What is number theory?

Number theory is the branch of mathematics that studies the properties of numbers. It is one of the oldest and most fundamental branches of mathematics, and it has applications in many other areas of mathematics, as well as in physics, computer science, and other fields.

Number theory is divided into two main branches: elementary and analytic number theories. 

Elementary number theory deals with the basic properties of integers, such as divisibility, primality, and factorization. Analytic number theory studies the distribution of numbers, such as the distribution of prime numbers. It is a more advanced branch of number theory that requires a strong foundation in mathematical analysis.

Uses of number theory

Number theory has many applications in other areas of mathematics and STEM. 

1. Algebra and Geometry: Number theory is used to study algebraic structures like rings and fields and geometric objects like lattices and curves.
2. Physics: Number theory is also used to study the properties of elementary particles and other quantum phenomena.
3. Computer science: It is used to develop cryptographic algorithms and other computer science applications.
4. Economics: Number theory also applies to game theory and other economic problems.

Why study number theory?

The many benefits of studying number theory include developing strong problem-solving and analytical skills. It is a prerequisite for many advanced mathematics courses and useful to study for students planning a career in physics, computer science, or economics.