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mass noun1The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

*‘courses in algebra, geometry, and Newtonian physics’**‘Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations.’**‘Aitken's mathematical work was in statistics, numerical analysis, and algebra.’**‘König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.’**‘He worked on algebra and graph theory, combining the two to produce his first outstanding contribution to matroid theory.’**‘He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.’**‘It was an exciting time with increasing mathematical activity in algebra.’**‘It is time to take a look at this most outstanding work on algebra in Greek mathematics.’**‘He wrote several books on arithmetic, algebra, geometry and astronomy.’**‘Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.’**‘Ernst Schröder's important work is in the area of algebra, set theory and logic.’**‘The mathematical topics that Delone studied include algebra, the geometry of numbers.’**‘I do not doubt that this is the most important work on general algebra that the Annalen has ever published.’**‘The book contained the elements of geometry and algebra in addition to the calculus.’**‘In short, his interest in classical algebra and number theory brought him to abstract semigroups.’**‘We have looked briefly at Zorn's contributions to algebra and to set theory.’**‘Pierre went on to study the latest mathematics, in particular studying algebra and geometry.’**‘He failed in his application for the chair of algebra and number theory at Uppsala University.’**‘Wall's research is mostly in the area of geometric topology and related algebra.’**‘They are the basis of mathematical logic, which in turn gives rise to Boolean algebra.’**‘It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration.’*

- 1.1A system of algebra based on given axioms.
*‘This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.…’**‘Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.’**‘In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven.’**‘Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest.’**‘His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras.’**‘The theorem states that all central division algebras over algebraic number fields are cyclic algebras.’**‘Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan.’**‘Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories.’**‘He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory.’**‘The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal.’**‘He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras.’**‘In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology.’**‘It completes the formation of the theory of free associative algebras and related classes of rings as an independent domain of ring theory.’**‘In 1923 he published important work on real and complex algebras of low dimension.’**‘Wedderburn made important advances in the theory of rings, algebras and matrix theory.’**‘He also published results on algebras which were fundamental in the study of algebraic number fields.’**‘He studied algebras and published papers on trigonometrical series.’**‘They made plans to write a joint paper on splitting fields of division algebras, which was to contain an example showing that the degree of a minimal splitting field can be arbitrarily large.’**‘On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming.’**‘Jordan algebras are called after the German physicist and mathematician Pascual Jordan.’*

**Origin**

Late Middle English from Italian, Spanish, and medieval Latin, from Arabic al-jabr ‘the reunion of broken parts’, ‘bone-setting’, from jabara ‘reunite, restore’. The original sense, ‘the surgical treatment of fractures’, probably came via Spanish, in which it survives; the mathematical sense comes from the title of a book, ‘ilm al-jabr wa'l-muqābala ‘the science of restoring what is missing and equating like with like’, by the mathematician al-Ḵwārizmī (see algorithm).

**Pronunciation**

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