__What is mathematics__

Mathematics is a science that starts from a logical deduction, which allows you to study the characteristics and links existing in abstract values such as numbers, icons, geometric figures or any other symbol. Mathematics is around everything the individual does.

It is the cornerstone of all everyday life, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. Since its inception in history, mathematical discovery has remained at the forefront of all highly civilized societies and has been used in even the most primitive cultures. The more complex society is, the more complex mathematical needs are.

__Origin and evolution of mathematics__

The origin of mathematics is closely linked to the history of one of the wisest civilizations in the world, ancient Egypt. In its history there are thousands of knowledge conceived by the mix between magic and science. With the modern age, mathematics became a secular and quantitative science.

The Sumerians were the first people to develop a counting system. Mathematicians developed arithmetic, which includes basic operations, fractions, multiplication, and square roots. The Sumerian system passed from the Akkadian Empire to the Babylonians in 300 BC. Then some 700 years later the Mayans in America developed the calendar system and became expert astronomers.

The work of mathematicians began as civilizations grew, the first to emerge was geometry, which calculates areas and volumes. Then in the 9th century the mathematician Muhammad ibn-Musa invented Älgebra, he developed fast methods for multiplying and finding numbers, known as algorithms.

Some Greek mathematicians left an indelible mark on the history of mathematics, among them are Archimedes, Apollonius, Pappus, Diophantus and Euclid, all from that time, then they began to work on trigonometry, which requires the measurement of angles and the calculation of functions trigonometric, which includes sine, cosine, tangent and their reciprocals.

Trigonometry is based on synthetic geometry developed by mathematicians like Euclid. For example, Ptolemy’s theorem who gives rules for the chord of sums and differences of angles, which correspond to the formulas of sums and difference for sines and cosines. In past cultures trigonometry was applied to astronomy and to the calculation of angles in the celestial sphere.

Euclid, a mathematician from the time of Ancient Greece, developed a definition of mathematics, which becomes an essential tool for students, which is the Euclidean division. This consists of dividing a non-zero integer number among others, with the aim of obtaining a result without having to perform the operation on a piece of paper. The Euclidean division is not only based on the simplicity of its realization, but on the possibility of carrying it out without the help of a calculator.

The mathematician John Napier (1550-1617) created the definition of the Neperian logarithm, represented it in a table of logarithms, through this tool products can be transformed into sums. This indispensable resource for use in modern mathematics is a must in learning for any beginner in mathematics.

René Descartes, philosopher, scientist, and mathematician, his greatest interest focused on mathematical problems and philosophy. In the year 1628 he resides in the Netherlands and dedicates himself to writing Philosophical Essays, which were published in the year 1637. These essays are made up of four parts, which are geometry, optics, meteors and the last part is the Discourse on Method , which describes his philosophical speculations.

Descartes is the creator of using the last letters of the alphabet to distinguish unknown quantities and the first ones for known quantities in Algebra.

His greatest contribution in mathematics was in the systematization of analytic geometry.

__Defination of Mathematics__

Mathematics is defined by most sources as the branch of human knowledge, which aims to study the different abstract entities, such as numbers or geometric figures, in terms of their properties and the relationships they can establish with each other. .

Likewise, the scientific community conceives Mathematics, more than as a science, as a set of formal languages, through which man can give an unambiguous expression and the correct context to the problems posed by the different scientific areas, and also humanistic, around the objects that they study and the phenomena that can be observed in them.

In this sense, Mathematics has become the main tool of Sciences, and other social and humanistic disciplines, when looking for a way to express situations or questions, referring to the Laws of Nature, so it is I could also say that Mathematics constitutes a Formal Language and a Tool with which modern man manages to express, and at the same time understand, how the world works, in relation to the different physical laws. However, every day there are more disciplines that use Mathematics for their own benefit, such as Psychology, which by using Statistics, manages to quantify, structure and understand the different probabilities that are given in reference to a population or a specific phenomenon.

__Branches of Mathematics__

Therefore, in addition to Formal Language and scientific tool, Mathematics stands out as a discipline of knowledge of a purely practical nature, because even though this discipline can be studied in a pure way, that is, without being related to another science, sooner or later His own study ends up revealing the practicality of what he has discovered.

However, although the word Mathematics is used to refer to this area of knowledge, in reality this discipline is constituted by a set of formal languages, which are classified by Science into branches, according to their position or area or purpose. study. In this regard, most mathematicians are guided by the classification proposed by the American Mathematical Society, an institution for which there are at least five thousand different branches within the discipline of Mathematics.

However, in order to simplify the classification of the branches of Mathematics, this entity has decided to identify at least four major areas, which differ according to their different objects of study, and which broadly can be pointed out as the following:

__Arithmetic__

Considered as the area of Mathematics whose purpose of study is quantity. It is considered the first branch of Mathematics to have been developed, historically speaking. Also known as Number Theory, Arithmetic basically encompasses among its main areas of study are the Elementary Theory of Numbers (integers, rational numbers, natural numbers, real numbers and complex numbers) as well as analytical number theory. , geometric number theory, algebraic number theory, computational theory, among others.

__Algebra__

Likewise, the classification of the branches of Mathematics considers a second great set whose study purpose has been the structure, and which is known by the name of Algebra. Likewise, among the different elements of studies covered by Algebra, the different sources propose to divide it into two classes:

**Elementary algebra**: which is in charge of studying the different arithmetic operations that can be established between natural numbers and integers.**Abstract Algebra**: Second, Abstract Algebra could be considered as the mathematical area that is concerned with studying and finding the right methods to adequately solve the equations. Similarly, abstract algebra is interested in polynomials and their structure, rings and fields, vectors, vector spaces.- In summary, it can be said then that Algebra seeks the understanding of structure, through the study of Combinatorics, Number Theory, Group Theory, Order Theory, Graph Theory, as well as the notions addressed by elementary algebra and abstract algebra.

__Geometry__

Among these four main purposes of the study of Mathematics, there is one that proposes the study of space, and that bearing the name of Geometry would basically be in charge of trying to understand, through the use of fundamental axioms and qualities, how they are and how The different spatial relationships behave, having then as branches of study Geometry, Trigonometry, Algebraic Geometry, Differential Geometry, Topology, Fractal Geometry, as well as Measurement Theory.

__Trignometry__

Trigonometry in principle is the branch of mathematics that studies the relationships between the angles and the sides of the triangles. For this it uses the trigonometric ratios, which are frequently used in technical calculations. Generally speaking, trigonometry is the study of the sine, cosine, tangent, cotangent, secant, and cosecant functions. It intervenes directly or indirectly in the other branches of mathematics and is applied in all those areas where precision measurements are required. Trigonometry is applied to other branches of geometry, as is the case of the study of spheres in space geometry.

It has numerous applications: triangulation techniques, for example, are used in astronomy to measure distances to nearby stars, in the measurement of distances between geographic points, and in satellite navigation systems.

__Calculation__

Finally, Mathematics has an area whose purpose is to study change, or in other words, in the result corresponding to the act of calculating. Among the mathematical branches that can be considered within Calculus, there are some such as Calculus, Vector Calculus, Dynamic Systems, Differential Equations, Chaos Theory, as well as complex analyzes.