Algebra

Introduction to Algebra

What is algebra?

Algebra is a branch of mathematics that deals with generalized arithmetical operations. It is a collection of rules for translating words into the symbolic notation of mathematics, in a manner that leaves their truth unchanged. It can otherwise be defined as a branch of mathematics concerning the study of Structure, Relation and Quantity.

Roots of Algebra

The name "Algebra" is derived from the book written by a Persian Mathematician, Muhammad bin M?s? al-Khw?rizm?. In 9th century he wrote Al-Kitab al-Jabr wa-l-Muqabala, a book on symbolic operations and systematic solutions for Linear and Quadratic equations. The word “Algebra” is derived from al-Jabr.

Symbols

Symbols are the specialty of Algebra. They make our work more convenient. For example, instead of listing the natural numbers as 1, 2, 3… we just say ‘N’. This symbolic representation helps us to generalize the characteristics of natural numbers. Algebra involves a lot of symbols. The following are the other few notations: C – Complex Numbers R – Real Numbers Q – Rational Numbers. Z – Integers. W – Whole Numbers.

Variables in Algebra

Variables are symbols that stand for unknown quantities. It must not necessarily be an alphabet. It can be any symbol. But, generally, we use x, y, z, etc. as variables. In the first algebra book, Khw?rizm? did not use any variable, even though it was all about solving equations. It is only in the 16th century that François Viète, a French mathematician, started using variables. To have a clear idea about the importance of variables, we can have a look at the following example: Mom gave Isaac a bag of apples. He did not count the apples in the bag but started eating them. After eating 3 apples, he found 4 apples were remaining in the bag. How would he find how many apples were there in the bag initially? Here, we go for variables. Let the number of apples be "x" initially. Isaac ate 3 apples. So, x – 3 will be remaining. But there are 4 apples remaining. So, x – 3 = 4. We need to get the value of x. We should get rid of that – 3. We add 3 on both the sides, which will not affect the equality.

Thus we have x = 7. So, there were 7 apples initially

Classification of Algebra

Algebra can roughly have four specialized branches:
• Elementary Algebra
• Abstract Algebra
• Linear Algebra
• Universal Algebra
  
  In Elementary Algebra, the number system and generalization of rules are studied. Constants,
  variables, expressions, and equations are the key concepts of elementary algebra.
  Abstract Algebra represents a further generalization of elementary algebra, by defining such
  constructs as groups, based on a set of initial assumptions, called axioms.
  Linear Algebra involves the extension of techniques from elementary algebra
  to the solution of systems of linear equations.
  In Universal Algebra the properties common to all algebras are studied.
  

Applications of Algebra

TAlgebra has very wide applications. Even in our everyday life we need some algebra knowledge. The principles of algebra are applied in all branches of mathematics, like calculus, geometry, topology, etc. It has its application in all sciences though.

Additional Links for Algebra

• Click here for samples
• Click here for Mathematics Dictionary

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