The word index is used in variety of senses in mathematics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and

• In perhaps the most frequent sense, an index is a superscript or subscript to a symbol. This article is about the terms 'subscript' and 'superscript' as used in typography This article is about the terms 'subscript' and 'superscript' as used in typography Superscript indices are often, but not always, used to indicate powers. Subscript indices are usually used to identify an element of a set or array or sequence of variables. In Computer science an array is a Data structure consisting of a group of elements that are accessed by indexing. See also index set, indexed family, and Index (information technology). In Mathematics, the elements of a set A may be indexed or labeled by means of a set J that is on that account called an index In Mathematics, an indexed family of sets is defined in stages beginning with the more general concept of an indexed family of elements, which is really just an alternative This is referring to Index in the context of Information Technology

• The index of a subgroup is the number of its left cosets (which is equal to the number of its right cosets). In Mathematics, if G is a group, H is a Subgroup of G, and g is an element of G, then gH In Mathematics, if G is a group, H is a Subgroup of G, and g is an element of G, then gH

• The index of a Fredholm operator is the dimension of its kernel minus the dimension of its cokernel. In Mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of Integral equations It is named in honour of Erik Ivar Fredholm In the various branches of Mathematics that fall under the heading of Abstract algebra, the kernel of a Homomorphism measures the degree to which the homomorphism

• The index of a real quadratic form Q is defined (but not always consistently) as p − q where Q can be written as a difference of p squared linear terms and q squared linear terms. In Mathematics, a quadratic form is a Homogeneous polynomial of degree two in a number of variables

• The index of a vector field v at an isolated zero is the degree of the map

taking points near the zero into the unit sphere. In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. This article is about the term "degree" as used in algebraic topology In Mathematics, a unit Sphere is the set of points of Distance 1 from a fixed central point where a generalized concept of distance may be used a closed This index is used in the statement of the Poincaré–Hopf theorem which relates the sum of the indices of a vector field to the Euler characteristic of the manifold. In Mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem In Mathematics, and more specifically in Algebraic topology and Polyhedral combinatorics, the Euler characteristic is a Topological invariant The hairy ball theorem is a special case. The hairy ball theorem of Algebraic topology states that there is no nonvanishing continuous Tangent vector field on the sphere Confer fixed point index. In Mathematics, the fixed point index is a concept in Topological fixed point theory and in particular Nielsen theory.

• "An index relates the value of a variable (or group of variables) to a base level, which is often the value on a particular date. The base level is set so that the index produces numbers that are easy to understand and compare. Indices are used to report on a wide variety of variables, including prices and wages, ultraviolet levels in sunlight, and even the readability of textbooks. " from Mathematics of Data Management published by McGraw-Hill Ryerson