The Art of Computer ProgrammingThe Art of Computer Programming (TAOCP) is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973.
Dimension theorem for vector spacesIn mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite (in the latter case, it is a cardinal number), and defines the dimension of the vector space. Formally, the dimension theorem for vector spaces states that: As a basis is a generating set that is linearly independent, the theorem is a consequence of the following theorem, which is also useful: In particular if V is finitely generated, then all its bases are finite and have the same number of elements.
Least-upper-bound propertyIn mathematics, the least-upper-bound property (sometimes called completeness or supremum property or l.u.b. property) is a fundamental property of the real numbers. More generally, a partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X. Not every (partially) ordered set has the least upper bound property. For example, the set of all rational numbers with its natural order does not have the least upper bound property.
Rank–nullity theoremThe rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the of f) and the nullity of f (the dimension of the kernel of f). It follows that for linear transformations of vector spaces of finite dimension, either injectivity or surjectivity implies bijectivity.
Multiple dispatchMultiple dispatch or multimethods is a feature of some programming languages in which a function or method can be dynamically dispatched based on the run-time (dynamic) type or, in the more general case, some other attribute of more than one of its arguments. This is a generalization of single-dispatch polymorphism where a function or method call is dynamically dispatched based on the derived type of the object on which the method has been called.
Pound sterlingSterling (ISO code: GBP) is the currency of the United Kingdom and nine of its associated territories. The pound (sign: £) is the main unit of sterling, and the word "pound" is also used to refer to the British currency generally, often qualified in international contexts as the British pound or the pound sterling. In British English, its most common nickname is "quid." Sterling is the world's oldest currency that is still in use and that has been in continuous use since its inception.
Turkish liraThe lira (Türk lirası; sign: ₺; ISO 4217 code: TRY; abbreviation: TL) is the official currency of Turkey and Northern Cyprus. One lira is divided into one hundred kuruş. Ottoman lira The lira, along with the related currencies of Europe and the Middle East, has its roots in the ancient Roman unit of weight known as the libra which referred to the Troy pound of silver. The Roman libra adoption of the currency spread it throughout Europe and the Near East, where it continued to be used into medieval times.
Integer matrixIn mathematics, an integer matrix is a matrix whose entries are all integers. Examples include binary matrices, the zero matrix, the matrix of ones, the identity matrix, and the adjacency matrices used in graph theory, amongst many others. Integer matrices find frequent application in combinatorics. and are both examples of integer matrices. Invertibility of integer matrices is in general more numerically stable than that of non-integer matrices.
Dollar signThe dollar sign, also known as peso sign, is a currency symbol consisting of a capital "S" crossed with one or two vertical strokes (ordependingontypeface),usedtoindicatetheunitofvariouscurrenciesaroundtheworld,includingmostcurrenciesdenominated"peso"and"dollar".Theexplicitlydouble−barredsigniscalledcifra~oinPortuguese.Thesignisalsousedinseveralcompoundcurrencysymbols,suchastheBrazilianreal(R) and the United States dollar (US$): in local use, the nationality prefix is usually omitted. Square-free integerIn mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 32. The smallest positive square-free numbers are Every positive integer can be factored in a unique way as where the different from one are square-free integers that are pairwise coprime.
