From Citizendium, the Citizens' Compendium
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- Algebraic geometry : Discipline of mathematics that studies the geometric properties of the objects defined by algebraic equations.
- Algebraic independence : The property of elements of an extension field which satisfy only the trivial polynomial relation.
- Algebraic number : A complex number that is a root of a polynomial with rational coefficients.
- Algebra : A branch of mathematics concerning the study of structure, relation and quantity.
- Basis (linear algebra) : A set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others.
- Binomial theorem : for any natural number n.
- Calculus : The elementary study of real (or complex) functions involving derivatives and integration.
- Catalog of special functions : Add brief definition or description
- Completing the square : Rewriting a quadratic polynomial as a constant multiple of a linear polynomial plus a constant.
- Complex number : Numbers of the form a+bi, where a and b are real numbers and i denotes a number satisfying .
- Content (algebra) : The highest common factor of the coefficients of a polynomial.
- Cubic equation : A polynomial equation with of degree 3 (i.e., x3+px2+qx+r=0).
- Cyclotomic polynomial : A polynomial whose roots are primitive roots of unity.
- Discriminant of a polynomial : An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences between the roots.
- E (mathematics) : Constant real number equal to 2.71828 18284 59045 23536... that is the base of the natural logarithms.
- Elementary function : Mathematical functions built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary arithmetic operations (+ – × ÷).
- Entire function : is a function that is holomorphic in the whole complex plane.
- Exponential growth : Increase of a quantity x with time t according to the equation x = Kat, where K and a are constants, a is greater than 1, and K is greater than 0.
- Fibonacci polynomials : Polynomial sequence which can be considered as a generalisation of the Fibonacci numbers.
- Field (mathematics) : An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
- Field extension : A field containing a given field as a subfield.
- Fraction (mathematics) : A concept used to convey a proportional relation between a part and the whole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).
- Fundamental Theorem of Algebra : Any nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a root.
- Galois theory : Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions.
- Gamma function : A mathematical function that extends the domain of factorials to non-integers.
- Graph coloring : Graph labelling, which assigns labels traditionally called 'colours' to elements of a graph subject to certain constraints.
- Group (mathematics) : Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation.
- Hall polynomial : The structure constants of Hall algebra.
- Holomorphic function : Function from to is called holomorphic in domain if for every open domain there exist derivative .
- Integer : The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
- Legendre-Gauss Quadrature formula : the specific approximation of the integral with the sum of N terms, which becomes exact for the polynomial integrand of order < 2N.
- Littlewood polynomial : A polynomial all of whose coefficients are plus or minus 1.
- Mathematics : The study of quantities, structures, their relations, and changes thereof.
- Minimal polynomial : The monic polynomial of least degree which a square matrix or endomorphism satisfies.
- Multiple (mathematics) : The product of an integer with another integer.
- Multiplication : The binary mathematical operation of scaling one number or quantity by another (multiplying).
- Null set : Add brief definition or description
- Number : One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring.
- Polynomial ring : Ring formed from the set of polynomials in one or more variables with coefficients in another ring.
- Quadratic equation : An equation of the form ax2 + bx + c = 0 where a, b and c are constants.
- Rational function : Function that can be expressed as a quotient of polynomials, excluding division by zero.
- Reaction rate : The amount of reactant or product that is formed or removed (in moles or mass units) per unit time per unit volume, in a particular reaction.
- Real number : A limit of the Cauchy sequence of rational numbers.
- Resultant (algebra) : An invariant which determines whether or not two polynomials have a factor in common.
- Ring (mathematics) : Algebraic structure with two operations, combining an abelian group with a monoid.
- Root of unity : An algebraic quantity some power of which is equal to one.
- Splitting field : A field extension generated by the roots of a polynomial.
- Transcendental number : A number which is not algebraic: that is, does not satisfy any polynomial with integer or rational coefficients.
- Trigonometric function : Function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, and cosecant.
- Vector space : A set of vectors that can be added together or scalar multiplied to form new vectors