Linear Algebra & Analytical Geometry

Description: This course is one of the general mathematical disciplines. Analytical geometry is a section of geometry, the basic concepts of which are simple geometric objects (points, lines, planes, and second-order curves and surfaces). The main research tools of analytical geometry are the coordinate method and elementary algebra methods. Linear algebra is a branch of mathematics that studies vectors, vector spaces, linear transformations, and systems of linear equations.

Amount of credits: 6

Пререквизиты:

• Математика. Школьный курс

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• The main goals are the following: • systems of linear algebraic equations; • developing in students a fairly broad view of analytical geometry; • study of the main method of analytical geometry - the coordinate method, • as well as the vector method, the method of geometric transformations; • study of the applications of these methods to the study of flat and spatial objects determined by equations of the first and second degrees; • development of students' mathematical culture and thinking, proof skills. This discipline creates the basis for mastering both mathematical and a number of physical sections.

Objective

• Main objectives of the course: • to form in students the concepts of linear algebra, various vector and point-vector spaces; • study straight lines, planes, lines and second-order surfaces in two-dimensional and three-dimensional spaces; • study affine transformations of the plane and their special cases; • learn to apply the apparatus of linear and vector algebra, the coordinate method, geometric and projective transformations to solve geometric problems.

Learning outcome: knowledge and understanding

Learning outcome: applying knowledge and understanding

Learning outcome: formation of judgments

Learning outcome: communicative abilities

Learning outcome: learning skills or learning abilities

Teaching methods

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

Key reading

• Курош А.Г. Курс высшей алгебры. - М.: Физматлит, 2017. — 431 с.
• Окунев Л.Я. Высшая алгебра. - М.: Высш.шк., 2013.
• Проскуряков И.В. Сборник задач по линейной алгебре. М.: Высш. шк., 2011.
• Александров П.С. Курс аналитической геометрии и линейной алгебры. – СПб.: Лань, 2016.
• Клетеник Д.В. Сборник задач по аналитической геометрии. – СПб.: ПРОФЕССИЯ, 2018.
• Рябушко А.П., Бархатов В. В и др. Индивидуальные задания по высшей математике. – Алматы: Образование и наука, 2015, Ч 1.

Further reading