# What Is Discrete Math? | Khan Academy Blog

## What is discrete mathematics?

Discrete mathematics is a branch of mathematics that focuses on the study of countable, distinct objects. It is often used in fields such as computer science, statistics, engineering, and cryptography.

## What is discreteness?

One key concept in discrete mathematics is the idea of “discreteness.” In mathematics, a set is said to be discrete if there is a certain amount of separation between its elements. For example, the set of integers is discrete because there is a clear, definable gap between each number. On the other hand, the set of real numbers is not discrete because there is no smallest amount of separation between two real numbers.

Discrete mathematics encompasses a wide range of topics. Here are a few key areas that you might encounter:

## What is combinatorics?

This area of discrete mathematics focuses on the study of combinations and permutations. It often deals with questions such as: How many ways can you arrange the letters in a word? How many different subsets can you create from a given set?

## What is graph theory?

Graph theory is the study of connections between objects. In graph theory, you represent the objects as “nodes” or “vertices” and the connections between them as “edges.” Graph theory can be used to analyze social networks, transportation networks, and even computer algorithms.

## What is number theory?

Number theory is the study of the properties of natural numbers. It focuses on topics such as divisibility, prime numbers, and modular arithmetic. Number theory is often used in cryptography to create secure encryption methods.

## What is logic?

Logic is the study of the principles of reasoning. In discrete mathematics, you often encounter symbolic logic, which uses symbols to represent logical statements. This form of logic can be used to create formal proofs, analyze algorithms, and build computer programs.

Discrete mathematics is a fascinating and broad field of study. If you are interested in computer science, statistics, engineering, or cryptography, understanding discrete mathematics will be essential to your success.