Algebra is an extension of arithmetic.

While arithmetic is concerned with dealing with numerical quantities, algebra is a set of tools for solving problems where one or more quantities are unknown and are represented by letters. In particular, algebra is used to solve equations.

Traditionally, letters at the beginning of the alphabet, a,b,c etc. are used to represent known quantities, whereas those at the end of the alphabet represent unknown quantities. The letters n,m etc. often represent whole numbers. Charles Babbage wrote a number of papers arguing for conventions such as this.

Algebra is now split into two branches:

• Elementary algebra is the direct extension of arithmetic, usually encountered as school algebra.
• Abstract algebra is the study of algebraic structures. These include rings, groups and fields.