What is the difference between the discrete mathematics and other mathematical courses?

Lecture 1. Introduction

Aims and objectives of the subject “Discrete mathematics and discrete structures”:

ü To introduce students to some main concepts and methods of discrete mathematics (sets, relations, elements of mathematical logic, Boolean algebra, graphs, combinatorial analysis, etc.)

ü To make students aware of some applications of discrete mathematics in the area of discrete information processing by computers

ü To teach students how to apply concepts and methods of discrete mathematics for solving their information processing problems (to be able to analyze the structure of discrete components and their relation in the problem and to design an algorithm that produces the required data).

About the word “discrete”:

In every day English, the word “discrete” means separate, distinct. A discrete element is easily distinguished from other elements in a group (set). It is recognized clearly.

In a continuous set, it’s not easy to say if a given value represent one element of a set or many values.

For example, value 3.14…. It may represent an infinite number of rational and irrational numbers depending on the digits that follow the digit “4”. A discrete element has only one unambiguous value.

What is the difference between the discrete mathematics and other mathematical courses?

Discrete mathematics studies mainly finite sets. It also does not use the limit value transition like .

On the other hand, in the course of calculus, almost all sets under consideration are infinite, like the set of rational numbers, the set of all values of a function, etc.

Sets studied in discrete mathematics are finite. But very often such finite sets contain a very large number of elements. For example, the set of all Boolean functions of 10 arguments contains elements. This is a huge number. A great number of elements in many sets makes it necessary to develop special methods for research and analysis of such sets.

The course of discrete mathematics consists of such main parts:

ü Set theory

ü Propositional logic

ü Predicate logic

ü Boolean algebra

ü Basics of counting

ü Types of algorithms and types of problems