# Discrete mathematics and algebra

Организатор: Финансовый университет при Правительстве РФ
Москва
Даты проведения:

С открытой датой

## Описание мероприятия

Язык обучения: английский

## Для кого эта программа

The course is designed to enable you to:

• obtain general knowledge about the areas of discrete mathematics and algebra
• understand a variety of methods used to construct mathematical proofs
• acquire an insight into applications such as coding and design

## Описание программы

This course is intended to give an introduction to the areas of mathematics known as discrete mathematics and the study of modern algebra. A key aim is to provide an insight into the interactions between these areas, in particular to modern applications such as coding and cryptography.

## Учебный план:

Counting: selections, inclusion-exclusion, partitions and permutations, Stirling numbers, generating functions, recurrence relations.

Graph Theory: basic concepts (graph, adjacency matrix, etc.), walks and cycles, trees and forests, colourings.

Set Systems: matching, finite geometries, block designs.

Abstract groups: revision of key concepts such as cyclic groups, subgroups, homomorphisms and Lagrange’s theorem. Conjugation and normal subgroups. Group actions.

Applications of algebra to discrete mathematics I: permutations, orbits and stabilisers, the orbit-stabiliser theorem; applications to counting problems.

Rings and polynomials: the Euclidean algorithm for polynomials, integral domains, ideals, factor rings, fields, field extensions.

Finite fields: construction, the primitive element theorem, and finite linear algebra.

Applications of algebra to discrete mathematics II: finite Geometry: designs, affine and projective planes.

Error-correcting codes: linear codes, cyclic codes, perfect codes.

## Результат обучения:

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

• demonstrate knowledge definitions, concepts and methods in the topics covered and how to apply these
• find and formulate simple proofs
• model situations in a mathematical way and derive useful results.

## Требования к поступающим:

If taken as part of a BSc degree, courses which must be passed before this courses may be attempted:

• MT2116 Abstract mathematics.
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