## What is Algebra:

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 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 Cuban mathematician Aurelio Baldor, which develops and deals with all the hypotheses of this science.

Etymologically, the word algebra is of Arabic origin which means "recomposition" or "reintegration". Algebra comes from the civilizations of Babylon and Egypt, before Christ, they used this method to solve equations of the first and second degree.

Then, continued in ancient Greece, the Greeks used algebra to express equations and theorems, such as: Pythagorean theorem. The most important mathematicians were Archimedes, Herón and Diopante.

In a figurative sense, in the case of being in a difficult situation 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's Algebra, officially known as "Modern Elemental Algebra", its authors being Dr. Mario Octavio González Rodríguez, and the American mathematician Dr. Julian Dossy Mancill. At this point, the students encouraged an error in the spelling of the surname, since Mancill should 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 carried out, 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 equal sign it is called an 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 a monomial, if there are two, a binomial, if there are three, a trinomial. In the case of being more than three terms, it is known as a polynomial.

• Polynomial.
• Laws of exponents and radicals.

## Elementary algebra

Elementary algebra develops all the basic concepts of algebra.

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

For its part, in algebra a letter represents the value assigned by the individual, and therefore, it can represent any value. However, when a letter is assigned a specific value in the problem, a 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 the solution or root.

## Boolean Algebra

Boolean algebra is used to represent two states or values, either this or that indicates whether a device is open or closed, if it is open it is because it conducts, otherwise (closed) it is because it does not conduct.

This system facilitates the systematic study of the behavior of the 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 the year 1843, by the 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 "The linear theory of extension."

## Abstract algebra

Abstract algebra is a part of mathematics that deals with the study of algebraic structures such as vectors, body, ring, group. This type of algebra can be called 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 mathematics and all natural sciences are based on, currently being used in all branches of mathematics.

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