history of algebra
Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis.
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
• As a single word without article, "algebra" names a broad part of mathematics (see below).
• As a single word with article or in plural, "algebra" denotes a specific mathematical structure. See algebra (ring theory) and algebra over a field.
• With a qualifier, there is the same distinction:
• Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
• With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
• Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all arecommutative algebras over the integers.
• Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to algebra. For example algebra of infinite series may denote the methods for computing with series without using the notions of infinite summation, limits andconvergence.
The Hellenistic mathematician Diophantus has traditionally been known as "the father of algebra"[77][78] but debate now exists as to whether or not Al-Khwarizmi deserves this title instead.[77]Those who support Diophantus point to the fact that the algebra found in Al-Jabr is more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[77]
Those who support Al-Khwarizmi point to the fact that he gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots,[79]
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
• As a single word without article, "algebra" names a broad part of mathematics (see below).
• As a single word with article or in plural, "algebra" denotes a specific mathematical structure. See algebra (ring theory) and algebra over a field.
• With a qualifier, there is the same distinction:
• Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
• With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
• Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all arecommutative algebras over the integers.
• Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to algebra. For example algebra of infinite series may denote the methods for computing with series without using the notions of infinite summation, limits andconvergence.
The Hellenistic mathematician Diophantus has traditionally been known as "the father of algebra"[77][78] but debate now exists as to whether or not Al-Khwarizmi deserves this title instead.[77]Those who support Diophantus point to the fact that the algebra found in Al-Jabr is more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[77]
Those who support Al-Khwarizmi point to the fact that he gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots,[79]