# WHAT IS ALGEBRA

What is Algebra? It's a field of mathematics, deals with symbols and the rules for manipulating those symbols. This field is a unifying thread of almost all branches of mathematics. Essential parts of this field are called elementary algebra, while the more abstract elements are known as abstract algebra. Therefore, it involves everything from elementary equations solving to the study of abstractions, for example, groups, rings, and fields.

Elementary algebra is considered a vital component in the study of mathematics, science, engineering, and it also has its applications in fields such as medicine and economics. On the other hand, abstracts algebra is a critical area in advanced mathematics that is studied mainly by professional mathematicians.

It plays an important function in the study of college algebra. This subject has a manifold of related meanings in mathematics as either a single word or with qualifiers.

• As a single word with no article, the term "algebra" refers to a broad part of mathematics
• As a single word with an item or in the plural," an algebra' or "algebras" stands for a specific mathematical structure whose absolute definition depends on the author.
• With a qualifier, the distinction is similar.
• Thus, it is a branch of mathematics that commenced with computations comparable to those of arithmetic, with letters that denote numbers. In the past as well as in the current teaching, the study of algebra begins with the solving of equations such as quadratic equations.

Before the 16th Century, mathematics was branched into arithmetic and geometry only. The emergence of algebra as a subfield of mathematics dates back from the 16th and 17th Century. During the 19th Century, many fields of mathematics made an appearance, and almost all of the areas used algebra.

## The history of algebra

The roots of algebra can be drawn back to the ancient Babylonians who came up with an advanced arithmetic system with which they were capable of doing calculations in an arithmetic way. They developed formulas to solve problems that are solved today using linear equations, quadratic equations, and indeterminate linear equations.

By comparison, most Egyptians of that age, as well as the Greek and the Chinese mathematicians in the first millennium, solved such equations by geometric methods. Greeks came up with a geometric algebra where sides of geometric objects represented terms, usually lines that had letters affiliated with them.

In the context of the theory of equations, a Greek mathematician, Diophantus is traditionally known as the "father of algebra," and in the context where algebra is identified with rules for manipulating and solving equations, Persian mathematician al- Khwarizmi is referred to as the "father of algebra." a controversy now exists on who is more entitled to the crown.

Those who support Diophantus point to the actuality that it is found in al-jabr is somewhat more elementary than the one found in arithmetic and that arithmetica is syncopated while al-jabr is entirely rhetorical.

Those who support al-Khwarizmi refer to the fact that he came up with the methods of "reduction" and "balancing." the termination of like terms on opposite sides of the equation, which the name al-jabr, in the beginning, referred to, and that he gave a comprehensive explanation of solving quadratic equations, supported by geometric proofs while treating algebra as a self-determining discipline in its own right.

His study was also no longer involved with a series of problems to be resolved, but a description which starts with primal terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly make up the actual object of study.

He also comprehensively studied an equation for its own sake and in a generic technique, insofar as it does not merely come into view in the course of solving a problem, but is exclusively called on to describe an infinite class of problems.

A Persian mathematician, Omar Khayyam is also credited with the identifications of the foundations of algebraic geometry. His book, treatise on demonstrations of problems of algebra, written in the year 1070, laid down the basics. This body is part of the Persian mathematics that was ultimately transmitted to Europe.

Another Persian mathematician, Sharaf al-din al-Tusi, found algebraic and numerical solutions to several cases of cubic equations.

## The modern history

Mathematician François viete's work on new algebra at the end of the 16th Century was a crucial step towards the modern form. Rene Descartes published la geometrie in 1963. He invented analytical geometry and introduced the modern algebraic notion. This was an advancement of the general algebraic solution of the cubic and quadratic equations that was developed in the 19th Century. Its development was derived from the interest in solving equations.

## Elementary Algebra

It is the most primitive form. It is taught to students who are thought not to know mathematics past he fundamental principles of arithmetic. While arithmetic deals with particular numbers, algebra introduces quantities without predetermined values, known as variables. This use of variables involves an application of algebraic notation and an understanding of the broad rules of the operators introduced in arithmetic.

Unlike abstract algebra, elementary algebra is not involved with algebraic structures outside the realm of real and compound numbers.

The use of variables to indicate quantities allows wide-ranging relationships between numbers to be formally and concisely expressed, and thus enables solving a full scope of problems. Many quantitative affairs in science and mathematics are expressed as algebraic equations.

## Abstract level

It is a subfield of algebra that extends similar concepts found in elementary algebra and arithmetic of numbers to more general concepts. abstract Algebra, is the study of algebraic structures.

Algebraic structures comprise groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract was formulated in the early 20th Century to tell between this area of study from the other parts of algebra.

The subject is an important life skill worth understanding well. It moves us further than basic math and prepares us for statistics and calculus. It is helpful for many jobs, some of which a student may enter as a second career. You can seek for algebra help by contacting us.

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