|
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' evolves through alternating ''moves'', each governed by well-defined rules, with the aim of achieving a specific winning condition. Unlike game theory, economic game theory, combinatorial game theory generally avoids the study of games of chance or games involving imperfect information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical techniques develop, the scope of analyzable games expands, and the boundaries of the field continue to evolve. Authors typically define the term "game" at the outset of academic papers, with definitions tailored to the specific game under analysis rather than reflecting the field’s full scope. Combinatorics, Comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians Playing Konane
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( – 415). She succeed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sudoku
Sudoku (; ; originally called Number Place) is a logic puzzle, logic-based, combinatorics, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed problem, well-posed puzzle has a single solution. French newspapers featured similar puzzles in the 19th century, and the modern form of the puzzle first appeared in 1979 puzzle books by Dell Magazines under the name Number Place. However, the puzzle type only began to gain widespread popularity in 1986 when it was published by the Japanese puzzle company Nikoli (publisher), Nikoli under the name Sudoku, meaning "single number". In newspapers outside of Japan, it first appeared in ''The Conway Daily Sun'' (New Hamp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game AI
In video games, artificial intelligence (AI) is used to generate responsive, adaptive or intelligent behaviors primarily in non-playable characters (NPCs) similar to human-like intelligence. Artificial intelligence has been an integral part of video games since their inception in 1948, first seen in the game ''Nim''. AI in video games is a distinct subfield and differs from academic AI. It serves to improve the game-player experience rather than machine learning or decision making. During the golden age of arcade video games the idea of AI opponents was largely popularized in the form of graduated difficulty levels, distinct movement patterns, and in-game events dependent on the player's input. Modern games often implement existing techniques such as pathfinding and decision trees to guide the actions of NPCs. AI is often used in mechanisms which are not immediately visible to the user, such as data mining and procedural-content generation. One of the most infamous example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tic-tac-toe
Tic-tac-toe (American English), noughts and crosses (English in the Commonwealth of Nations, Commonwealth English), or Xs and Os (Canadian English, Canadian or Hiberno-English, Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid, one with Xs and the other with Os. A player wins when they mark all three spaces of a row, column, or diagonal of the grid, whereupon they traditionally draw a line through those three marks to indicate the win. It is a solved game, with a forced draw assuming Best response, best play from both players. Names In American English, the game is known as "tic-tac-toe". It may also be spelled "tick-tack-toe", "tick-tat-toe", or "tit-tat-toe". In Commonwealth English (particularly British English, British, South African English, South African, Indian English, Indian, Australian English, Australian, and New Zealand English), the game is known as "noughts and crosses", alternatively spelled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New Yorker
''The New Yorker'' is an American magazine featuring journalism, commentary, criticism, essays, fiction, satire, cartoons, and poetry. It was founded on February 21, 1925, by Harold Ross and his wife Jane Grant, a reporter for ''The New York Times''. Together with entrepreneur Raoul H. Fleischmann, they established the F-R Publishing Company and set up the magazine's first office in Manhattan. Ross remained the editor until his death in 1951, shaping the magazine's editorial tone and standards. ''The New Yorker''s fact-checking operation is widely recognized among journalists as one of its strengths. Although its reviews and events listings often focused on the Culture of New York City, cultural life of New York City, ''The New Yorker'' gained a reputation for publishing serious essays, long-form journalism, well-regarded fiction, and humor for a national and international audience, including work by writers such as Truman Capote, Vladimir Nabokov, and Alice Munro. In the late ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go Endgame
The game of Go has simple rules that can be learned very quickly but, as with chess and similar board games, complex strategies may be employed by experienced players. Go opening theory The whole board opening is called fuseki. An important principle to follow in early play is "corner, side, center." In other words, the corners are the easiest places to take territory, because two sides of the board can be used as boundaries. Once the corners are occupied, the next most valuable points are along the sides, aiming to use the edge as a territorial boundary. Capturing territory in the middle, where it must be surrounded on all four sides, is extremely difficult. The same is true for founding a living group: Easiest in the corner, most difficult in the center. The first moves are usually played on or near the 4-4 star points in the corners, because in those places it is easiest to gain territory or influence. In order to be totally secure alone, a corner stone must be placed on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'' is the peer review, peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' cover the full range of List of academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer-assisted Proof
Automation describes a wide range of technologies that reduce human intervention in processes, mainly by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines. Automation has been achieved by various means including mechanical, hydraulic, pneumatic, electrical, electronic devices, and computers, usually in combination. Complicated systems, such as modern factories, airplanes, and ships typically use combinations of all of these techniques. The benefit of automation includes labor savings, reducing waste, savings in electricity costs, savings in material costs, and improvements to quality, accuracy, and precision. Automation includes the use of various equipment and control systems such as machinery, processes in factories, boilers, and heat-treating ovens, switching on telephone networks, steering, stabilization of ships, aircraft and other applications and vehicles with reduced human ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solved Game
A solved game is a game whose outcome (win, lose or tie (draw), draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance. Overview A two-player game can be solved on several levels: Ultra-weak solution : Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides . This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any details of the perfect play. Weak solution : Provide one algorithm for each of the two players, such that the player using it can achieve at least the optimal outcome, regardless of the opponent's moves, from the start of the game, using reasonable computational resources. Strong solution : Provide an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Checkers
Checkers (American English), also known as draughts (; English in the Commonwealth of Nations, Commonwealth English), is a group of Abstract strategy game, strategy board games for two players which involve forward movements of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers is developed from alquerque. The term "checkers" derives from the Check (pattern), checkered board which the game is played on, whereas "draughts" derives from the verb "to draw" or "to move". The most popular forms of checkers in Anglophone countries are American checkers (also called English draughts), which is played on an 8×8 checkerboard; Russian draughts, Turkish draughts and Armenian draughts, all of them on an 8×8 board; and international draughts, played on a 10×10 board – with the latter widely played in many countries worldwide. There are many other variants played on 8×8 boards. Canadian checkers and Malaysian/Singaporean checkers (also locally known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solved Game
A solved game is a game whose outcome (win, lose or tie (draw), draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance. Overview A two-player game can be solved on several levels: Ultra-weak solution : Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides . This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any details of the perfect play. Weak solution : Provide one algorithm for each of the two players, such that the player using it can achieve at least the optimal outcome, regardless of the opponent's moves, from the start of the game, using reasonable computational resources. Strong solution : Provide an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
