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mathematics and Laurent
In mathematics, the Laurent series of a complex function f ( z ) is a representation of that function as a power series which includes terms of negative degree.
Laurent says: What are mathematics helpful for?
In mathematics, the principal part has several independent meanings, but usually refers to the negative-power portion of the Laurent series of a function.
In mathematics, the Stieltjes constants are the numbers that occur in the Laurent series expansion of the Riemann zeta function:

mathematics and polynomial
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients ( or equivalently — by clearing denominators — with integer coefficients ).
Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only.
In mathematics, Horner's method ( also known as Horner scheme in the UK or Horner's rule in the U. S .) is either of two things: ( i ) an algorithm for calculating polynomials, which consists in transforming the monomial form into a computationally efficient form ; or ( ii ) a method for approximating the roots of a polynomial.
In mathematics, a polynomial is an expression of finite length constructed from variables ( also called indeterminates ) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
In advanced mathematics, polynomials are used to construct polynomial rings, a central concept in abstract algebra and algebraic geometry.
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree.
In mathematics, a transcendental number is a ( possibly complex ) number that is not algebraic — that is, it is not a root of a non-constant polynomial equation with rational coefficients.
* Equally spaced polynomial in mathematics
In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half-plane of the complex plane, that is, the real part of every zero is negative.
* Reciprocal polynomial, in mathematics
" One such example of his impact on pure mathematics is his framework for understanding the Jones polynomial using Chern – Simons theory.
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.
In mathematics, a Diophantine equation is an equation of the form P ( x < sub > 1 </ sub >, ..., x < sub > j </ sub >, y < sub > 1 </ sub >, ..., y < sub > k </ sub >)= 0 ( usually abbreviated P (,)= 0 ) where P (,) is a polynomial with integer coefficients.
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in ( D + 1 )- dimensional space defined as the locus of zeros of a quadratic polynomial.
In mathematics, if L is a field extension of K, then an element a of L is called an algebraic element over K, or just algebraic over K, if there exists some non-zero polynomial g ( x ) with coefficients in K such that g ( a )= 0.
A quadratic function, in mathematics, is a polynomial function of the form
In mathematics, a polynomial is said to be irreducible if it cannot be factored into the product of two or more non-trivial polynomials whose coefficients are of a specified type.
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series ; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus ; in numerical analysis as Gaussian quadrature ; in finite element methods as Shape Functions for beams ; and in physics, where they give rise to the eigenstates of the quantum harmonic oscillator.
In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial.
In mathematics, a polynomial sequence, i. e., a sequence of polynomials indexed by
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to ' prove ' them.

mathematics and named
In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.
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.
In mathematics, a Cauchy sequence ( pronounced ), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
* In Canadian junior high schools, an annual national mathematics competition ( Gauss Mathematics Competition ) administered by the Centre for Education in Mathematics and Computing is named in honour of Gauss,
In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.
In the essay a blind English mathematician named Saunderson argues that since knowledge derives from the senses, then mathematics is the only form of knowledge that both he and a sighted person can agree about.
In pure mathematics, the magnitude of a googolplex could be related to other forms of large-number notation such as tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation, though neither googol nor googolplex are anywhere near the largest representable or even specifically named numbers.
A mathematics center has been named in his honor at the University of Idaho in Moscow, Idaho.
In mathematics, a generalized mean, also known as power mean or Hölder mean ( named after Otto Hölder ), is an abstraction of the Pythagorean means including arithmetic, geometric, and harmonic means.
In 2006, Harvey Mudd was also named one of the " new Ivy leagues " by Kaplan and Newsweek, while the mathematics department won the first American Mathematical Society Award for Exemplary Program.
In mathematics, a Mersenne number, named after Marin Mersenne ( a French monk who began the study of these numbers in the early 17th century ), is a positive integer that is one less than a power of two:
He returned to Alexandria, and began determinedly studying the works of Aristotle under Olympiodorus the Elder ( he also began studying mathematics during this period as well with a teacher named Heron ( no relation to Hero of Alexandria who was also known as Heron ).
Descartes ' influence in mathematics is equally apparent ; the Cartesian coordinate system — allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system ( and conversely, shapes to be described as equations ) — was named after him.
In combinatorial mathematics, a Steiner system ( named after Jakob Steiner ) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2.
Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox.
The award is named after Alan Turing, mathematician and reader in mathematics at the University of Manchester.
Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order ( number of elements ) of every subgroup H of G divides the order of G. The theorem is named after Joseph Lagrange.
In mathematics, specifically in real analysis, the Bolzano – Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space R < sup > n </ sup >.
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937.
There are three programming languages named after him, Haskell, Brooks and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.
Dalton's early life was highly influenced by a prominent Eaglesfield Quaker named Elihu Robinson, a competent meteorologist and instrument maker, who got him interested in problems of mathematics and meteorology.
In mathematics, a Dedekind cut, named after Richard Dedekind, is a partition of the rational numbers into two non-empty parts A and B, such that all elements of A are less than all elements of B, and A contains no greatest element.
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (

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