数学

学士全日制 4年可申请助学金

专业介绍

I. The content of science

Fannie from teaching goal – future teachers vital imagination with practical activities in summary go , geometric concept and relationships students by conscious accordingly to be mastered and to life to be able to implement aspiration , their future work in the activity practical importance profession provider mathematician knowledge , skill and qualifications formation and from development consists of .

Fannie of teaching task – students from geometry information complex with just to introduce myself not , maybe students logical thinking , theorems practical issues to solve hand to know , as well to students education directions related knowledge to give

II. Main theoretical part (lectures)

II.I. Science content following topics includes :

Topic 1. Vectors and they on linear actions

Vectors . Vectors add and subtract . Vector number multiplication . Vector space

Topic 2. Vector on the right projection .

The point right on the line and on the plain orthogonal projection . Direction according to projection . Vector right on the line and on the plain projection , its properties .

Topic 3. Linear free and linear connected vectors .

Linear free and linear connected vectors family . Linear free and linear connected of vectors Properties of vectors . coplanarity conditions .

Topic 4. Vector space some .

Vectors given to the base see coordinates and their properties . Coordinates with given vectors on actions .

Topic 5. Vectors scalar k о ' time .

The modulus and direction of a vector cosines of vectors scalar k о ' time . Two vector between angle . Scalar I'm sorry . coordinates through expression .

Topic 6. Vectors vector and mixture multiplication .

Left and о ' ng systems . Vectors vector k о ' moment and mixed k о ' time . Properties , applications .

Topic 7. Coordinates with given of vectors vector and mixed k о ' parts .

Topic 8. On the plain affine and Descartes coordinates system replacement .

Affine coordinates system replacement . Descartes coordinates system replacement .

Topic 9. On the plains and in space coordinates other systems .

Pole and Descartes coordinates between connection . Spherical and cylindrical coordinates systems .

Topic 10. On the plains right of the line various equations .

Algebraic line and his/her order . Correct . of the line various surrender methods . On the plain right of the line various equations .

Topic 11. On the plain right of lines mutual situation .

From the point right up to the line distance . Parallel line lines between distance . On the plain right of lines mutual situations .

Topic 12. True lines handle and tie

That's right lines handle and I'm sorry . That's right . angular Descartes coordinates in the system right line and with him related metric issues .

Topic 13. Ellipse , properties .

Second orderly lines . Ellipse definition . Canonical equation , properties .

Topic 14. Hyperbola , properties .

Hyperbole definition . Canonical equation , properties . Hyperbola asymptotes .

Topic 15. Parabola, properties .

Definition of a parabola , canonical equation . Properties . Second orderly of the line tricks and directives .

Topic 16. Second orderly of the line pole in coordinates equation .

Canonical equation with given second orderly line : ellipse , hyperbola , parabola pole coordinates in the system equation .

Topic 17. Second orderly of the line general equation , center .

General equation with given second orderly line . Second orderly of the line center

Topic 18. Second orderly line and right of the line situation .

Second orderly of the line right line with intersection . Asymptotic directions . Try . and asymptotes

Topic 19. Second orderly Line main directions .

Second orderly line diameter . Main directions and symmetry arrows .

Topics 20-21. Second orderly line general equation canonical to look to bring

Coordinate arrows twist and parallel migration using central and decentralized second orderly of the line general equation canonical to look to bring

Topic 22. On the plains substitutions

The sets reflection and exchange , Exchanges Group . Movement and his/her properties .

Topic 23. Motion on a plane

Motion on a plane and his/her properties of the movement analytical Expression . Types of movement . Movement son symmetries to the product spread

Topic 24. In space affine and Descartes coordinates system replacement .

Affine coordinates system replacement . Descartes coordinates system replacement .

Topic 25. Plain surrender methods .

In space coordinates Method of the plane surrender methods . Plain general equation . Ax+By+C and Ax+By+Cz+D Geometric meaning of the polynomial notation. Checking the position of the plane relative to the coordinate system .

Topic 26. Plains each other situation .

Two and three of the plain each other situation . From the point to the plain distance

Topic 27. Plains handle and Is it connected ?

Plains handle and Is it connected? That 's right . angular Descartes coordinates in the system to the plain circle some issues .

Topic 28. In space right line

In space right of the line surrender methods . Correct of lines in space mutual location . Two right line behind corner

Topic 29. In space right line and of the plain situation

Two to cry right line between distance from point right up to the line distance That's right line with of the plain mutual location .

Topic 30. Second orderly surfaces .

Cylindrical and cone surfaces . Rotation surfaces . Cylinder

Topic 31. Ellipsoid and hyperboloids . Their properties .

Topic 32. Cone and his/her sections .

Topic 33. Paraboloids . Their properties .

Topic 34. Second orderly surface right linear makers . Try plain .

Topic 35. Second orderly the diametrical and symmetry Plane . Main directions .

Topic 36 . n dimensional linear and affine spaces

Topic 37. Linear and quadratic uniforms

Topic 38. Normal appearance square shape

III. Practical exercises according to instruction and recommendations .

Practical exercises for following topics recommendation is being done :

1 . Vectors and they on linear operations . Radius vector

2. Vectors given to the base see coordinates and their properties .

3. Vectors scalar multiples

4. Vectors vector and mixture multiples

5. affine and Descartes coordinates systems .

6. On the plain affine coordinates system replacement

7. On the plain Descartes coordinates system replacement

8. Polar coordinates system .

9. Spherical coordinates system

10. Cylindrical coordinates system

11. On the plain right of the line various equations .

12. On the plain from the point right up to the line distance . Parallel line lines between distance

13. On the plain right of lines mutual situation .

14. On the plain right lines handle and tie

15. Ellipse definition . Canonical equation , properties .

16. Hyperbole definition . Canonical equation , properties .

17. Parabola definition , canonical equation , properties .

18. Second orderly of the line pole in coordinates equation .

19. General equation with given second orderly line center and diameter .

20. General equation with given second orderly line headings and symmetry axes . Asymptote

21. Second orderly line general equation canonical to look to bring

22. In space affine coordinates system replacement .

23. In space Descartes coordinates system replacement .

24. Plain various equations to compile .

25. From the point to the plain and parallel planes between distance

26. Of the plains each other situation .

27. Plains handle and Is it connected ?

28. In space right of the line various equations .

29. In space from the point right to the line distance . and parallel straight lines between distance

30. Plain and right of the line mutual situation .

31. Second orderly surfaces . Cylindrical and cone surfaces .

3 2. Ellipsoid and his/her properties .

33. Hyperbaloid and his/her properties .

34. Parabaloid and his/her properties .

35. Second orderly surface right linear makers

36. Second orderly the diametrical and symmetry flatness

IV. Independent learning and independent work

When conducting independent learning, students are expected to prepare for practical classes; complete homework; review the topics of the materials covered; and master the theoretical knowledge topics intended for independent learning. The goal of independent learning is to consolidate the theoretical knowledge gained and obtain additional knowledge based on the specified topics. In this case, students should consolidate the knowledge gained in lectures by completing practical classes.

Independent education for recommendation attainable topics :

1. Vectors algebra elements elementary in geometry applications .

2. Vectors geometric in proofs applications .

3. Second orderly line general equation check and to make

4. Second orderly surface general equation canonical to look to bring

5. Spatial of figures plain with sections to make

6. Geometry the basics historical Commentary , Axioms system to explain ,

7. Axioms to the system wearable requirements . Lobachevsky geometry .

8. Barycentric coordinates using elementary geometry issues solve

9. Flat and spatial figures image to make . Complete and wrong images .

10. On the plain geometric of making various methods .

11. Circle and ruler using insoluble issues

12. 𝒏 - dimensional Euclid movement in space .

13. Same sex figures . Axonometry . Polke-Schwarz Theorem . Flat and spatial figures image to make

14. Of the plains each other situation . Plains handle and joint

15. Motion on a plane , its types , analytical expression .

16. Second orderly surfaces classification .

17. Geometric in matters complex of numbers applications .

18. Motion on a plane , its the most simple types , analytical expression .

19. Similarity replacement and Homothety . Similar replacement group and his/her part group

20. One ruler with executable geometric makings .

21. Parallel projection method with flat figures images to make

22. Convex many things .

23. Quadratic form and quadric . Quadratic uniform canonical to look to bring

24. Movement in space .

25. 𝒏 - dimensional vector and affine spaces . 𝒌 - dimensional plain .

26. Affine permutations . Affine substitutions groupE ⁿ in space similar substitutions .

V. Science education results ( formed) competencies )

Fannie to master as a result student :

· Within the framework of the tasks to be carried out in the process of mastering the subject "Analytical Geometry", the bachelor should have an idea of analytical geometry, higher and linear algebra;

·basic concepts of planimetry and their practical applications, theoretical foundations of the stereometry course, basic concepts of Euclidean and Lobachevsky geometry; the system of Gilbert and Weyl axioms, and knowledge of geometric constructions;

·Mathematics, as a special way of knowing the world, the integrity of its concepts and representations; the ability to understand the elements of vector algebra, permutations in space and their properties, affine and Euclidean spaces, linear and quadratic forms, permutations of quadratic forms, geometric constructions in the plane, and geometric constructions in space;

·Must be able to use mathematical symbols to express quantitative and qualitative relationships between objects, be able to connect theoretical and practical knowledge between mathematical disciplines, explore analytical and numerical solutions to solve examples and problems, have basic understanding of the basic concepts and methods of analytical geometry, constructive geometry, fundamentals of geometry, and multidimensional geometry, and be able to justify them in problems.

VI. Education technologies and methods :

Lectures ;
Practical training ;
Interactive case studies ;
Presentations ;
In groups work ;
Team with work and protection to do ;

VII. Credit to take for requirements :

To science related theoretical and methodological concepts complete mastery , analysis the results correct reflection bring to get , to study processes about independent under observation to conduct and current , intermediate control in the forms given task assignments completion , final control work submission .

Home literature

1. N. D. Dodajanov , M. Sh . Juraeva . Geometry . 1st name , T. " Shooter " , 1996.