algebra

Mathematics

2022

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

Algebra is the branch of mathematics that studies structures that operate in fixed patterns.

What is algebra?

Algebra is one of the main branches of the math. Its object of study are structures abstract patterns 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.

Put more simply, it is the branch of mathematics that deals with operations with and between symbols, generally represented by letters. Its name comes from Arabic al-ŷabr ("Reintegration" or "recomposition").

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

The logic, pattern recognition and reasoning inductive Y deductive are some of the mental capacities that it requires, fosters and develops.

History of algebra

Al Juarismi created algebra in the 9th century.

Algebra was born in Arab culture, around AD 820. C., date in which the first treaty on the matter was published: Al-kitāb al-mukhtaṣar fī ḥisāb al-ŷarabi waˀl-muqābala, that is to say, "Compendium of calculation by reintegration and comparison", work of the Persian mathematician and astronomer Muhammad ibn Musa al-Jwarizmi, known as Al Juarismi.

There the sage offered the systematic solution of linear and quadratic equations, using symbolic operations. These methods then they developed into the mathematics of medieval Islam and turned algebra into a discipline independent mathematics, along with arithmetic and geometry.

These studies eventually made their way to the West. Thanks to them, abstract algebra emerged in the 19th century, based on the consolidation of complex numbers during previous centuries, the fruit of thinkers such as Gabriel Cramer (1704-1752), Leonhard Euler (1707-1783) and Adrien-Marie Legendre ( 1752-1833).

What is algebra for?

Algebra is extremely useful within the field of mathematics, but it also has great applications in everyday life. Lets carry out budgets, billing, calculations costs, benefits and Profits.

In addition, other important operations in the accounting, management and even engineering, are based on algebraic calculations that handle one or more variables, expressing them in logical relationships and detectable patterns.

The use of algebra allows individuals to better deal with complex and abstract concepts, expressing them in a simpler and more orderly way using algebraic notation.

Branches of algebra

The main ramifications of algebra are two:

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

Algebraic language

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

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

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

Algebraic expressions

Algebra has multiple formulas to solve its polynomials.

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

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