**Algebra** is known as the **branch of mathematics in which operations are generalized using numbers, letters and signs that symbolically represent a number or other mathematical entity**.

**According to Baldor**, algebra is the branch of mathematics that studies the quantity considered in the most general way possible. In this sense, it can be noted that the teaching of algebra is dominated by the work “Algebra de Baldor”, a book by the Cuban mathematician Aurelio Baldor, who develops and deals with all the hypotheses of this science.

**Etymologically**, the word algebra is of Arabic origin meaning “recomposition” or “reintegration.” Algebra proceeds from the civilizations of Babylon and Egypt, before Christ, used that method to solve first and second degree equations.

Then, he continued in ancient Greece, the Greeks used algebra to express equations and theorems, such as: Pythagorean theorem. The most relevant mathematicians were Archimedes, Heron and Diofante.

**In a figurative sense**, in the case of being in a situation difficult to understand or resolve, it can be expressed; This is algebra!

On the other hand, it can be noted that apart from the book identified above, another book used in Latin America, is Mancil Algebra, officially known as “Modern Elemental Algebra”, being its authors Dr. Mario Octavio González Rodríguez, and the American mathematician Dr. Julian Dossy Mancill. At this point, the students encouraged an error in the surname writings, since Mancill must be written instead of Mancil.

## Algebraic expressions

In relation to the study of algebra, algebraic expressions are the set of numbers, and by symbols represented by letters that manifest an unknown value, being called as unknown or variable.

The symbols are related through signs that indicate the operations that need to be performed, either multiplication, addition, subtraction, among others, in order to achieve the result of the variables. In this sense, the terms are distinguished or separated by means of signs, and in the case of being separated by the sign of equality is called equation.

There are different types of expressions which are differentiated by the number of terms present, in the case of being one it is called monomial, if there are two, binomial, if three, trinomial. In the case of more than three terms, it is known as a polynomial.

## Elementary algebra

Elementary algebra develops all the basic concepts of algebra.

According to this point, a difference can be observed with arithmetic. In arithmetic, quantities are expressed by numbers with certain values. That is, 30 expresses a single value, and to express another one, a different number must be reported.

On the other hand, in algebra a letter represents the value assigned by the individual, and therefore, can represent any value. However, when a given value is assigned to a letter in the problem, another value other than the one assigned cannot represent the same problem.

For example: 3x + 5 = 14. The value that satisfies the unknown in this case is 3, this value is known as solution or root.

## Boolean Algebra

Boolean algebra, is that used to represent two states or values either this (1) or (0) that indicates if a device is open or closed, if it is open it is because it drives, otherwise (closed) it is because no he drives.

This system facilitates the systematic study of the behavior of logical components.

Boolean variables are the basis of programming thanks to the use of the binary system , which is represented by the numbers 1 and 0.

## Linear algebra

Linear algebra is mainly responsible for the study of vectors, matrices, systems of linear equations. However, this type of algebra division extends to other areas such as engineering, computing, among others.

Finally, linear algebra dates from 1843, by Irish mathematician, physicist and astronomer Willian Rowan Hamilton when he created the term vector, and created the quaternions. Also, with the German mathematician Hermann Grassman when in 1844 he published his book “Linear Theory of Extension.”

## Abstract algebra

Abstract algebra is a part of mathematics that is responsible for the study of algebraic structures such as vectors, body, ring, group. This type of algebra can be called as modern algebra, in which many of its structures were defined in the 19th century.

It was born with the objective of understanding more clearly the complexity of the logical statements that are based on mathematics and all natural sciences, currently being used in all branches of mathematics.