Algebra

Major advances in the beginning of 20th century was the formalization of abstract algebra and topology; these two fields were deeply influenced by the pure mathematics philosophy.

The converse of Lagrange's theorem states that if d is a divisor of the order of a group G, then there exists a subgroup H where |H| = d.

A vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication

A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the imaginary unit, whose meaning will be explained further below.

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry.

Algebra studies two main families of equations: polynomial equations and, among them, the special case of linear equations.

it was named when algebra was synonymous with the theory of equations

a major unsolved problem in algebraic geometry and complex geometry

Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions

Abstract algebra is the name that is commonly given to the study of algebraic structures.

Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures.

Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval

a system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which common solutions are sought

In mathematics, the Casas-Alvero conjecture is a problem about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001.

In mathematics, the Ax-Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck.

Boris Delaunay worked in the fields of modern algebra, the geometry of numbers

Brahmagupta developed some algebraic notation and presents methods to solve quardatic equations.

later on genetics where he introduced genetic algebras

known for work in many parts of abstract algebra

He wrote a number of influential research papers in abstract algebra.

Gyula Kőnig worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.

His main publications were on quadratic forms and algebraic groups.

Faulhaber was a 'Cossist', an early algebraist.

Non-commutative polynomials and cyclic algebras

best known for his work in the field of algebra

He worked mainly in abstract algebra

taking up a study of the quaternion algebra

Ernst Schröder was a German mathematician who did important work is in the area of algebra, set theory and logic.

Bauer's mathematical research dealt with algebra, geometric problems, spherical harmonics, the gamma function, and generalized continued fractions.

linear associative algebra and number theory on the pure side

his work on the theory of differential equations from the algebraic viewpoint, which he called differential algebra

He began to work in more general algebraic structures around 1936 when he became interested in generalising the familiar elementary properties of groups into more general settings.

known for his work on combinatorial problems in nonassociative algebra and group theory

notable for research in abstract algebra, algebraic geometry, and functional analysis

the first to provide a general solution for all third-degree polynomials

van Roomen (29 September 1561-4 May 1615), also known as Adrianus Romanus, was a mathematician, professor of medicine and medical astrologer from the Duchy of Brabant in the Habsburg Netherlands who was active throughout Central Europe in the late

Girard worked on algebra, trigonometry and arithmetic.

Recorde virtually established the English school of mathematics and first introduced algebra into England.

A mathematician and physicist who studied in Italy, England and Belgium, his best results are mainly in physics, especially optics, and mathematics.

Alexander Anderson (c. 1582 in Aberdeen, c. 1620 in Paris) was a Scottish mathematician. == Life == He was born in Aberdeen, possibly in 1582, according to a print which suggests he was aged 35 in 1617.

Claude Gaspar Bachet Sieur de Méziriac (9 October 1581-26 February 1638) was a French mathematician and poet born in Bourg-en-Bresse, at that time belonging to Duchy of Savoy.

His Tractatus de limitibus aequationum was reprinted in England in 1807; in it, he finds upper and lower bounds for the solutions to quadratic equations and cubic equations, as simple functions of the coefficients of these equations.

While Rolle's forte was always Diophantine analysis, his most important work was a book on the algebra of equations, called Traité d'algèbre, published in 1690.

The Tschirnhaus transformation, by which he removed certain intermediate terms from a given algebraic equation, is well known.

Flamsteed calles him a good algebraist.

Unusually for the time, the textbook focused exclusively on algebra but did not cover geometry at all.

He contributed to the theory of equations in his posthumous De reductione aequationum of 1713, in which he was the first to take literal coefficients in algebra as indifferently positive or negative.

His book Guiljip (구일집, 九一集) contained the most advanced results of its time on setting up and solving equations, and he has been called the greatest mathematician of Joseon.

He was acquainted with John Collins, who persuaded him to write his work on algebra.

using a resolvent of sixth degree

Algèbre de Viète d'une Méthode nouuelle, claire et facile

In mathematics, he concentrated on expanding the scope of algebra in the theory of equations, and on mathematical tables.

The symbols were used in Teutsche Algebra, published in 1659.

Balam was the author of Algebra, or the Doctrine of composing, inferring, and resolving an Equation (1653).

a great algebraist and a great Whig

Thomas Baker (1625?, 1689) was an English mathematician notable for producing a solution of biquadratic equations.

This book helped teach basic principles and rules of algebra.

There is an unpublished manuscript by Ricci, devoted to algebra, in the library of the Mathematical Institute of Genoa.

In 1700 a tutor taught him algebra and geometry, and in 1702 he attended Attercliffe Academy, near Sheffield, for logic and metaphysics.

Colin Maclaurin (; Scottish Gaelic: Cailean MacLabhruinn ; February 1698-14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra.

In the meantime, he continued his studies in the fields of algebra, geometry, probability theory and number theory, which were based on the works of Kästner, Leonhard Euler and Georg Simon Klügel.

A System of Popular Algebra (John Taylor, London, 1826?).

Kelil Heshbon a Hebrew language manual on algebra and trigonometry

seven text books on algebra, geometry, mechanics and calculus

In 1770 he published Elements of Algebra for the use of Students in Universities

In Treatise on Algebra, Peacock attempted to give algebra a logical treatment comparable to Euclid

No less popular was Introduction to Algebra (1782).

was thus led from logic to algebra

he shows the solutions of cubic and biquadratic equations using new methods

Dissertation on the use of the negative sign in algebra

Algebraical Problems, a schoolbook

Zhu Shijie or Chu Shih-Chieh was a Chinese mathematician who developed methods for handling simultaneous equations.

Stifel was the first, who had a standard method to solve quadratic equations.

he published An Elementary Treatise on Algebra with a dedication to Gregory

announced holding lectures on e.g. calculating on the lines of a calculating board and on algebra

His work is a highly syncopated approach to algebra

Bavio se teorijom skupova, matematičkom logikom, apstraktnom algebrom

He is best known for his work in differential algebra and especially differential Galois theory.

Beyond the applications of Gröbner bases in computational algebra

The Latimer-MacDuffee theorem is a theorem in abstract algebra, a branch of mathematics.

he was chiefly an algebraist

George Chrystal is best remembered today for Algebra: a two volume work which was completed by 1889.

Linear associative algebras

Ernst Jacobsthal was a German mathematician who wrote papers in such diverse fields as algebra, analysis, function theory and number theory.

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to i

In elementary algebra, a difference of two squares is one squared number (the number multiplied by itself) subtracted from another

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ a x 2 + b x + c +b

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup gene

In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

z ) = x ⋅ y + x ⋅ z is always true in elementary algebra.

In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial x 5 + x + a .

In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at

In mathematics, if A is an associative algebra over K, then an element a of A is an algebraic element over K, or just algebraic ov

In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments b

In algebra, a sextic (or hexic) polynomial is a polynomial of degree six.

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers, usually

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic f

In abstract algebra, Ado's theorem is a theorem characterizing finite-dimensional Lie algebras.

Gamas's theorem is a result in multilinear algebra which states the necessary and sufficient conditions for a tensor symmetrized b

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

modern abstract algebra

abstract algebra

development of algebra

Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics.

This work describes Bring's contribution to the algebraic solution of equations.

Brioschi published in Italy various algebraic theories

whose work on new algebra was an important step towards modern algebra

Nouvelle méthode pour la résolution des équations numériques

He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions in October 1843 and then discovering their generalization the octonions himself (he called them octaves) later that same year.

A significant algebraist, he proved that a finite division algebra is a field (Wedderburn's little theorem), and part of the Artin-Wedderburn theorem on simple algebras.

Charles Hermite (French: [ʃaʁl ɛʁmit]; 24 December 1822-14 January 1901) was a French mathematician who studied analysis, number theory, and algebra.

Frank Morley (September 9, 1860, October 17, 1937) was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry.

Bézout is also acknowledged for his work on algebra, despite being much occupied with his teaching duties, leaving him with relatively little time for algebra research.

Alexandru Froda (July 16, 1894, October 7, 1973) was a Romanian mathematician with contributions in the field of mathematical analysis, algebra, number theory and rational mechanics.

Arthur Cayley (; 16 August 1821-26 January 1895) was an English mathematician who worked mostly on algebra.

Sir William Rowan Hamilton (4 August 1805-2 September 1865) was an Irish mathematician, physicist, and astronomer who made numerous major contributions to algebra, classical mechanics, and optics.

Algebra Polynomials

Algebra Scalar Algebra

Algebra Algebraic Equations

Algebra Vector Algebra

Algebra Algebraic Equations

Algebra General Algebra

Algebra Vector Algebra

Algebra Sums

Algebra Forms

Algebra Algebraic Equations

Algebra Algebraic Equations

Algebra Quaternions and Clifford Algebras

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex

of P. It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is

In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition

Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers -

by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients.

Joseph Hidulphe Vincent-is a theorem that isolates the real roots of polynomials with rational coefficients. Even though Vincent's

after the Italian mathematician Giacomo Candido, is an identity for real numbers. It states that for two arbitrary real numbers

polynomial to be irreducible

In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum.

In mathematics, a quintic function is a function of the form g ( x ) = a x 5 + b

In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B

a thesis on alternative algebras

who worked in abstract algebra, functional analysis and topological vector spaces

Hyman Bass is an American mathematician, known for work in algebra and in mathematics education.

Algebra Polynomials

Alexander Ostrowski was a Ukrainian-born mathematician who worked on a wide variety of topics in both analysis and algebra.

Christoff Rudolff was a German mathematician whose book Coss is the first German algebra book.

Ernst Witt was a German mathematician and a leading algebraist. He proved important results on Lie algebras.

Heinrich Weber was a German mathematician whose main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.

Garrett Birkhoff was an American mathematician best known for the algebra book he wrote with Saunders Mac Lane.

Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learnt from Tartaglia.

Ferrari was an Italian scholar who started as Cardan's secretary and went on to devise the solution of the quartic equation.

Tartaglia was an Italian mathematician who was famed for his algebraic solution of cubic equations which was eventually published in Cardan's Ars Magna .

Rafael Bombelli was an Italian mathematician who wrote an influential algebra text and made free use of both negative numbers and complex numbers.