## Algebra and Number Theory

Algebra and number theory are two very important elements that make up the areas of mathematics. This in conjunction with geometry and analysis. These four areas are very important for the development of mathematics.

## Algebra

One of the oldest areas that mathematics covers is this. In turn, it is in charge of studying the composition of elements of uncertain groupings according to certain norms. At first, these elements were taken as numerical quantities and it is then that it is known that algebra was developed as an extension of arithmetic.

## Number theory

Number theory also belongs to a specific area of â€‹â€‹mathematics, which is responsible for analyzing the properties of digits. Specifically, he is in charge of studying the problems that arise from integers. Algebra and number theory are closely related to arithmetic and it is the number theorists who are in charge of studying this branch.

## Fields of number theory

Depending on the techniques used and the solutions to problems, number theory can be divided into different fields.

### Elementary number theory

This branch is responsible for the analysis of the integer digits, without having to do one of the other methods that comes from the other areas of mathematics. Techniques such as simplicity, Euclid’s algorithm, exploration of perfect digits, and congruences are awarded to this field.

### Analytical number theory

In algebra and number theory, he uses the calculation and study of holomorphic functions as instruments, in order to face questions related to whole digits. The most widely used methods in this theory are the prime number theorem and Riemann’s theory. Waring’s problem and the prime number conjecture are also used.

In algebra and additive number theory it constitutes the problems of representation of the digits in a more difficult way. The methods used in this field have a lot to do with those that have been mentioned in the other techniques, such as the Goldbach conjecture. However, these are complemented by other methods such as the Hardy Littlewood circle.

### Algebraic number theory

This field is the one most closely related to algebra, since algebraic numbers are studied in depth. These are what belong to the roots of varieties with rational coefficients.

### Geometric number theory

With algebra and number theory, this field is known as the geometry of numbers, since as its name indicates, it is made up of geometric figures. As a method it uses the Minkowski proposition, which explains a lot about the frequent points in prominent ensemble and the studies that have to do with round planes.

### Computational number theory

This field deals with the analysis of the relevant algorithms of algebra and number theory. These quick figures for studying the primary digits and integer factoring are widely used in cryptography.

### Combinatorial number theory

It is based on seeking solutions to the problems of number theory, including combinatorial doctrines and their statements. The topic of this theory is based on the systems covered, the zero-sum problems, the numerous concrete sets, among others. In this method, algebraic and analytical techniques are usually combined in a good way.

Algebra and number theory are two important branches of mathematics, which has helped the progress and solutions of different problems, thanks to the use of specific equations.

Studying and learning about anything is essential for life. Obtaining knowledge and being able to multiply it is the way humanity has passed all its wisdom from generation to generation.

Mathematics is part of all this knowledge disseminated and studied throughout history, from ancient times to the present. Everything that exists both in the world and in the universe is related to mathematicians, so they constitute fundamental knowledge.