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Course Title
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Geometry
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Year of study, speciality |
1, specialty “Mathematics and Information Technologies”
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Semester of study |
2 |
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4 |
Credit points |
4 |
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Name of the lecturer, scientific degree, occupation |
associate professor Vladimir V. Suvorov,PhD in Mathematics, Department of Geometry, Topology and Methods of Teaching Mathematics |
| 6 | Goals of studying | Development of skills of using existing experience when working in changed axiomatic, the ability to interpolate methods to a wider class of objects: in this case, to multidimensional affine and Euclidean spaces, as well as spaces of first and second order figures in them. The acquisition by the students of a sufficient amount of knowledge, skills and abilities in the field of geometry for their use in the study of other mathematical disciplines |
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7 |
Prerequisites
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Mathematical analysis, Algebra and number theory, Introduction to mathematics |
| 8 | Contents | Affine spaces . The coordinate method in. Planes in affine space. Affine mappings. Isomorphisms of affine spaces. Affine transformations. Geometry of an affine group. Affine equivalence of planes and pairs of planes. Figures of the second order (quadrics) in a real affine space . Normal equations of second order figures in .Euclidean spaces . Group of motions of . Angles and distances in. Investigation of second-order surfaces in space .Curves in space : ways of setting, arc length, curvature, torsion.Surfaces in space : ways of setting, fundamental forms, normal and principal curvatures, classification of points. |
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9 |
Recommendedliterature |
1. Kononov S.G. Analytic geometry: – Minsk: BSU, 2014. – 238 p (in Russian). 2. Milovanov M.V., Tyshkevich R.I., Fedenko A.S. Algebra and Analytic Geometry: in 2 volumes: – Minsk: Vysheishaya shkola, 1984. – Volume 2. – 302 p. (in Russian). 3. Burdun A.A., Murashko E.A., Tolkachov M.M., Fedenko A.S. A Collection of problems in algebra and analytic geometry. – Minsk: Universitetskoe, 1989. – 285 p. (in Russian). 4. Differential geometry (Edited by Fedenko A.S.): – Minsk: BSU, 1982. – 255 p. (in Russian). 5. A book of problems on differential geometry: Edited by Fedenko A.S. – M., Nauka, 1979. – 272 p. (in Russian). |
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Teaching methodology |
Lectures, solving problems, discussions, consultations. |
| 11 | Language of instruction | Russian |
| 12 | Requirements for study during the semester | – individual and collective tasks; – test papers.The final evaluation is made taking into account:40% – assessment of current academic performance,60% – result during the exam |
| 13 | Examination methodology | Examination |