# Algebra

## Algebra

The world of Algebra is a world of unknown, abstract things. Just as a detective carries out various investigations to track an unknown criminal, so do we use various algebraic operations to reach an unknown solution to a mathematical problem

Algebra is taught in almost all schools across the globe. So, here’s presenting to you an overview of this subject.

#### What is Algebra?

The very word, Algebra, invokes pictures of alphabets like a, b, x, y etc. in my mind.
This is because Algebra is a branch of mathematics that uses symbols and letters to represent an unknown.

#### History of Algebra

It is believed, that the ancient people of Babylonia, used an advanced system of calculations in their daily life. Such calculations are used today to solve equations in Algebra. So we can say that the Babylonians are a source of the origin of Algebra.

However, the roots of Algebra has also been traced back to the ancient Indian Mathematics that had a direct influence on Muhammad bin Mūsā al – Khwārizmi (c 780 – 850), a Persian mathematician, who wrote a book in Arabic, Al – kitab al – Jabr wa – l – Muqabala, in the 9th century A.D. It is from ai - jabr that Algebra gets its name.

#### Symbols and letters

Algebra is full of symbols and letters as that is the very substance of this branch of mathematics. They are useful, as they are easier to write and save space and time.

#### A list of few symbol used:

 Symbol Meaning C Composite numbers R Real numbers Q Rational numbers Z Integers W Whole numbers + Addition - Subtraction = Equal to > Greater than

#### Variables

These are the alphabets that are used, to denote the unknown numbers or quantities, in Algebra. Variables may not always be alphabets; they can be anything, e.g., symbols.

For example, to solve:
------- + 2 = 20

Instead of saying or writing “dash” or “empty space” every time we refer to the problem, we can use ,
x + 2 = 20

Here x is that unknown number which when added to 2 gives 20.

Although nothing about variables has been told by the Persian mathematician in his book, variables were first used by a French mathematician, François Vièta, at the end of 16th century A.D.

A few things related to Algebra

#### Algebraic terms

: These are the basic units of an algebraic expression. They consist of a number and one or more variables.

#### For example,

the term 25ab. 25 is called the Numerical co-efficient of the term.

#### Algebraic expressions

: They are a collection of algebraic terms that are separated by the various arithmetical operations and they do not have an “=” sign.

For example, 25ab + 30ab – 12ab

#### Algebraic equations

: They are statements stating that two expressions are equal. So, they contain an “=” sign.

For example, 7x + 4 = 12y - 9

Classifications of Algebra

#### Elementary Algebra

This contains the basic concepts of algebra

#### Abstract or Modern algebra

This is a further study of Elementary Algebra.

#### Linear Algebra

This branch of algebra deals with some specific properties of vector space (including matrices).

#### Universal Algebra

As the name suggests, it deals with the properties that are common to all algebraic structures.

#### Algebraic number theory

Here we study the various properties of numbers as we find in the algebraic system.

#### Algebraic combinatory

: Here we use abstract algebraic methods to study combinatorial questions.

#### Uses

Finally, to wrap it up, I would like to tell you that Algebra is that branch of mathematics that is used in Arithmetic and also in Geometry.