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Encyclopedia > Index (mathematics)

In mathematics, an index is a superscript or subscript to a symbol. Superscript indices are often, but not always, used to indicate powers. Subscript indices are usually used to label a set or sequence of variables. See also index set and family (mathematics). Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... A superscript is a number, figure, or symbol that appears above the normal line of type. ... A subscript is a number, figure or indicator, that appears below the normal line of type, when used in a formula, mathematical expression or description of a chemical compound. ... In mathematics, exponentiation is a process generalized from repeated (or iterated) multiplication, in much the same way that multiplication is a process generalized from repeated addition. ... In mathematics, an index set is another name for a function domain. ... In mathematics, an index set is another name for a function domain. ...

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 a subgroup of G, and g an element of G, then gH = { gh : h an element of H } is a left coset of H in G, and Hg = { hg : h an element of H } is a right coset of H in G... In mathematics, if G is a group, H a subgroup of G, and g an element of G, then gH = { gh : h an element of H } is a left coset of H in G, and Hg = { hg : h an element of H } is a right coset of H in G...

The index of a Fredholm operator is the dimension of its kernel minus the dimension of its cokernel. In mathematics, a Fredholm operator is a bounded linear operator between two Banach spaces whose range is closed and whose kernel and cokernel are finite-dimensional. ... 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 fails to be injective. ... In abstract algebra, the cokernel of a homomorphism f : X → Y is the quotient of Y by the image of f. ...

The index of a real quadratic form Q is defined (but not always consistently) as pq 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. ...

You can notice Pascal's Triangle:

` 1 1 1 1 2 1 1 3 3 1 `

1 4 6 4 1

Results from FactBites:

 Mathematics - Academic Kids (2446 words) Mathematics is also used to refer to the insight gained by mathematicians by doing mathematics, also known as the body of mathematical knowledge. Nowadays, mathematics derives much inspiration from the natural sciences and it is not uncommon for new mathematics to be pioneered by physicists, although it may need to be recast into more rigorous language. Nonetheless mathematics is often imagined to be nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.
 UniMelb UGHB96 : Sci : Index of Mathematics subjects (2281 words) Mathematics is the oldest of the exact sciences, and among the oldest of all intellectual disciplines. A knowledge of mathematics is invaluable for professional life in the pure and applied sciences, as well as in commerce, industry and technology, and an understanding of mathematics is invaluable in making sense of a rapidly changing and increasingly technologically complex world. The Department of Mathematics offers a variety of subjects at first, second and third year levels which are designed to prepare students for professional careers in mathematics or to help with studies in other disciplines, and to provide training in logical reasoning and to cultivate analytical skills.
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