Polynomial

The graph of a polynomial function of degree 3 Etymology[edit] According to the Oxford English Dictionary, polynomial succeeded the term binomial, and was made simply by replacing the Latin root bi- with the Greek poly-, which comes from the Greek word for many. The word polynomial was first used in the 17th century.[1] Notation and terminology[edit] It is a common convention to use upper case letters for the indeterminates and the corresponding lower case letters for the variables (arguments) of the associated function. It may be confusing that a polynomial P in the indeterminate X may appear in the formulas either as P or as P(X). Normally, the name of the polynomial is P, not P(X). In particular, if a = X, then the definition of P(a) implies This equality allows writing "let P(X) be a polynomial" as a shorthand for "let P be a polynomial in the indeterminate X". Definition[edit] A polynomial in a single indeterminate can be written in the form where For example: is a term. then is from

Linear function In mathematics, the term linear function refers to two different, although related, notions:[1] As a polynomial function[edit] In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero). For a function of any finite number independent variables, the general formula is and the graph is a hyperplane of dimension k. A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. In this context, the other meaning (a linear map) may be referred to as a homogeneous linear function or a linear form. As a linear map[edit] In linear algebra, a linear function is a map f between two vector spaces that preserves vector addition and scalar multiplication: Some authors use "linear function" only for linear maps that take values in the scalar field;[4] these are also called linear functionals. See also[edit]

Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. Background[edit] First incompleteness theorem[edit] Diagonalization[edit] B.

How to Murder Time » Podcasters without portfolio Game AI for Developers Gamasutra - The Art & Business of Making Games Theory and Principles of Game Design Mana Obscura | Tales of Magic from Strange Worlds Roger Wallis Roger Wallis at the Pirate Bay trial. Professor Roger Wallis, (born 8 August 1941 in Rugby, England) is a musician, journalist and researcher.[1] He is a resident of Sweden since 1963, and has been an adjunct professor of multimedia at the Royal Institute of Technology in Stockholm, and is now an emeritus.[2] He has written several books on the music industry with Krister Malm. Among other achievements, he has founded the record company MNW, and been appointed to the board of STIM. He testified in the Pirate Bay trial in February 2009.

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