Download or read book Game of Nim Graph Theory written by Rebecca Rapoport and published by Math Lab for Kids. This book was released on 2018-08 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math Lab for Kids proves that math is more than just numbers--the hands-on activities in this book make learning math fun! With Game of Nim and Graph Theory, kids learn winning strategies for Nim, a game first played in China more than 1,000 years ago, and explore the famous Bridges of Königsberg problem that spawned an entire field of mathematics. No expensive supplies are required! Everything needed to complete the activities are included or can be found around the house. Math Lab for Kids: Game of Nim and Graph Theory will give kids a great experience and a solid foundation in a subject that's more important than ever.
Download or read book Combinatorial Games on Graphs written by Trevor K. Williams and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games along with some educational tools were developed in the pursuit of the solution of these games. The game of Nim is at least centuries old, possibly originating in China, but noted in the 16th century in European countries. It consists of several stacks of tokens, and two players alternate taking one or more tokens from one of the stacks, and the player who cannot make a move loses. The formal and intense study of Nim culminated in the celebrated Sprague-Grundy Theorem, which is now one of the centerpieces in the theory of impartial combinatorial games. We study a variation on Nim, played on a graph. Graph Nim, for which the theory of Sprague-Grundy does not provide a clear strategy, was originally developed at the University of Colorado Denver. Graph Nim was first played on graphs of three vertices. The winning strategy, and losing position, of three vertex Graph Nim has been discovered, but we will expand the game to four vertices and develop the winning strategies for four vertex Graph Nim. Graph Theory is a markedly visual field of mathematics. It is extremely useful for graph theorists and students to visualize the graphs they are studying. There exists software to visualize and analyze graphs, such as SAGE, but it is often extremely difficult to learn how use such programs. The tools in GeoGebra make pretty graphs, but there is no automated way to make a graph or analyze a graph that has been built. Fortunately GeoGebra allows the use of JavaScript in the creation of buttons which allow us to build useful Graph Theory tools in GeoGebra. We will discuss two applets we have created that can be used to help students learn some of the basics of Graph Theory. The game of thrones is a two-player impartial combinatorial game played on an oriented complete graph (or tournament) named after the popular fantasy book and TV series. The game of thrones relies on a special type of vertex called a king. A king is a vertex, k, in a tournament, T, which for all x in T either k beats x or there exists a vertex y such that k beats y and y beats x. Players take turns removing vertices from a given tournament until there is only one king left in the resulting tournament. The winning player is the one which makes the final move. We develop a winning position and classify those tournaments that are optimal for the first or second-moving player.
Download or read book An Introduction to Combinatorial Game Theory written by L. R. Haff and published by . This book was released on 2016-06-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text to the area of mathematics known as Combinatorial Game Theory. Starting with Nim, a variety of combinatorial games are introduced as well as the tools to analyze them.
Download or read book Game Theory Alive written by Anna R. Karlin and published by American Mathematical Soc.. This book was released on 2017-04-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.
Download or read book Games of No Chance 3 written by Michael H. Albert and published by Cambridge University Press. This book was released on 2009-05-29 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.
Download or read book Games of No Chance 4 written by Richard J. Nowakowski and published by Cambridge University Press. This book was released on 2015-04-16 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial games are the strategy games that people like to play, for example chess, Hex, and Go. They differ from economic games in that there are two players who play alternately with no hidden cards and no dice. These games have a mathematical structure that allows players to analyse them in the abstract. Games of No Chance 4 contains the first comprehensive explorations of misère (last player to move loses) games, extends the theory for some classes of normal-play (last player to move wins) games and extends the analysis for some specific games. It includes a tutorial for the very successful approach to analysing misère impartial games and the first attempt at using it for misère partisan games. Hex and Go are featured, as well as new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.
Download or read book Combinatorial Game Theory written by Richard J. Nowakowski and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-08-22 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elwyn Berlekamp, John Conway, and Richard Guy wrote ‘Winning Ways for your Mathematical Plays’ and turned a recreational mathematics topic into a full mathematical fi eld. They combined set theory, combinatorics, codes, algorithms, and a smattering of other fi elds, leavened with a liberal dose of humor and wit. Their legacy is a lively fi eld of study that still produces many surprises. Despite being experts in other areas of mathematics, in the 50 years since its publication, they also mentored, talked, and played games, giving their time, expertise, and guidance to several generations of mathematicians. This volume is dedicated to Elwyn Berlekamp, John Conway, and Richard Guy. It includes 20 contributions from colleagues that refl ect on their work in combinatorial game theory.
Download or read book The Theory of Graphs written by Claude Berge and published by Courier Corporation. This book was released on 2001-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise, well-written text illustrates development of graph theory and application of its principles in methods both formal and abstract. Practical examples explain theory's broad range, from behavioral sciences, information theory, cybernetics, and other areas, to mathematical disciplines such as set and matrix theory. 1966 edition. Includes 109 black-and-white illustrations.
Download or read book Lessons in Play written by Michael Albert and published by CRC Press. This book was released on 2007-07-02 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial games are games of pure strategy involving two players, with perfect information and no element of chance. Starting from the very basics of gameplay and strategy, the authors cover a wide range of topics, from game algebra to special classes of games. Classic techniques are introduced and applied in novel ways to analyze both old and
Download or read book Matt DeVos and Deborah A Kent written by Matt DeVos and published by American Mathematical Soc.. This book was released on 2016-12-27 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. Designed as a textbook for an undergraduate mathematics class and with ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.
Download or read book The Game of Nim on Graphs written by Lindsay Anne Erickson and published by . This book was released on 2011 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Numbers and Games written by John H. Conway and published by CRC Press. This book was released on 2000-12-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class that includes both real numbers and ordinal numbers: surreal numbers. The second edition presents developments in mathematical game theory, focusing on surreal numbers and the additive theory of partizan games.
Download or read book Mathematical Games and How to Play Them written by Steven Vajda and published by Courier Corporation. This book was released on 2008-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This refreshingly authoritative look at recreational mathematics illustrates winning strategies that use the methods of algebra, geometry, combinatorics, number theory, graph theory, and other branches of mathematics. Its lucid analyses of the rules and theories of mathematical games include skill-enhancing exercises, plus references, appendixes, and detailed explanations. 1992 edition.
Download or read book Introducing Game Theory and its Applications written by Elliott Mendelson and published by CRC Press. This book was released on 2016-02-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical study of games is an intriguing endeavor with implications and applications that reach far beyond tic-tac-toe, chess, and poker to economics, business, and even biology and politics. Most texts on the subject, however, are written at the graduate level for those with strong mathematics, economics, or business backgrounds. In
Download or read book Graph Theory with Applications to Engineering and Computer Science written by Narsingh Deo and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outstanding introductory treatment, geared toward advanced undergraduates and graduate students who require knowledge of graph theory. The first nine chapters constitute an excellent overview; the remaining chapters are more advanced and provide material for a variety of courses. 1974 edition.
Download or read book The Dots and Boxes Game written by Elwyn R. Berlekamp and published by CRC Press. This book was released on 2000-07-18 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The game of Dots-and-Boxes, the popular game in which two players take turns connecting an array of dots to form squares, or boxes has long been considered merely a child's game. In this book, however, the author reveals the surprising complexity of the game, along with advanced strategies that will allow the reader to win at any level of gamepla
Download or read book A Course In Game Theory written by Thomas S Ferguson and published by World Scientific. This book was released on 2020-07-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory is a fascinating subject. We all know many entertaining games, such as chess, poker, tic-tac-toe, bridge, baseball, computer games — the list is quite varied and almost endless. In addition, there is a vast area of economic games, discussed in Myerson (1991) and Kreps (1990), and the related political games [Ordeshook (1986), Shubik (1982), and Taylor (1995)]. The competition between firms, the conflict between management and labor, the fight to get bills through congress, the power of the judiciary, war and peace negotiations between countries, and so on, all provide examples of games in action. There are also psychological games played on a personal level, where the weapons are words, and the payoffs are good or bad feelings [Berne (1964)]. There are biological games, the competition between species, where natural selection can be modeled as a game played between genes [Smith (1982)]. There is a connection between game theory and the mathematical areas of logic and computer science. One may view theoretical statistics as a two-person game in which nature takes the role of one of the players, as in Blackwell and Girshick (1954) and Ferguson (1968).Games are characterized by a number of players or decision makers who interact, possibly threaten each other and form coalitions, take actions under uncertain conditions, and finally receive some benefit or reward or possibly some punishment or monetary loss. In this text, we present various mathematical models of games and study the phenomena that arise. In some cases, we will be able to suggest what courses of action should be taken by the players. In others, we hope simply to be able to understand what is happening in order to make better predictions about the future.
