Discrete mathematics

Discrete mathematics is the branch of mathematics that deals with structures which are finite or infinite, as long as they can be counted one by one. In contrast to analysis and continuous topics, discrete mathematics works with objects that can be separated into clearly distinct units.

 

It includes, among others, set theory, logic, combinatorics, graphs, number theory and algorithms. These areas form the foundation of modern computer science, information security, and much of theoretical data science.

 

In discrete mathematics, one works with objects that can be counted one by one, e.g. integers, vertices of a graph, or elements of a set. Discrete means that we look at separate units rather than continuous quantities such as lines and functions.

 

Example: The set of even numbers is an infinite but countable set:

 

$$ \large \{0, 2, 4, 6, 8, \ldots\} $$

 

 

Applications

Discrete mathematics is used in many areas of mathematics and computer science:

 

• Combinatorics: counting and calculating possibilities, e.g. how many ways a selection can be made.
• Graphs: modeling of networks, e.g. transport, communication, or social networks.
• Logic: formal systems for deriving truth values and conclusions.
• Cryptography: security systems based on number theory and algorithms.
• Algorithms: efficient step-by-step methods for computation and problem solving.

 

 

Why is it important?

Discrete mathematics provides the theoretical foundations for large parts of modern technology.

Programming languages, databases, networks, and security systems are all built on methods and ideas from it. 

At the same time, it is an area that develops mathematical skills for logical thinking and problem solving.