# Algebra

Организатор: Финансовый университет при Правительстве РФ
Москва
Даты проведения:

С открытой датой

## Описание мероприятия

Язык обучения: английский

## Описание программы

This unit develops a student’s proficiency in working with the mathematical methods of algebra and develops the student’s understanding of the theoretical concepts (such as vector space) behind these methods

The objectives specifically include:

• to enable students to acquire skills in the methods of algebra, as required for their use in further mathematics subjects and economics-based subjects
• to prepare students for further units in mathematics and/or related disciplines

Assessment

This course is assessed by a three-hourunseen written examination.

## Учебный план:

Matrices, vectors and their geometry: Vectors and matrices, the algebra of vectors and matrices; Cartesian and vector equations of a straight line; normal vectors and planes; the Cartesian and vector equations of a plane; extension to higher dimension.

Systems of linear equations: Systems of linear equations and their expression in matrix form; Solving systems of linear equations using row operations; consistent and inconsistent systems; systems with free variables; range and rank of a matrix; general solution of linear systems.

Matrix inversion and determinants: finding inverses using row operations; determinants; matrix inversion using cofactors; Cramer’s rule; input-output analysis.

Sequences, series and difference equations: Arithmetic and Geometric Progressions; sums of numbers, squares and cubes; solving firstorder difference equations; application of first-order difference equations to financial problems; the cobweb model; Second-order difference equations.

Vector spaces and related concepts: Vector spaces; subspaces, including those associated with matrices; linear span; linear independence and dependence; bases and dimension; coordinates; linear transformations.

Diagonalisation of matrices: eigenvalues and eigenvectors; diagonalisation of a matrix and its connection with eigenvectors; finding powers of matrices using diagonalisation;

Applications of diagonalisation: Markov chains; using diagonalisation to solve systems of differential equations

## Результат обучения:

At the end of the course and having completed the essential reading and activities students should be able to:

• use the concepts, terminology, methods and conventions covered in the unit to solve mathematical problems in this subject
• solve unseen mathematical problems involving understanding of these concepts and application of these methods
• see how algebra can be used to solve problems in economics and related subjects
• demonstrate knowledge and understanding of the underlying principles of algebra.

## Требования к поступающим:

The course may not be taken with MT105b Mathematics 2

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