Algebra (Meaning and Explanation)

We explain what algebra is, its history, branches and what it is for. Also, language and algebraic expressions.

What is algebra?

Algebra is one of the main branches of mathematics. Its object of study are abstract structures operating in fixed patterns, within which there are usually more than numbers and arithmetic operations: also letters, which represent concrete operations, variables, unknowns or coefficients.

In simpler terms, it is the branch of mathematics that deals with operations with and between symbols generally represented by letters. Its name comes from Arabic al-jabr (“reintegration” or “recomposition”).

Algebra is one of the branches of mathematics that has the greatest applications. It allows you to represent the formal problems of everyday life. For example, algebraic equations and variables allow unknown proportions to be calculated.

Logic, pattern recognition, and inductive and deductive reasoning are some of the mental abilities that it requires, encourages, and develops.

history of algebra

algebra history creator — Al Juarismi created algebra in the 9th century.

The algebra was born in Arab culture, around the year 820 AD. c date on which the first treatise on the matter was published: Al-kitāb al-mukhtaṣar fī ḥisāb al-jarabi waˀl-muqābalathat is, “Compendium of calculation by reintegration and comparison”, the work of the Persian mathematician and astronomer Muhammad ibn Musa al-Khwarizmi, known as Al Juarismi.

There the wise man offered the systematic solution of linear and quadratic equations, using symbolic operations. These methods were later developed in the mathematics of medieval Islam and made algebra an independent mathematical discipline, alongside arithmetic and geometry.

What is algebra for?

Algebra is extremely useful in the field of mathematics, but it also has great applications in everyday life. Allows you to carry out budgets, billing, cost calculations, benefits and profits.

Furthermore, other important operations in accounting, administration and even engineering are based on algebraic calculations that handle one or several variables, expressing them in logical relationships and detectable patterns.

Handling algebra allows individuals to better deal with complex and abstract concepts expressing them in a simpler and more orderly way through algebraic notation.

Branches of algebra

The main ramifications of algebra are two:

Elementary algebra As its name indicates, it comprises the most basic precepts of the subject, introducing in arithmetic operations a series of letters (symbols) that represent unknown quantities or relationships. This is, fundamentally, the management of equations and variables, unknowns, coefficients, indices or roots.
Abstract algebra Also called modern algebra, it represents a higher degree of complexity compared to elementary algebra, since it is dedicated to the study of algebraic structures or algebraic systems, which are sets of operations that can be associated with elements of a recognizable pattern group.

algebraic language

Algebra requires, above all, its own way of naming its statements, different from the arithmetic language (composed only of numbers and symbols), appealing to traditional and complex relationships, variables and operations.

You may be interested: Examples of Algorithms

It is a more synthetic language than arithmetic, which allows you to express general relationships through short statements. It also allows us to include in the formal pattern those terms that we do not yet know (the variables) but whose link with the rest is known.

This is how equations arise, for example, whose form of resolution involves the rearrangement of the algebraic terms to “clear” the unknown.

Algebraic expressions

algebra formula — Algebra has multiple formulas to solve its polynomials.

algebraic expressions are the way of writing the algebraic language. In them we will recognize numbers and letters (variables), but also other types of signs, and provisions, such as coefficients (numbers before a variable), degrees (superscripts) and the usual arithmetic signs. In general terms, algebraic expressions can be classified into two:

Monomials A single algebraic expression, which has in itself all the information required to solve it. For example: 6X² + 32y⁴.
Polynomials Chains of algebraic expressions, that is, chains of monomials, which have a global meaning and must be solved together. For example: 3n5y³+23n⁵y8z³– π² 3n – 22+26n⁴.