What Is Discrete Math? | Khan Academy Weblog

What’s discrete arithmetic?

Discrete arithmetic is a department of arithmetic that focuses on the research of countable, distinct objects. It’s typically utilized in fields similar to laptop science, statistics, engineering, and cryptography.

What’s discreteness?

One key idea in discrete arithmetic is the thought of “discreteness.” In arithmetic, a set is claimed to be discrete if there’s a certain quantity of separation between its components. For instance, the set of integers is discrete as a result of there’s a clear, definable hole between every quantity. Alternatively, the set of actual numbers just isn’t discrete as a result of there is no such thing as a smallest quantity of separation between two actual numbers.

Discrete arithmetic encompasses a variety of subjects. Listed here are a number of key areas that you simply would possibly encounter:

What’s combinatorics?

This space of discrete arithmetic focuses on the research of mixtures and permutations. It typically offers with questions similar to: What number of methods are you able to prepare the letters in a phrase? What number of completely different subsets are you able to create from a given set?

What’s graph concept?

Graph concept is the research of connections between objects. In graph concept, you signify the objects as “nodes” or “vertices” and the connections between them as “edges.” Graph concept can be utilized to research social networks, transportation networks, and even laptop algorithms.

What’s quantity concept?

Quantity concept is the research of the properties of pure numbers. It focuses on subjects similar to divisibility, prime numbers, and modular arithmetic. Quantity concept is usually utilized in cryptography to create safe encryption strategies.

What’s logic?

Logic is the research of the ideas of reasoning. In discrete arithmetic, you typically encounter symbolic logic, which makes use of symbols to signify logical statements. This type of logic can be utilized to create formal proofs, analyze algorithms, and construct laptop applications.

Discrete arithmetic is an interesting and broad area of research. In case you are excited about laptop science, statistics, engineering, or cryptography, understanding discrete arithmetic will likely be important to your success.