We present one of the most important courses in mathematics: «Algebra», where the Greatest Mathematicians have achieved more achievements, in addition to benefiting other subjects such as Geometry, for example.
What is Algebra?
To answer this question we are going to go back thousands of years where man in his need to preserve his existence and achieve his own development had to measure, calculate concrete situations that surrounded him; that is, quantify time, mass, weight, volume, etc. thus giving the origin of the concept of quantity.
Later they were able to represent these quantities in abstract concepts of numbers and signs that facilitated the calculations in order to better understand and understand their reality.
The basic operations that man carried out were elevated to a higher level, thanks to characters of history such as Newton, Euler, Gauss, Fermat and other great mathematicians, thus building an abstract and coherent system of signs and numbers, thus giving rise to ALGEBRA as part of mathematics, a very useful tool for man.
Algebra is, in essence, the doctrine of mathematical operations analyzed from an abstract and generic point of view, independent of numbers or concrete objects.
Then, to see this brief introduction we can now define the ALGEBRA.
Definition of Algebra
«We define ALGEBRA as the branch of mathematics in which letters, numbers or symbols are used to represent arithmetic relationships».
Algebra is the foundation on which Mathematics is based; it could very well be considered the universal language of civilization.
The word algebra comes from a book written in 830 by the mathematician Mohamed ibn Musa Al-Khwarizmi, entitled Al – jabr w’al muqábala, which means restoration and simplification.
Like Arithmetic, the fundamental operations of Algebra are addition, subtraction, multiplication, division, potentiation and root.
Arithmetic, however, is not capable of generalizing mathematical relations, like Pythagoras’ theorem, which says that in a right triangle the area of the square on the side equal to the hypotenuse is equal to the sum of the areas of the squares on the side equal to the legs.
Arithmetic only gives particular cases of this relationship, for example: 3; 4 and 5 since:
3² + 4²= 5².
Algebra, on the other hand, can give a generalization that fulfills the conditions of the theorem:
a² + b² = c²
A number multiplied by itself is called a square, and is represented by superscript 2.
For example, the notation of 3*3 is 3²; in the same way, a*a is equal to a².
Classical Algebra, which deals with solving equations, uses symbols instead of specific numbers and arithmetic operations to determine how to use those symbols. Modern Algebra has evolved from classical algebra by paying more attention to mathematical structures, and mathematicians view modern algebra as a set of objects with rules that connect or relate to them.
Thus, in its most general form, a good definition of algebra is: «Algebra is the language of mathematics».
Finally, to mention that this page tries to approach the student with a clear and simple language seeking to develop the deductive reasoning and its dexterity in the resolution of problems. Thus, we strive in each publication to bring you the best of the basics of Algebra.