Delivered at:: Big Data and Information Retrieval School

Course type:: Compulsory course

When:: 1 year, 1-4 module

Instructors

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.
Bilinear and Quadratic Forms.
Euclidean Spaces.
Analytic Geometry.
Linear Operators.

Assessment Elements

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

Interim Assessment

2024/2025 2nd module
The 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 first semester, I_1, is obtained by the following formula: I_1 = Round_1(3/10*E_1 + 7/10*C_1)
2024/2025 4th module
The 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)

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

Authors

MEDVED NIKITA YUREVICH
MAZHUGA ANDREY MIKHAYLOVICH

Bachelor’s Programme 'Data Science and Business Analytics'

Linear Algebra and Geometry