Algebra

Algebra is ane o the maist basic brainches o mathematics. Tho it isna aesie defined, it is chairacterised bi the uiss o seembols tae represent some operations, an o letters tae represent nummers or ither elements.

Clessification

Algebra can be spleet up intae thir fields:

Basic algebra studies the parteiculars o an operations on naitural nummers, integers, raitional an real nummers, an hou a bodie can solve equations wi variables.
Linear algebra is a theory o vector spaces, pairt o it bein the theory o linear equation an o matrices. Ideas an methods frae linear algebra can be uised in monie sindrie brainches o mathematics. For exemplar, the chief ettle o the study o functional analysis is infinite vector spaces.
Abstract algebra studies algebraic structurs like groups, rings an bodies that generalises concepts frae basic algebra.

History

Algebra, like coontin an geometry, is ane o the auldest brainches o mathematics. The name comes frae a beuk bi the Arabian mathemateecian Al-Khwarizmi cried Kitab al-jabr wa al-muqabalah ("The beuk o summary anent calculatin bi transposeition an reduction").

Algebra wis cleckit for tae help solve equations. The solutions o linear an quadratic equations wis aareadies kent lang syne. In the 16t century Italian mathemateecians fund solutions tae cubic an quartic equations. In 1799 Gauss shawed that “ilka algebraic equation o degree n, haes n ruits (solutions), rael or imaginar”.

At the stairt o the 19t century Niels Abel an Evariste Galois pruived that the solutions o equations o degree bigger nor 4 canna be expressed uisin coeffeicients o the equation an algebraic operations juist—that is, the'r nae generalisation o the quadratic, cubic or quartic formulae tae heicher degrees.

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