[permalink] [id link]
In mathematics, factorization ( also factorisation in British English ) or factoring is the decomposition of an object ( for example, a number, a polynomial, or a matrix ) into a product of other objects, or factors, which when multiplied together give the original.
from
Wikipedia
Some Related Sentences
mathematics and factorization
Methods for breaking modern cryptosystems often involve solving carefully constructed problems in pure mathematics, the best-known being integer factorization.
In mathematics, a unique factorization domain ( UFD ) is a commutative ring in which every non-unit element, with special exceptions, can be uniquely written as a product of prime elements ( or irreducible elements ), analogous to the fundamental theorem of arithmetic for the integers.
In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field ( or more generally any Dedekind domain ) can be described by a certain group known as an ideal class group ( or class group ).
In number theory, a branch of mathematics, the special number field sieve ( SNFS ) is a special-purpose integer factorization algorithm.
* Prime decomposition of integers, see fundamental theorem of arithmetic ( for the mathematics ) or integer factorization ( for applications )
In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z as
In mathematics, the Weierstrass factorization theorem in complex analysis, named after Karl Weierstrass, asserts that entire functions can be represented by a product involving their zeroes.
In recreational mathematics, Maris – McGwire – Sosa pairs or MMS pairs are two consecutive natural numbers such that adding each number's digits ( in base 10 ) to the digits of its prime factorization gives the same sum.
mathematics and also
Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.
The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.
Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.
It is also commonly used in mathematics in algebraic solutions representing quantities such as angles.
The term may be also used loosely or metaphorically to denote highly skilled people in any non -" art " activities, as well — law, medicine, mechanics, or mathematics, for example.
He also applied mathematics in generalizing physical laws from these experimental results.
Despite being quite religious, he was also interested in mathematics and science, and sometimes is claimed to have contradicted the teachings of the Church in favour of scientific theories.
He was educated at the Collège des Quatre-Nations ( also known as Collège Mazarin ) from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics.
His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.
He is also noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.
In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.
It can also be used in topics as diverse as mathematics, gastronomy, fashion and website design.
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
He won a scholarship to the University and majored in mathematics, and also studied astronomy, physics and chemistry.
His father, Étienne Pascal ( 1588 – 1651 ), who also had an interest in science and mathematics, was a local judge and member of the " Noblesse de Robe ".
In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.
Bioinformatics also deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, structural biology, software engineering, data mining, image processing, modeling and simulation, discrete mathematics, control and system theory, circuit theory, and statistics.
It can also be used to denote abstract vectors and linear functionals in mathematics.
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.
The term can also be applied to some degree to functions in mathematics, referring to the anatomy of curves.
Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics.
It has also given rise to a new theory of the philosophy of mathematics, and many theories of artificial intelligence, persuasion and coercion.
Most undergraduate programs emphasize mathematics and physics as well as chemistry, partly because chemistry is also known as " the central science ", thus chemists ought to have a well-rounded knowledge about science.
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.
mathematics and factorisation
In number theory, a branch of mathematics, the Stark – Heegner theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers.
mathematics and British
He later gained three more O-levels by correspondence course, in the British Constitution, mathematics and economics.
He learned additional concepts in mathematics from the British mathematician Roger Penrose.
A lucid statement of this is found in an essay written by the British mathematician G. H. Hardy in defense of pure mathematics.
He studied mathematics, metaphysics, and philosophy under Professor William Small, who introduced the enthusiastic Jefferson to the writings of the British Empiricists, including John Locke, Francis Bacon, and Isaac Newton.
* July 4 – Ruth Lawrence, 13, achieves a first in mathematics at Oxford University, becoming the youngest British person ever to earn a first-class degree and the youngest known graduate of Oxford University.
Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics.
British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton ( see Cambridge Mathematical Tripos ).
Sun Yat-sen then studied at Iolani School where he learned English, British history, mathematics, science, and Christianity.
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear.
However, the link between the Riemann hypothesis and the Prime Number Theorem had been known before in Continental Europe, and Littlewood also wrote later in his book A mathematician ’ s miscellany that his actually only rediscovered result did not shed a bright light on the isolated state of British mathematics at the time.
Through the interest of Sir George Leonard Staunton, to whose son he taught mathematics, he was attached on the first British embassy to China from 1792-94 as comptroller of the household to Lord Macartney.
Frank Plumpton Ramsey ( 22 February 1903 – 19 January 1930 ) was a British mathematician who, in addition to mathematics, made significant and precocious contributions in philosophy and economics before his death at the age of 26.
( British universities were still focused on classics and mathematics and not laboratory science.
Sir Thomas Little Heath ( 5 October 1861 – 16 March 1940 ) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer.
In mathematics, and particularly topology, a fiber bundle ( or, in British English, fibre bundle ) is intuitively a space which locally " looks " like a certain product space, but globally may have a different topological structure.
He helped found the modern British school of pure mathematics.
* Lewis Carroll, pen name of British author Charles Dodgson, lectured in mathematics at Christ Church, Oxford.
* John Dalton, British chemist and physicist, taught mathematics at schools and colleges in Manchester, Oxford and York
Johnny Ball ( born Graham Ball, 23 May 1938 ) is a British television personality, a populariser of mathematics and the father of BBC Radio 2 DJ Zoë Ball.
A second debate by him on mathematics (" quadratic equations ") was reprinted by the British Association for the History of Mathematics and by the American equivalent body, and from thence it is cited by Puzzi in a recent text " The Equation They Couldn't Solve ".
Geoffrey Hinton FRS ( born 6 December 1947 ) is a British born informatician most noted for his work on the mathematics and applications of neural networks, and their relationship to information theory.
After completing high school in Richmond, BC, he received a Bachelor of Applied Science in Engineering Physics from the University of British Columbia in 1972 and did postgraduate work in engineering with specialization in applied mathematics and fluid dynamics at the University of Western Ontario.
* Ronald Brown ( mathematician ) ( born 1935 ), British professor of mathematics at Bangor University
1.332 seconds.