Algebra points out the branch of mathematics whose object of study is the combination of elements of abstract structures according to certain rules . The word algebra is of Arabic origin and its meaning refers to a recomposition or reintegration. The elements studied in this discipline could originally be interpreted as quantities or numbers. Given its characteristics, algebra was, at first, a kind of extension and generalization of arithmetic .

However, today this discipline has areas that have nothing to do with arithmetic. Some examples of them are abstract algebra, exterior or homology, among others. The difference between arithmetic and algebra is found in the elements they use. Thus, elementary arithmetic uses fundamental numbers and operations, while algebra introduces symbols.

The symbols used in algebra are generally letters that represent unknown parameters or quantities. Algebra is a branch of mathematics that makes calculations with non-numerical elements.The expressions that are formulated in algebra are called algebraic formulas . These formulas tend to express a general principle or rule. For this reason, this discipline represents one of the main branches of mathematics. Other important branches within mathematics include geometry, analysis and number theory.

The origin of algebra is attributed to Muhammad ibn Musa al-Jwarizmi, a Persian mathematician and astronomer. This scientist wrote a treaty circa 820 AD entitled: “Compendium of calculation by reintegration and comparison.” In this treaty, Al Jwarizmi proposed symbolic operations to solve linear and quadratic equations systematically. The methods introduced by this mathematician promoted the development of this science in medieval Islam. In addition, it gave a prominent and independent place to algebra as a discipline. Which means that it was separated and differentiated from arithmetic and geometry. Some consider algebra as the art of calculating with non-numerical mathematical objects .

Aspects and characteristics of algebra There is an adjective related to algebra , it is the term algebraic that generally describes something linked to algebra. In this way, it is usually used to describe or name structures, formulas, expressions, etc. You can also point out a certain relationship with the solutions of equations, extensions, numbers or algebraic expressions. It is important to mark a certain classification in algebra where there is an elementary and an abstract type. Elementary algebra is the form of this discipline that is usually taught in math courses.

As for the abstract type, it is what is called the study of algebraic structures. In general, algebra consists in the study of combinations of finite chains of signs . Thus, it can be distinguished from the mathematical analysis that involves the study of limits and sequences that may exist in an infinite amount of elements. Algebra originally provided a system to solve calculations algorithmically. The methods allowed algebra could solve linear equations, indeterminate and second grade . It was a novelty at the time, since other mathematicians tried to solve this type of equations with geometric methods. The mathematicians of Ancient Greece even created a method that unifies algebra and geometry.