The World As A Mathematical Game

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The World As A Mathematical Game

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Author : Giorgio Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-24

The World As A Mathematical Game written by Giorgio Israel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-24 with Science categories.

Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his boundless mathematical capacity, von Neumann developed a conception of the world as a mathematical game, a world globally governed by a universal logic in which individual consciousness moved following different strategies: his vision guided him from set theory to quantum mechanics, to economics and to his theory of automata (anticipating artificial intelligence and cognitive science). This book provides the first comprehensive scientific and intellectual biography of John von Neumann, a man who perhaps more than any other is representative of twentieth century science.

Mathematical Game Theory

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Author : Ulrich Faigle
language : en
Publisher: World Scientific
Release Date : 2022-02-25

Mathematical Game Theory written by Ulrich Faigle and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-25 with Mathematics categories.

What is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly 'rational' human behavior in search of appropriate 'winning strategies'. This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate 'actively' when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.

Number Games Around The World Navigators Grade 4

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Author : Marc Gave
language : en
Publisher:
Release Date : 2002

Number Games Around The World Navigators Grade 4 written by Marc Gave and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Games categories.

Presents the history of games and other activities, based on mathematical concepts, from different countries and cultures.

Around The World In Eighty Games

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Author : Marcus du Sautoy
language : en
Publisher: Basic Books
Release Date : 2023-11-07

Around The World In Eighty Games written by Marcus du Sautoy and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-07 with Mathematics categories.

A “fun” and “unexpected” (The Economist) global tour of the world’s greatest games and the mathematics that underlies them Where should you move first in Connect 4? What is the best property in Monopoly? And how can pi help you win rock paper scissors? Spanning millennia, oceans and continents, countries and cultures, Around the World in Eighty Games gleefully explores how mathematics and games have always been deeply intertwined. Renowned mathematician Marcus du Sautoy investigates how games provided the first opportunities for deep mathematical insight into the world, how understanding math can help us play games better, and how both math and games are integral to human psychology and culture. For as long as there have been people, there have been games, and for nearly as long, we have been exploring and discovering mathematics. A grand adventure, Around the World in Eighty Games teaches us not just how games are won, but how they, and their math, shape who we are.

Around The World In 80 Games A Mathematician Unlocks The Secrets Of The Greatest Games

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Author : Marcus du Sautoy
language : en
Publisher: HarperCollins UK
Release Date : 2023-10-12

Around The World In 80 Games A Mathematician Unlocks The Secrets Of The Greatest Games written by Marcus du Sautoy and has been published by HarperCollins UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-12 with Mathematics categories.

An award-winning mathematician explores the maths behind the games we love and why we love to play them. Where should you move first in Connect 4? What is the best property in Monopoly? And how can pi help you win rock paper scissors?

Board Games Round The World

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Author : Robert Charles Bell
language : en
Publisher:
Release Date : 1988

Board Games Round The World written by Robert Charles Bell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Board games categories.

The Language Of Game Theory

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Author : Adam Brandenburger
language : en
Publisher: World Scientific
Release Date : 2014-03-12

The Language Of Game Theory written by Adam Brandenburger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Mathematics categories.

This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program — now called epistemic game theory — extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Contents:An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler)Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel)Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel)Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg)Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger)Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel)Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler)Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg) Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience. Keywords:Game Theory;Epistemic Game Theory;Foundations;Applied Mathematics;Social Neuroscience;Rationalizability;Nash Equilibrium;Probability;UncertaintyKey Features:Focuses on epistemic game theory — an emerging approach to game theoryLikely strong interest in these tools from other disciplines, includingtheoretical computer science, mathematical logic, and social neuroscienceProminent co-author team: Robert Aumann (Hebrew University, Nobel Laureate 2005); Lawrence Blume (Cornell University); Eddie Dekel (Northwestern University and Tel Aviv University); Amanda Freedeneurg (Arizona State University); H Jerome Keisler (University of Wisconsin Madison)Reviews: "Adam Brandenburger's work on the knowledge requirements implicit in game theory has become classic. These are of profound importance in understanding the relevance of game theory and, indeed, economic theory in general to the real economy. It is very good to have them collected, with an introduction that brings out the underlying themes." Kenneth J Arrow Stanford University, USA "Over the past decade epistemic game theory has emerged as one of the principled alternatives to more traditional approaches to economic interactions and Adam Brandenburger has played a central role in that emergence. For anyone interested in epistemic game theory, or game theory in general, this book is a must have. But even more important is the opportunity this volume, and epistemic game theory in general, presents to empirical scientists. As Brandenburger notes in his Introduction, until now epistemic game theory has been a theoretical discipline. This volume should make it clear, however, that it could be — and likely soon will be — an empirical undertaking. Anyone interested in behavioral, psychological, or neurobiological studies of how we make decisions during strategic play will find in this volume a profoundly fascinating set of empirically testable hypotheses just waiting to be examined." Paul Glimcher New York University, USA "Three hundred years ago, Francis Waldegrave found the first minimax solution of a matrix game. But in his correspondence with mathematicians Pierre Rémond de Montmort and Nicolaus Bernoulli, Waldegrave counseled that epistemic considerations involving knowledge, beliefs, uncertainty, and incomplete information also mattered. The principal practitioners of game theory, with the notable exceptions of John Harsanyi and Robert Aumann, have ignored this advice. In recent years, these two theorists have been joined by Adam Brandenburger, whose work on epistemic game theory has been collected in this splendid volume. Eight classic papers by Brandenburger with a number of co-authors present an authoritative view of the field while an insightful introduction provides a roadmap to research both present and future." Harold W Kuhn Princeton University, USA "This book features a collection of foundational papers by Adam Brandenburger in epistemic game theory. Though still evolving, this approach marks a tectonic shift in game theory by offering a new, epistemic dimension which might be compared to the introduction of synchronized sound to motion pictures in the early 20th century: it might not immediately provide a complete picture, but it has the potential of changing the field forever." Sergei N Artemov The Graduate Center of the City University of New York, USA "Adam Brandenburger has played a leading role in developing the program of epistemic game theory, the goal of which is to provide a deeper and clearer foundation for game theory as a whole. This volume collects a remarkable body of work by Brandenburger and his collaborators, in which penetrating conceptual analysis and the development of a rich mathematical theory go hand in hand. The work offers much of great interest to computer scientists, who will see many connections with their study of recursive and corecursive structures, of processes and their logics, and of multi-agent systems; and to mathematicians and logicians interested in making precise models of the reflexive structures inherent in systems containing rational agents who can reason about the system of which they form a part. I hope that this timely collection will help to stimulate cross-disciplinary work on these fundamental topics." Samson Abramsky Oxford University, UK "Games are playgrounds where players meet and interact, guided by streams of information and opinion. Adam Brandenburger's work has been instrumental in creating a new rich epistemic framework doing justice to both games and their players. This timely book will help a broader audience learn and appreciate the resulting theory." Johan van Benthem University of Amsterdam, The Netherlands and Stanford University, USA "Economics, so grounded in the notion of equilibrium, has required substantial foundational work on reasoning about reasoning — epistemics — in interacting situations (games). Yet, if plain reasoning is difficult enough, just imagine epistemics. Adam Brandenburger, as is evident from the elegant and clear chapters of this book, is a master of the trade. His highly regarded research, always subtle and deep, is of the kind that establishes milestones while at the same time opening up vistas to new, and unexpected, frontiers. This book is specialized, certainly, but it is a must." Andreu Mas-Colell Universitat Pompeu Fabra, Spain “The papers in this book had a huge impact on the field, created an inter– and multi–discipliner research within the intersection of economics, philosophy, mathematics and computer science, and also inspired countless amount of PhD dissertations. Brandenburger's work contains very precise and beautiful mathematics, an earthly reading of epistemics and a puzzling innovation.” Zentralblatt MATH

Math Around The World

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Author : Beverly Braxton
language : en
Publisher: University of California, Berkeley, Lawrence Hall of Science
Release Date : 2000

Math Around The World written by Beverly Braxton and has been published by University of California, Berkeley, Lawrence Hall of Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Education categories.

A collection of eight games from four continents that use mathematics as students participate. The activities also provide opportunities for students to explore the geography and history connected to the games and broaden their awareness of other cultures.

Mathematical Games And How To Play Them

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Author : Steven Vajda
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01

Mathematical Games And How To Play Them written by Steven Vajda and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

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.

Number Games Around The World

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Author : Marc Gave
language : en
Publisher: Benchmark Education Company
Release Date : 2011

Number Games Around The World written by Marc Gave and has been published by Benchmark Education Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematical recreations categories.

A world history of games and other activities based on mathematical concepts.