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, a Laurent polynomial ( named

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, 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.

In mathematics, the Bernoulli numbers B < sub > n </ sub > are a sequence of rational numbers with deep connections to number theory.

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 mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:

Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics.

The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody.

* Homology ( mathematics ), a procedure to associate a sequence of abelian groups or modules with a given mathematical object

In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems.

In mathematics, given an infinite sequence of numbers

In mathematics, more specifically in general topology and related branches, a net or Moore – Smith sequence is a generalization of the notion of a sequence.

In mathematics, a sequence is an ordered list of objects ( or events ).

There are various and quite different notions of sequences in mathematics, some of which ( e. g., exact sequence ) are not covered by the notations introduced below.

In mathematics a topological space is called separable if it contains a countable dense subset ; that is, there exists a sequence of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

* Series ( mathematics ), the sum of a sequence of terms

* Word ( mathematics ), an ordered sequence of symbols chosen from a predetermined set or alphabet

The Dirac delta function as the limit ( in the sense of distribution ( mathematics ) | distributions ) of the sequence of zero-centered normal distribution s as a → 0

In applied mathematics, the delta function is often manipulated as a kind of limit ( a weak limit ) of a sequence of functions, each member of which has a tall spike at the origin: for example, a sequence of Gaussian distributions centered at the origin with variance tending to zero.

This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.

In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

There is no prize awarded for mathematics, but see Abel Prize.