Bachelor
2021/2022

# Linear Algebra and Geometry

Category 'Best Course for New Knowledge and Skills'

Type:
Compulsory course

Area of studies:
Applied Mathematics and Information Science

Delivered by:
Big Data and Information Retrieval School

Where:
Faculty of Computer Science

When:
1 year, 1-4 module

Mode of studies:
offline

Open to:
students of one campus

Language:
English

ECTS credits:
10

Contact hours:
144

### Course Syllabus

#### Abstract

The course introduces students to the elements of linear algebra and analytic geometry provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results. We will approach the subject from both a practical point of view (learning methods and acquiring computational skills relevant for problem-solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts). Topics covered include matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year. There is no formal prerequisites for this course. However, a reasonable knowledge of some of the fundamentals of high school mathematics such as: working with rational and real numbers, fractions, basic algebraic manipulations, geometry, and some trigonometry is assumed. Familiarity with basic mathematical concepts (sets, functions and etc.) is a plus. Calculus is not required for this course.

#### Learning Objectives

- Students will understand the mathematical concepts and terminology involved in linear algebra and analytic geometry.
- Students will gain an acceptable level of computational proficiency involving the procedures in linear algebra and analytic geometry.
- Students will understand the axiomatic structure of some mathematical objects and learn to construct simple proofs.
- Students will be able to apply his or her knowledge to some applications of linear algebra and analytic geometry.
- Students will be introduced to abstract mathematical reasoning and the art of reading, writing and understanding rigorous mathematical proofs.

#### Expected Learning Outcomes

- Student will be able to use computational techniques and algebraic skills essential for the study of systems of linear equations, matrix algebra, complex numbers, vector spaces, bilinear and quadratic forms, eigenvalues and eigenvectors, orthogonality and diagonalization, etc.
- Students will be able to critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra and analytic geometry.
- Students will be able to work collaboratively with peers and instructors to acquire mathematical understanding and to formulate and solve problems and present solutions.
- Students will be able to work collaboratively with peers and instructors to acquire mathematical understanding and to formulate and solve problems and present solutions.

#### Course Contents

- Matrices and Matrix Algebra.
- Systems of Linear Equations.
- Permutations.
- Determinants.
- Fields and Complex Numbers.
- Vector Spaces.
- Bilinear and Quadratic Forms.
- Euclidean Spaces.
- Analytic Geometry.
- Linear Operators.

#### Assessment Elements

- 1st module In-class Written TestWritten work up to 90 minutes.
- 3rd module In-class Written TestWritten work up to 90 minutes.
- 2nd module In-class Oral Test
- 4th module In-class Oral Test
- 2nd module Written ExamWritten work up to 160 minutes. The exam may be carried out online via distance learning platforms.
- 4th module Written ExamThe exam may be carried out online via distance learning platforms. Письменный экзамен, длительность 100 минут. Можно пользоваться калькуляторами (нельзя телефоном). Выолненная работа фотографируется/ сканируется прикрепляется в гугл форме. Ссылка на гугл форму в чате Zoom
- 1st semester QuizzesThe average grade of all the quizzes in the 1st semester.
- 2nd semester QuizzesThe average grade of all the quizzes in the 2nd semester.
- 1st semester Homework assignmentsThe average grade of all the homework assignments in the 1st semester.
- 2nd semester Homework assignmentsThe average grade of all the homework assignments in the 2nd semester.

#### Interim Assessment

- 2021/2022 2nd moduleThe cumulative course grade for the first semester, C_1, is obtained without rounding by the following formula: C_1 = 5/16*O_1 + 4/16*W_1 + 4/16*Q_1 + 3/16*H_1. The intermediate course grade for the i-th semester, I_1, is obtained by the following formula: I_1 = Round_i(3/10*E_1 + 7/10*C_1), where O_1 is the grade for the first in-class oral test; W_1 is the grade for the first in-class written test; Q_1 is the average grade of all the quizzes in the first semester; H_1 is the average grade of all the homework assignments in the first semester; E_1 is the grade for the first exam.
- 2021/2022 4th moduleThe cumulative course grade for the second semester, C_2, is obtained without rounding by the following formula: C_2 = 5/16*O_2 + 4/16*W_2 + 4/16*Q_2 + 3/16*H_2. The intermediate course grade for the second semester, I_2, is obtained by the following formula: I_2 = Round_2(3/10*E_2 + 7/10*C_2), where O_2 is the grade for the second in-class oral test; W_2 is the grade for the second in-class written test; Q_2 is the average grade of all the quizzes in the second semester; H_2 is the average grade of all the homework assignments in the second semester; E_2 is the grade for the second exam.

#### Bibliography

#### Recommended Core Bibliography

- Anthony, M., & Harvey, M. (2012). Linear Algebra : Concepts and Methods. Cambridge, UK: Cambridge eText. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=443759

#### Recommended Additional Bibliography

- Linear algebra with applications, Leon, S. J., 2002