Definition of algebra in English:

algebra

noun ˈaldʒɪbrəˈældʒəbrə

mass noun

1The 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
Example sentencesExamples
- The book contained the elements of geometry and algebra in addition to the calculus.
- They are the basis of mathematical logic, which in turn gives rise to Boolean algebra.
- The mathematical topics that Delone studied include algebra, the geometry of numbers.
- 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.
- He wrote several books on arithmetic, algebra, geometry and astronomy.
- In short, his interest in classical algebra and number theory brought him to abstract semigroups.
- 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.
- Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations.
- It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration.
- It was an exciting time with increasing mathematical activity in algebra.
- Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.
- Wall's research is mostly in the area of geometric topology and related algebra.
- Ernst Schröder's important work is in the area of algebra, set theory and logic.
- 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.
- We have looked briefly at Zorn's contributions to algebra and to set theory.
- It is time to take a look at this most outstanding work on algebra in Greek mathematics.
- I do not doubt that this is the most important work on general algebra that the Annalen has ever published.
1. 1.1 A system of algebra based on given axioms.
  Example sentencesExamples
  Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.
  In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology.
  The theorem states that all central division algebras over algebraic number fields are cyclic algebras.
  Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories.
  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.
  His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras.
  Jordan algebras are called after the German physicist and mathematician Pascual Jordan.
  In 1923 he published important work on real and complex algebras of low dimension.
  It completes the formation of the theory of free associative algebras and related classes of rings as an independent domain of ring theory.
  The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal.
  He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory.
  Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan.
  In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven.
  Wedderburn made important advances in the theory of rings, algebras and matrix theory.
  This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.…
  Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest.
  On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming.
  He studied algebras and published papers on trigonometrical series.
  He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras.
  He also published results on algebras which were fundamental in the study of algebraic number fields.

Derivatives

algebraist

noun ˌaldʒɪˈbreɪɪstˌældʒəˈbreɪɪst

Early algebraists had to prove their formulas by geometry.
Example sentencesExamples
- Or he might want to train future algebraists and maybe attract a few Ph.D. students for himself.
- Few algebraists seriously think about writing the great American comprehensive algebra text.
- Problems such as these still seem to present a formidable challenge to the ingenuity of algebraists.
- In other words, like many other algebraists, Chinese or not, he demonstrates algebra by using it…

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).

Bone-setting does not seem to have much to do with mathematics, but there is a connection in the word algebra. It comes from the Arabic al-jabr ‘the reunion of broken parts’, used specifically to refer to the surgical treatment of fractures and to bone-setting. Algebra was used in this meaning in English in the 16th century. The mathematical sense comes from the title of a 9th-century Arabic book ilm al-jabr wa'l-mukabala, ‘the science of restoring what is missing and equating like with like’, written by the mathematician al-Kwarizmi (c.790–c.840).

Definition of algebra in US English:

algebra

nounˈældʒəbrəˈaljəbrə

1The 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
Example sentencesExamples
- Ernst Schröder's important work is in the area of algebra, set theory and logic.
- We have looked briefly at Zorn's contributions to algebra and to set theory.
- He wrote several books on arithmetic, algebra, geometry and astronomy.
- Aitken's mathematical work was in statistics, numerical analysis, and algebra.
- They are the basis of mathematical logic, which in turn gives rise to Boolean algebra.
- He failed in his application for the chair of algebra and number theory at Uppsala University.
- He worked on algebra and graph theory, combining the two to produce his first outstanding contribution to matroid theory.
- Wall's research is mostly in the area of geometric topology and related algebra.
- It is time to take a look at this most outstanding work on algebra in Greek mathematics.
- König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.
- It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration.
- Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.
- The book contained the elements of geometry and algebra in addition to the calculus.
- It was an exciting time with increasing mathematical activity in algebra.
- Pierre went on to study the latest mathematics, in particular studying algebra and geometry.
- 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.
- In short, his interest in classical algebra and number theory brought him to abstract semigroups.
- He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.
- Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations.
1. 1.1 A system of algebra based on given axioms.
  Example sentencesExamples
  Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories.
  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.
  Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.
  The theorem states that all central division algebras over algebraic number fields are cyclic algebras.
  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.
  He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory.
  On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming.
  He studied algebras and published papers on trigonometrical series.
  Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest.
  Wedderburn made important advances in the theory of rings, algebras and matrix theory.
  In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology.
  The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal.
  Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan.
  His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras.
  He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras.
  This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.…
  Jordan algebras are called after the German physicist and mathematician Pascual Jordan.
  He also published results on algebras which were fundamental in the study of algebraic number fields.
  In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven.

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).

单词	algebra
释义	Definition of algebra in English: algebra noun ˈaldʒɪbrəˈældʒəbrə mass noun 1The 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 Example sentencesExamples The book contained the elements of geometry and algebra in addition to the calculus. They are the basis of mathematical logic, which in turn gives rise to Boolean algebra. The mathematical topics that Delone studied include algebra, the geometry of numbers. 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. He wrote several books on arithmetic, algebra, geometry and astronomy. In short, his interest in classical algebra and number theory brought him to abstract semigroups. 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. Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations. It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration. It was an exciting time with increasing mathematical activity in algebra. Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics. Wall's research is mostly in the area of geometric topology and related algebra. Ernst Schröder's important work is in the area of algebra, set theory and logic. 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. We have looked briefly at Zorn's contributions to algebra and to set theory. It is time to take a look at this most outstanding work on algebra in Greek mathematics. I do not doubt that this is the most important work on general algebra that the Annalen has ever published. 1.1 A system of algebra based on given axioms. Example sentencesExamples Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic. In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. The theorem states that all central division algebras over algebraic number fields are cyclic algebras. Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories. 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. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. Jordan algebras are called after the German physicist and mathematician Pascual Jordan. In 1923 he published important work on real and complex algebras of low dimension. It completes the formation of the theory of free associative algebras and related classes of rings as an independent domain of ring theory. The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal. He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory. Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan. In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven. Wedderburn made important advances in the theory of rings, algebras and matrix theory. This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.… Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest. On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming. He studied algebras and published papers on trigonometrical series. He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras. He also published results on algebras which were fundamental in the study of algebraic number fields. Derivatives algebraist noun ˌaldʒɪˈbreɪɪstˌældʒəˈbreɪɪst Early algebraists had to prove their formulas by geometry. Example sentencesExamples Or he might want to train future algebraists and maybe attract a few Ph.D. students for himself. Few algebraists seriously think about writing the great American comprehensive algebra text. Problems such as these still seem to present a formidable challenge to the ingenuity of algebraists. In other words, like many other algebraists, Chinese or not, he demonstrates algebra by using it… 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). Bone-setting does not seem to have much to do with mathematics, but there is a connection in the word algebra. It comes from the Arabic al-jabr ‘the reunion of broken parts’, used specifically to refer to the surgical treatment of fractures and to bone-setting. Algebra was used in this meaning in English in the 16th century. The mathematical sense comes from the title of a 9th-century Arabic book ilm al-jabr wa'l-mukabala, ‘the science of restoring what is missing and equating like with like’, written by the mathematician al-Kwarizmi (c.790–c.840). Definition of algebra in US English: algebra nounˈældʒəbrəˈaljəbrə 1The 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 Example sentencesExamples Ernst Schröder's important work is in the area of algebra, set theory and logic. We have looked briefly at Zorn's contributions to algebra and to set theory. He wrote several books on arithmetic, algebra, geometry and astronomy. Aitken's mathematical work was in statistics, numerical analysis, and algebra. They are the basis of mathematical logic, which in turn gives rise to Boolean algebra. He failed in his application for the chair of algebra and number theory at Uppsala University. He worked on algebra and graph theory, combining the two to produce his first outstanding contribution to matroid theory. Wall's research is mostly in the area of geometric topology and related algebra. It is time to take a look at this most outstanding work on algebra in Greek mathematics. König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis. It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration. Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics. The book contained the elements of geometry and algebra in addition to the calculus. It was an exciting time with increasing mathematical activity in algebra. Pierre went on to study the latest mathematics, in particular studying algebra and geometry. 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. In short, his interest in classical algebra and number theory brought him to abstract semigroups. He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory. Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations. 1.1 A system of algebra based on given axioms. Example sentencesExamples Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories. 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. Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic. The theorem states that all central division algebras over algebraic number fields are cyclic algebras. 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. He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory. On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming. He studied algebras and published papers on trigonometrical series. Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest. Wedderburn made important advances in the theory of rings, algebras and matrix theory. In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal. Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras. This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.… Jordan algebras are called after the German physicist and mathematician Pascual Jordan. He also published results on algebras which were fundamental in the study of algebraic number fields. In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven. 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).
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