пособие. –Минск: БГУ, 2014. 2.Милованов М.В., Тышкевич Р.И., Феденко А.С.Алгебра и аналитическая геометрия: в 2 ч.:учебное пособие. – Минск: Вышэйшая школа,1984.

3.Александров П.С.Курс аналитической геометрии и линейной алгебры: учебник. –М., Наука, 1979.

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Teaching methodology

Lectures, solving problems, discussions, consultations

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Language of instruction  

Russian

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Requirements for study during the semester

– individual and collective tasks;

– short tests.

The final evaluation is made taking into account:

  40% – assessment of current academic performance, 60% – result during the exam

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Examination methodology

Oral examination