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Algebra

Index Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. [1]

189 relations: Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī, Abelian group, Abstract algebra, Addition, Al-Karaji, Alexandria, Algebra over a field, Algebra tile, Algebraic combinatorics, Algebraic equation, Algebraic geometry, Algebraic number theory, Algebraic structure, Algebraic topology, Algorithm, Analytic geometry, Ancient Egyptian mathematics, Arabic, Areas of mathematics, Arithmetic, Arithmetica, Arthur Cayley, Associated Press, Associative algebra, Associative property, Augustus De Morgan, Axiomatic system, Babylonian mathematics, Bhāskara II, Binary operation, Boolean algebra, Boolean algebra (structure), Brahmagupta, Brāhmasphuṭasiddhānta, C*-algebra, Calculus, Category theory, Chinese mathematics, Classification of finite simple groups, Closure (mathematics), Commutative algebra, Commutative property, Commutative ring, Complemented lattice, Complex number, Computer algebra, Computer program, Constant (mathematics), Constructible number, Cubic function, ..., Cyclic group, Determinant, Diophantine equation, Diophantus, Distributive lattice, Distributive property, Division (mathematics), Element (mathematics), Elementary algebra, Equation, Euclid's Elements, Euclidean vector, Expression (mathematics), Exterior algebra, F-algebra, F-coalgebra, Factorization of polynomials, Fibonacci, Field (mathematics), Field of sets, Finitary relation, Finite group, Finite set, François Viète, Function (mathematics), Gabriel Cramer, Galois theory, Geometry, George Peacock, Gottfried Wilhelm Leibniz, Greek mathematics, Gresham College, Group (mathematics), Group theory, Hellenistic period, Hero of Alexandria, Heyting algebra, Historia Mathematica, History of algebra, Homological algebra, Hopf algebra, Identity element, Indeterminate equation, Indian mathematics, Integer, Integral domain, Inverse element, Japanese mathematics, Joseph-Louis Lagrange, Josiah Willard Gibbs, K-theory, La Géométrie, Leonhard Euler, Lie algebra, Like terms, Linear algebra, Linear equation, List of linear algebra topics, List of mathematical symbols, Logic, MacTutor History of Mathematics archive, Mahāvīra (mathematician), Mass–energy equivalence, Mathematical analysis, Mathematics, Mathematics in medieval Islam, Mathematics Subject Classification, Matrix (mathematics), Matrix multiplication, Measure (mathematics), Medieval Latin, Modular arithmetic, Monad (category theory), Monoid, Muhammad ibn Musa al-Khwarizmi, Multilinear algebra, Multiplication, Natural number, Negative number, Non-associative algebra, Number, Number theory, Octonion, Omar Khayyam, Operation (mathematics), Outline of algebra, Paolo Ruffini, PDF, Penguin Books, Permutation group, Persian people, Plato, Polynomial, Polynomial greatest common divisor, Primary education, Quadratic equation, Quadratic formula, Quartic function, Quasigroup, Quaternion, Quintic function, Rational number, Real number, Reduction (mathematics), Relation algebra, Relational algebra, René Descartes, Resolvent (Galois theory), Rhetorical modes, Rhind Mathematical Papyrus, Ring (mathematics), Ring theory, Secondary education, Seki Takakazu, Semigroup, Set (mathematics), Set theory, Sharaf al-Dīn al-Ṭūsī, Sigma-algebra, Simple group, Springer Science+Business Media, Subtraction, Symmetric algebra, Tensor algebra, Term (logic), The Compendious Book on Calculation by Completion and Balancing, The Nine Chapters on the Mathematical Art, Theory of equations, Topological space, Truth value, Universal algebra, University of St Andrews, Variable (mathematics), Vector (mathematics and physics), Vector space, Vertex operator algebra, Zero of a function, Zhu Shijie, 0. Expand index (139 more) »

Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī

Abū al-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qalaṣādī (1412–1486) was a Muslim Arab mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence.

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Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

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Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Al-Karaji

(c. 953 – c. 1029) was a 10th-century Persian mathematician and engineer who flourished at Baghdad.

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Alexandria

Alexandria (or; Arabic: الإسكندرية; Egyptian Arabic: إسكندرية; Ⲁⲗⲉⲝⲁⲛⲇⲣⲓⲁ; Ⲣⲁⲕⲟⲧⲉ) is the second-largest city in Egypt and a major economic centre, extending about along the coast of the Mediterranean Sea in the north central part of the country.

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Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

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Algebra tile

Algebra tiles are mathematical manipulatives that allow students to better understand ways of algebraic thinking and the concepts of algebra.

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Algebraic combinatorics

Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Algebraic number theory

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.

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Algebraic structure

In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.

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Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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Ancient Egyptian mathematics

Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. 300 BC, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt.

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Arabic

Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.

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Areas of mathematics

Mathematics encompasses a growing variety and depth of subjects over history, and comprehension requires a system to categorize and organize the many subjects into more general areas of mathematics.

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Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

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Arithmetica

Arithmetica (Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD.

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Arthur Cayley

Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.

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Associated Press

The Associated Press (AP) is a U.S.-based not-for-profit news agency headquartered in New York City.

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Associative algebra

In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.

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Axiomatic system

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

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Babylonian mathematics

Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC.

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Bhāskara II

Bhāskara (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhaskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer.

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Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

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Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

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Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

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Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

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Brāhmasphuṭasiddhānta

The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628.

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C*-algebra

C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

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Chinese mathematics

Mathematics in China emerged independently by the 11th century BC.

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Classification of finite simple groups

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below.

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Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.

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Commutative algebra

Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

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Complemented lattice

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Computer algebra

In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.

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Computer program

A computer program is a collection of instructions for performing a specific task that is designed to solve a specific class of problems.

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Constant (mathematics)

In mathematics, the adjective constant means non-varying.

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Constructible number

In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length || can be constructed with compass and straightedge in a finite number of steps.

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Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Diophantine equation

In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).

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Diophantus

Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

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Distributive lattice

In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other.

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Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

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Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

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Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

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Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

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Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Expression (mathematics)

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

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Exterior algebra

In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.

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F-algebra

In mathematics, specifically in category theory, F-algebras generalize algebraic structure.

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F-coalgebra

In mathematics, specifically in category theory, an F-coalgebra is a structure defined according to a functor F. For both algebra and coalgebra, a functor is a convenient and general way of organizing a signature.

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Factorization of polynomials

In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

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Fibonacci

Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Field of sets

In mathematics a field of sets is a pair \langle X, \mathcal \rangle where X is a set and \mathcal is an algebra over X i.e., a non-empty subset of the power set of X closed under the intersection and union of pairs of sets and under complements of individual sets.

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Finitary relation

In mathematics, a finitary relation has a finite number of "places".

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Finite group

In abstract algebra, a finite group is a mathematical group with a finite number of elements.

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Finite set

In mathematics, a finite set is a set that has a finite number of elements.

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François Viète

François Viète (Franciscus Vieta; 1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Gabriel Cramer

Gabriel Cramer (31 July 1704 – 4 January 1752) was a Genevan mathematician.

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Galois theory

In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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George Peacock

George Peacock FRS (9 April 1791 – 8 November 1858) was an English mathematician.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

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Gresham College

Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Hellenistic period

The Hellenistic period covers the period of Mediterranean history between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire as signified by the Battle of Actium in 31 BC and the subsequent conquest of Ptolemaic Egypt the following year.

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Hero of Alexandria

Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.

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Heyting algebra

In mathematics, a Heyting algebra is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that c ∧ a ≤ b is equivalent to c ≤ a → b. From a logical standpoint, A → B is by this definition the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound.

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Historia Mathematica

Historia Mathematica: International Journal of History of Mathematics is an academic journal on the history of mathematics published by Elsevier.

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History of algebra

As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète.

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Homological algebra

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.

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Hopf algebra

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.

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Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

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Indeterminate equation

An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2x.

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Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Integral domain

In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

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Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.

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Japanese mathematics

denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867).

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Josiah Willard Gibbs

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics.

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K-theory

In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme.

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La Géométrie

La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes.

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Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

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Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

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Like terms

In algebra, like terms are terms that have the same variables and powers.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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List of linear algebra topics

This is a list of linear algebra topics.

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List of mathematical symbols

This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.

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Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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MacTutor History of Mathematics archive

The MacTutor History of Mathematics archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland.

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Mahāvīra (mathematician)

Mahāvīra (or Mahaviracharya, "Mahavira the Teacher") was a 9th-century Jain mathematician from Karnataka, India.

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Mass–energy equivalence

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula: E.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Mathematics in medieval Islam

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).

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Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

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Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

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Medieval Latin

Medieval Latin was the form of Latin used in the Middle Ages, primarily as a medium of scholarly exchange, as the liturgical language of Chalcedonian Christianity and the Roman Catholic Church, and as a language of science, literature, law, and administration.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Monad (category theory)

In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is an endofunctor (a functor mapping a category to itself), together with two natural transformations.

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Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

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Muhammad ibn Musa al-Khwarizmi

There is some confusion in the literature on whether al-Khwārizmī's full name is ابو عبد الله محمد بن موسى الخوارزمي or ابو جعفر محمد بن موسی الخوارزمی.

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Multilinear algebra

In mathematics, multilinear algebra extends the methods of linear algebra.

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Negative number

In mathematics, a negative number is a real number that is less than zero.

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Non-associative algebra

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative.

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Number

A number is a mathematical object used to count, measure and also label.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Octonion

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.

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Omar Khayyam

Omar Khayyam (عمر خیّام; 18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet.

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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Outline of algebra

Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity.

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Paolo Ruffini

Paolo Ruffini (September 22, 1765 – May 10, 1822) was an Italian mathematician and philosopher.

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PDF

The Portable Document Format (PDF) is a file format developed in the 1990s to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.

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Penguin Books

Penguin Books is a British publishing house.

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Permutation group

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).

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Persian people

The Persians--> are an Iranian ethnic group that make up over half the population of Iran.

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Plato

Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Polynomial greatest common divisor

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials.

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Primary education

Primary education and elementary education is typically the first stage of formal education, coming after preschool and before secondary education (The first two grades of primary school, Grades 1 and 2, are also part of early childhood education).

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Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

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Quadratic formula

In elementary algebra, the quadratic formula is the solution of the quadratic equation.

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Quartic function

In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

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Quasigroup

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Reduction (mathematics)

In mathematics, reduction refers to the rewriting of an expression into a simpler form.

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Relation algebra

In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.

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Relational algebra

Relational algebra, first created by Edgar F. Codd while at IBM, is a family of algebras with a well-founded semantics used for modelling the data stored in relational databases, and defining queries on it.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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Resolvent (Galois theory)

In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has, roughly speaking, a rational root if and only if the Galois group of p is included in G. More exactly, if the Galois group is included in G, then the resolvent has a rational root, and the converse is true if the rational root is a simple root.

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Rhetorical modes

Rhetorical modes (also known as modes of discourse) describe the variety, conventions, and purposes of the major kinds of language-based communication, particularly writing and speaking.

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Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Ring theory

In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers.

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Secondary education

Secondary education covers two phases on the International Standard Classification of Education scale.

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Seki Takakazu

, also known as,Selin, was a Japanese mathematician and author of the Edo period.

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Semigroup

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Sharaf al-Dīn al-Ṭūsī

(c. 1135 – c. 1213) was an Iranian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages).

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Sigma-algebra

In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.

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Simple group

In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

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Symmetric algebra

In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is the free commutative unital associative algebra over K containing V. It corresponds to polynomials with indeterminates in V, without choosing coordinates.

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Tensor algebra

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.

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Term (logic)

In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

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The Compendious Book on Calculation by Completion and Balancing

The Compendious Book on Calculation by Completion and Balancing (الكتاب المختصر في حساب الجبر والمقابلة, Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala; Liber Algebræ et Almucabola) is an Arabic treatise on mathematics written by Persian polymath Muḥammad ibn Mūsā al-Khwārizmī around 820 CE while he was in the Abbasid capital of Baghdad.

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The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE.

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Theory of equations

In algebra, the theory of equations is the study of algebraic equations (also called “polynomial equations”), which are equations defined by a polynomial.

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Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

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Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

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Universal algebra

Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.

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University of St Andrews

The University of St Andrews (informally known as St Andrews University or simply St Andrews; abbreviated as St And, from the Latin Sancti Andreae, in post-nominals) is a British public research university in St Andrews, Fife, Scotland.

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Variable (mathematics)

In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.

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Vector (mathematics and physics)

When used without any further description, vector usually refers either to.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Vertex operator algebra

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory.

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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Zhu Shijie

Zhu Shijie (1249–1314), courtesy name Hanqing (汉卿), pseudonym Songting (松庭), was one of the greatest Chinese mathematicians living during the Yuan Dynasty.

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0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

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References

[1] https://en.wikipedia.org/wiki/Algebra

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