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G. H. Hardy, A Mathematician's Apology (1940) He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one. John Edensor Littlewood, Littlewood's Miscellany (1986) The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by ...
Principal value. In mathematics, specifically complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued. A simple case arises in taking the square root of a positive real number. For example, 4 has two square roots: 2 and −2; of these the positive root ...
Square root. Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 52 (5 squared). In mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1] For example, 4 and −4 are square roots of 16 ...
Principal ideal domain. In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a commutative ring without nonzero zero divisors) in which every ideal is principal (that is, is formed by the multiples of a single element). Some authors such as Bourbaki refer to PIDs as principal rings.
Contents. The Principles of Mathematics consists of 59 chapters divided into seven parts: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. In chapter one, "Definition of Pure Mathematics", Russell asserts that : The fact that all Mathematics is Symbolic Logic is one of the greatest ...
Matrix (mathematics) An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix. In mathematics, a matrix (pl.: matrices) is a rectangular array or table of ...
Two divisors are said to be linearly equivalent if their difference is principal, so the divisor class group is the group of divisors modulo linear equivalence. For a variety X of dimension n over a field, the divisor class group is a Chow group; namely, Cl(X) is the Chow group CH n−1 (X) of (n−1)-dimensional cycles. Let Z be a closed ...
Principal branch. In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function. Most often, this applies to functions defined on the complex plane.