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Patrick Michael Grundy
Patrick Michael Grundy (16 November 1917, Yarmouth, Isle of Wight – 4 November 1959) was an English mathematician and statistician. He was one of the eponymous co-discoverers of the Sprague–Grundy function and its application to the analysis of a wide class of combinatorial games. Biography Grundy received his secondary education from Malvern College, to which he had obtained a Major Scholarship in 1931, and from which he graduated in 1935. While there, he demonstrated his aptitude for mathematics by winning three prizes in that subject. After leaving school he entered Clare College, Cambridge, on a Foundation Scholarship, where he read for the Mathematical Tripos from 1936 to 1939, earning first class honours in Part II and a distinction in Part III. The work for which he is best known appeared in his first paper, ''Mathematics and Games'', first published in the Cambridge University Mathematical Society's magazine, '' Eureka'' in 1939, and reprinted by the same m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yarmouth, Isle Of Wight
Yarmouth is a town, port and civil parish in the west of the Isle of Wight, off the south coast of England. The town is named for its location at the mouth of the small Western Yar river. The town grew near the river crossing, originally a ferry, which was replaced with a road bridge in 1863.A Timeline History of Yarmouth compiled by Ian Dallison on behalf of The Yarmouth Society History 
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Impartial Games
In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between player 1 and player 2 is that player 1 goes first. The game is played until a terminal position is reached. A terminal position is one from which no moves are possible. Then one of the players is declared the winner and the other the loser. Furthermore, impartial games are played with perfect information and no chance moves, meaning all information about the game and operations for both players are visible to both players. Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, Subtract a square, Notakto, and poset games. Go and chess are not impartial, as each player can only place or move pieces of their own color. Games such as poker, dice or dominos Dominoes is a family of tile-based games played with gaming p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Hull
The University of Hull is a public research university in Kingston upon Hull, a city in the East Riding of Yorkshire, England. It was founded in 1927 as University College Hull. The main university campus is located in Hull and is home to the Hull York Medical School, a joint initiative with the University of York. Students are served by Hull University Union. The first chancellor of the university was Michael Willoughby, 11th Baron Middleton, Lord Middleton (1954–1969), followed by Henry Cohen, 1st Baron Cohen of Birkenhead, Lord Cohen (1970–1977), Richard Wilberforce, Baron Wilberforce, Lord Wilberforce (1978–1994), and Robert Armstrong, Baron Armstrong of Ilminster, Lord Armstrong (1994–2006). Virginia Bottomley (Baroness Bottomley of Nettlestone) was installed as the current chancellor in April 2006. History University College The foundation stone of University College Hull, then an external college of the University of London, was laid in 1927 by Prince Albert, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Module (mathematics)
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of ''module'' generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers. Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication. Modules are very closely related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. Introduction and definition Motivation In a vector space, the set of scalars is a field and acts on the vectors by scalar multiplication, subject to certain axioms such as the distributive law. In a module, the scalars need only be a ring, so the module conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769. Following the reorganization in 1998, they are now awarded under the names Smith-Knight Prize and Rayleigh-Knight Prize. History The Smith Prize fund was founded by bequest of Robert Smith upon his death in 1768, having by his will left £3,500 of South Sea Company stock to the University. Every year two or more junior Bachelor of Arts students who had made the greatest progress in mathematics and natural philosophy were to be awarded a prize from the fund. The prize was awarded every year from 1769 to 1998 except 1917. From 1769 to 1885, the prize was awarded for the best performance in a series of examinations. In 1854 George Stokes included an examination question on a particular theorem that William Thomson had written to him about, which is now known as Stokes' theorem. T. W. Körner notes Only a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ring Theory)
In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may not correspond directly to the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cambridge
, mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Scholars of the University of Cambridge , type = Public research university , endowment = £7.121 billion (including colleges) , budget = £2.308 billion (excluding colleges) , chancellor = The Lord Sainsbury of Turville , vice_chancellor = Anthony Freeling , students = 24,450 (2020) , undergrad = 12,850 (2020) , postgrad = 11,600 (2020) , city = Cambridge , country = England , campus_type = , sporting_affiliations = The Sporting Blue , colours = Cambridge Blue , website = , logo = University of Cambridge logo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grundy Number
In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring strategy that considers the vertices of the graph in sequence and assigns each vertex its first available color, using a vertex ordering chosen to use as many colors as possible. Grundy numbers are named after P. M. Grundy, who studied an analogous concept for directed graphs in 1939. The undirected version was introduced by .. Example For example, for a path graph with four vertices, the chromatic number is two but the Grundy number is three: if the two endpoints of the path are colored first, the greedy coloring algorithm will use three colors for the whole graph. Atoms defines a sequence of graphs called -''atoms'', with the property that a graph has Grundy number at least if and only if it contains a -atom. Each -atom is formed from an independent set and a -atom, by adding one edge from each vertex of the -atom to a ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Coloring
In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but they do not in general use the minimum number of colors possible. Different choices of the sequence of vertices will typically produce different colorings of the given graph, so much of the study of greedy colorings has concerned how to find a good ordering. There always exists an ordering that produces an optimal coloring, but although such orderings can be found for many special classes of graphs, they are hard to find in general. Commonly used strategies for vertex ordering involve placing higher-degree vertices earlier than lower-degree vertices, or choosing vertices with fewer available colors in preference to vertices that are less c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Colouring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color. Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems are often stated and studied as-is. This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
