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Book
Tic tac toe and other three-in-a-row games from ancient Egypt to the modern computer
Authors: ---
ISBN: 0690043163 Year: 1982 Publisher: New York (N.Y.): Crowell

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Abstract

Traces the history and development of the three-in-a-row game for two players, popular all over the world, that is similar to games played in ancient Egypt.


Book
The mathematics of various entertaining subjects : research in recreational math
Authors: --- ---
ISBN: 1400881331 9781400881338 Year: 2015 Publisher: Princeton, NJ : Princeton University Press,

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The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more. Looking at a plethora of eclectic games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

Keywords

Mathematical recreations. --- Mathematical recreations --- Research. --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education --- Mathematics. --- Mathematic --- Amazing Asteroid. --- Atoll. --- Begird. --- Bernstein's Bijection. --- Chromatic Combat. --- Cookie Monster number. --- Cookie Monster. --- Devious Dice. --- Eluding Execution. --- EndGame. --- Fibonacci sequence. --- Flipping Fun. --- Flush. --- Full House. --- Get the Giraffe. --- Gilbreath numbers. --- Gilbreath permutations. --- Graeco-Latin squares. --- Hamming weight. --- Heartless Poker. --- Hex. --- Knop's puzzle. --- Leonhard Euler. --- Norman Gilbreath. --- SET. --- Sperner's Lemma. --- Straight. --- Super-n-nacci sequence. --- The Game of Y. --- The New York Times. --- Tower of Hanoi. --- Traveling Salesman Problem. --- Tribonacci sequence. --- Zeckendorf representation. --- advanced mathematics. --- affine plane. --- affine planes. --- algorithms. --- baseball. --- card effects. --- card games. --- card moves. --- card tricks. --- chess. --- coding theory. --- coin-weighing puzzles. --- connection games. --- continued fractions. --- cookies. --- coupling. --- crossword networks. --- crossword puzzle difficulty. --- crossword puzzles. --- decomposition. --- delta-to-wye transformation. --- dissection puzzles. --- divination puzzles. --- dualism. --- electrical power distribution. --- epidemics. --- error correction. --- error detection. --- error-correcting codes. --- find-and-label problem. --- flexagons. --- folding puzzles. --- game-theoretic perspective. --- generalizations. --- generator assignment. --- graphical objects. --- group structures. --- ice cream trick. --- infinite families. --- iterative stochastic process. --- just-find problem. --- linear code. --- magic tricks. --- mathematical exhibits. --- mathematical puzzles. --- maze design. --- mazes. --- minimum spanning tree. --- multiple-pans problem. --- museums. --- n-nacci sequence. --- network properties. --- network structure. --- one-move puzzles. --- packing puzzles. --- parallel scales. --- parallel weighing problem. --- period-four move. --- period-four principles. --- phyllotactic mazes. --- playing cards. --- poker. --- probability. --- random graph process. --- random moves. --- random walks. --- rearrangement puzzles. --- recreational mathematics. --- recreational problems. --- seeded stippling. --- simple objects. --- simplex. --- squash. --- surreal numbers. --- symmetries. --- tetraflexagons. --- tic-tac-toe. --- unique solutions. --- vortex tiles. --- weighing puzzles. --- winning strategies.


Book
Noncooperative game theory : an introduction for engineers and computer scientists
Author:
Year: 2017 Publisher: Princeton, NJ : Princeton University Press,

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Noncooperative Game Theory is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. João Hespanha shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to "the game" solve the original design problem? Using the fundamentals of game theory, Hespanha explores these issues and more.The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria-such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, Hespanha examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty-the unforgiving variable that can wreck engineering designs. Hespanha looks at such standard topics as zero-sum, non-zero-sum, and dynamics games and includes a MATLAB guide to coding.Noncooperative Game Theory offers students a fresh way of approaching engineering and computer science applications.An introduction to game theory applications for students of engineering and computer science Materials presented sequentially and in an easy-to-understand fashionTopics explore zero-sum, non-zero-sum, and dynamics gamesMATLAB commands are included

Keywords

Noncooperative games (Mathematics) --- Game theory --- Cooperative games (Mathematics) --- MATLAB. --- Minimax Theorem. --- N-player game. --- Nash equilibrium. --- Separating Hyperplane Theorem. --- Sudoku puzzle. --- action space. --- action. --- admissible Nash equilibrium. --- advertising campaign. --- alternate play. --- average security level. --- battle of the sexes. --- behavioral policy. --- behavioral saddle-point equilibrium. --- best-response equivalent games. --- bilateral symmetric game. --- bimatrix game. --- bimatrix potential. --- chicken game. --- circuit design. --- completely mixed Nash equilibrium. --- computational complexity. --- computer science. --- congestion game. --- continuous time cost-to-go. --- continuous time differential. --- continuous time dynamic programming. --- continuous time dynamic. --- convex analysis. --- convex hull. --- decoupled game. --- design methodology. --- differential game. --- discrete time cost-to-go. --- discrete time dynamic programming. --- discrete time dynamic. --- distributed resource allocation. --- dummy game. --- dynamic game. --- engineering. --- extensive form game representation. --- feedback game. --- fictitious play. --- finite one-player. --- game theory. --- graphical method. --- hyperplane. --- identical interests. --- information structure. --- linear program. --- linear quadratic dynamic. --- minimum. --- mixed Nash equilibrium. --- mixed action space. --- mixed policy. --- mixed saddle-point equilibrium. --- mixed security policy. --- multi-stage game. --- network routing. --- non-feedback game. --- non-zero-sum. --- noncooperative game theory. --- open-loop policy. --- open-loop. --- optimization-based design. --- order interchangeability property. --- policy. --- potential game. --- probability distribution. --- pure N-player game. --- pure policy. --- recursive computation. --- regret. --- robust design. --- rock-paper-scissors. --- rope-pulling. --- saddle-point equilibrium. --- security level. --- security policy. --- simultaneous play. --- single-stage game. --- state feedback information structure. --- state-feedback policy. --- stochastic policy. --- strictly dominating policy. --- symmetry game. --- tic-tac-toe. --- tree structure. --- uncertainty. --- variable termination time. --- war of attrition. --- weakly dominating policy. --- zebra in the lake. --- zero sum dynamic. --- zero-sum matrix. --- zero-sum two-person. --- zero-sum.

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