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Regular version of the site
Bachelor 2022/2023

# Linear Algebra and Geometry

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type: Compulsory course (Data Science and Business Analytics)
Area of studies: Applied Mathematics and Information 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 are 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 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.
• Euclidean Spaces.
• Analytic Geometry.
• Linear Operators.

#### Assessment Elements

• Oral test (1st semester)
• Oral test (2nd semester)
• Written test (1st semester)
• Written test (2nd semester)
• Quizzes (1st semester)
The cumulative course grade for the first semester will contain the average grade of all the quizzes in the 1st semester
• Quizzes (2nd semester)
The cumulative course grade for the second semester will contain the average grade of all the quizzes in the 2nd semester
• Home assignments (1st semester)
The cumulative course grade for the first semester will contain the average grade of all the Home assignments in the 1st semester
• Home assignments (2nd semester)
The cumulative course grade for the second semester will contain the average grade of all the Home assignments in the 2nd semester
• Written exam (1st semester)
• Written exam (2nd semester)

#### Interim Assessment

• 2022/2023 2nd module
The cumulative course grade for the first semester, C1, is obtained without rounding by the following formula: C1 = 5/16*O1 + 4/16*W1 + 4/16*Q1 + 3/16*H1. The intermediate course grade for the first semester, I1, is obtained by the following formula: I1 = Round1(3/10*E1 + 7/10*C1),
• 2022/2023 4th module
The cumulative course grade for the second semester, C2, is obtained without rounding by the following formula: C2 = 5/16*O2 + 4/16*W2 + 4/16*Q2 + 3/16*H2. The intermediate course grade for the second semester, I2, is obtained by the following formula: I2 = Round2(3/10*E2 + 7/10*C2)

#### 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

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

#### Authors

• MEDVED NIKITA YUREVICH
• MAZHUGA ANDREY MIKHAYLOVICH