The branch of mathematics responsible for studying numbers and their corresponding properties. As in the case of arithmetic , the basic operations of algebra are: addition, subtraction, division and multiplication, in addition to root calculations.
From an etymological point of view, the word algebra has its origins in the Arabic al-gabr and can be defined as the recomposition of something that has been broken into pieces. At first this concept had no relation to mathematical operations, it referred to the art of replacing bones after a fracture or dislocation.
Why is algebra useful?
Unlike arithmetic that only works with numbers and their operations, it provides the possibility of working with symbols instead of numbers, in addition, it has three very important repercussions for the field of mathematics.
First, it allows simple arithmetic equations to be generalized so that they can constitute a law. On the other hand, it also allows you to reference numbers that are not known, but which can be discovered by formulating and solving the equations. And finally, it gives us the possibility of establishing mathematical relationships between quantities.
Elementary and Abstract Algebra
It can be divided into two well-differentiated branches: the elementary and the abstract. The first includes the most basic concepts of mathematics, while the abstract studies algebraic structures.
algebra in antiquity
As with the history of mathematics in general, the origin of algebra can be found in the ancient civilizations of Babylon and Egypt. These were the first places that could solve quadratic and linear equations, in addition to equations indeterminate by multiple unknowns (in the case of the Babylonians).
For many scholars, the Alexandrian mathematician Diophantus is considered the father of algebra. He united the Egyptian and Babylonian tradition, extending and improving it in his book “As Arithméticas”, which presents many solutions to the indeterminate equations that are still surprising to this day.
From then on, the study of algebra reached the Islamic world, ending up improving what they called the science of reduction, definitively boosting algebra as an essential part of mathematical studies.
The definitive confirmation of these advances would be consolidated from the moment that Arab mathematicians developed fundamental concepts of modern algebra such as binomials and polynomials.