History

A origins of algebra may be traced to the cultures of the ancient Egyptians and Babylonians who utilized an early nature and severity of algebra to solve linear, quadratic, and indeterminate equations to a higher degree 3,000 years ago.

About 300 BC Greek mathematician Euclid in Book 2 of his Elements addresses quadratic equations, although in a strictly geometrical fashion.

In 100 BC algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu, The Nine Chapters of Mathematical Art.

In the area of 150 AD Greek mathematician Hero of Alexandria treats algebraic equations within 3 volumes of maths.

Around 200 AD Greek mathematician Diophantus, often known as a "father of algebra", writes his renowned Arithmetica, a function featuring solutions of algebraical equations & on the theory of statistics.

Indian mathematician, Aryabhattthe (476 AD) found whole total solutions to linear eqautions by a method same to the modern 1. Bhaskara II (1114 AD), world health organization wrote bijaganita (algebrthe), was a 1st to recognize that a caring total has Two square roots. A Hindus recognized that quadratic equations use at times 2 roots, & involved negative also when irrational roots. It treated indeterminate quadratic equations.

A word algebra itself is from either a title of the treatise 1st written by Persian mathematician Al-Khwarizmi in 820 AD titled: Kitab al-mukhtasar fi Hisab Al-Jabr wa-al-Moghabalah meaning The book of sum-up on calculating by transposition & reduction. A word al-jabr (from either which algebra is derived) means "reunion", "connection" or even "completion".

Algebra was introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci around 1202.

Classification

Algebra can be about divided into a resulting categories: elementary algebra, in which a properties of operations on the real number system are recorded using symbols when "place holders" to denote constants and variables, and a system governing mathematical expressions and equations involving these symbols are exposed (note that this ordinarily includes a subject matter naturally known as medium algebra & college algebra); abstract algebra, sometimes besides known as modern algebra, where algebraic structures such as groups, rings and fields are axiomatically defined and investigated; linear algebra, in which a specific properties of vector spaces are studied (including matrices); universal algebra, in which properties park to completely algebraical structures come exposed.

Inside advanced studies, self-evident algebraical systems prefer groups, rings, fields, & algebras above the field come investigated when in contact with the natural geometric structure (a topology) which is compatible with a algebraical structure. A listings includes

Normed linear spaces Banach spaces Hilbert spaces Banach algebras Normed algebras Topological algebras Topological groups

Algebras
A word algebra is likewise utilized for various algebraic structures: algebra over a field algebra over a set Boolean algebra sigma-algebra F-algebra and F-coalgebra in category theory