# Discrete Mathematics Tutorial

Last updated : May 09, 2023

## What is Discrete Mathematics?

Discrete signify distinct and separate. Discrete mathematics is the study of discrete mathematical structures rather than continuous ones. Discrete mathematics deals with countable or finite values. Integers, graphs, and logic statements are some of examples of countable or finite structures. On the other hand, continuous mathematics structures work with structures that may change smoothly and require real numbers.

### Definition

*"Discrete Mathematics plays a fundamental role in Computer Science and is an essential background for almost all of the advanced courses like theory of computation, compilers, databases, operating systems, algorithms and data structures etc."*

Hence, Discrete Mathematics studies discrete items; the concepts and notations of discrete mathematics are important to study different application areas like computer algorithms, programming languages, cryptography, automated theorem proving, and software development.

## Why discrete mathematics is important to computer science?

Discrete Mathematics plays a vital role in computer science and engineering because of its usefulness in computer technology, discrete mathematics has seen a surge in popularity during the last few decades. This is because discrete mathematics focuses on the study of very small sets of numbers. On the other hand, computer implementations are very important when it comes to bringing concepts from discrete mathematics to applications in the real world, such as in operations research.

Concepts and notations from discrete mathematics are helpful in the study and description of objects and issues in all areas of computer science, such as to develop computer algorithms, programming languages, cryptography, flow charts, computer networks using graphs, logic building, automated theorem proving, and software development.

Mainly, Discrete Mathematics is concerned with graphs, combinatorics, sets, logical propositions, and so on. It employs logical concepts to mathematically describe and reason with essential data kinds and structures that are utilized to develop algorithms, systems, and software, among other things.

To restate, one of the primary reasons for its significance is that the information contained in a computer can be saved and altered distinctly, and this is one of the reasons why this is so important. In a nutshell, one may claim that the computer has limited precision.

## What is the purpose of discrete mathematics?

The purpose of discrete mathematics:

- Validating the mathematical reasoning behind the logic.
- To find out the association between discrete sets.
- To find out the total number of possible configurations for a set of given items.
- To examine the processes with a fixed number of stages may be analyzed.
- It provides the groundwork on which more sophisticated mathematical work may be built.

In this context, followings are the key aspects of discrete mathematics:

**Logic and Proof Techniques**: Using logic, we may judge the soundness of an argument.**Basic Number Theory**: It's a branch of mathematics; number theory is concerned with the 'study of the characteristics of integers.'**Sets**: Concerned with the fundamental study of sets.**Relations and Functions**: Relations and functions are used to describe the relationship between the object from one set to the other set, and the sets must not be empty.**Combinatorics**: Combinatorics is the study of organizing objects. For instance, there are different ways to compose a word using five letters.**Big O**: For the growth of functions.

This Discrete Mathematics tutorial contains all the basic to advance discrete mathematics topics like functions, algebra, graph theory, logic, combinatorics, probability, graph, set theory, and many more.

## Discrete Mathematics Tutorial Topics

- Set Theory: What It Is, Types, Symbols, and Examples
- Set: Cardinality, Notations, Construction, Operations
- Group Theory and Its Types in Discrete Mathematics
- Discrete Mathematics Functions, Their Types, and Examples
- Algebraic Structure and Properties of Structure
- Permutation Group and Its Types
- Types of Relations in Discrete Mathematics
- Properties of Binary Relation in a Set
- Rings and Types of Rings in Discrete Mathematics
- Finite-state Machine: What It Is, Components, and Types
- Normal Forms and Their Types
- Propositional Logic in Discrete Mathematics
- Operations in Propositional Logic in Discrete Mathematics

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