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Lessons in Play

  • Livre Relié
  • 344 Nombre de pages
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"The wisdom and joy outshining from this 2nd edition, beat even the original. The helpful preludes for student and instructor, pre... Lire la suite
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"The wisdom and joy outshining from this 2nd edition, beat even the original. The helpful preludes for student and instructor, prefacing each chapter, have elevated subtly in additional reader-friendliness; new subsections and a new case study were added. An interesting new Chapter 10 trades complex yet complete computation of a game's strategy, with a simplified slightly approximate winning strategy. The last chapter, which awards the reader with a flavor of cutting edge research, was updated with a section on scoring games. The book is a must for novice and expert alike." -Aviezri Fraenkel, Weizmann Institute of Science, Israel

Michael Albert - University of Otago Richard Nowakowski - Dalhousie University David Wolfe - Dalhousie University

This second edition of Lessons in Play reorganizes the presentation of the popular original text in combinatorial game theory to make it even more widely accessible. Starting with a focus on the essential concepts and applications, it then moves on to more technical material. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more detail and abstract results. Features Employs a widely accessible style to the explanation of combinatorial game theory Contains multiple case studies Expands further directions and applications of the field Includes a complete rewrite of CGSuite material

Combinatorial Games 0.1 Basic Terminology Problems 1 Basic Techniques 1.1 Greedy 1.2 Symmetry 1.3 Parity 1.4 Give Them Enough Rope! 1.5 Strategy Stealing 1.6 Change the Game! 1.7 Case Study: Long Chains in Dots & Boxes Problems 2 Outcome Classes 2.1 Outcome Functions 2.2 Game Positions and Options 2.3 Impartial Games: Minding Your Ps and Ns 2.4 Case Study: Roll The Lawn 2.5 Case Study: Timber 2.6 Case Study: Partizan Endnim Problems 3 Motivational Interlude: Sums of Games 3.1 Sums 3.2 Comparisons 3.3 Equality and Identity 3.4 Case Study: Domineering Rectangles Problems 4 The Algebra of Games 4.1 The Fundamental Definitions 4.2 Games Form a Group with a Partial Order 4.3 Canonical Form 4.4 Case Study: Cricket Pitch 4.5 Incentives Problems 5 Values of Games 5.1 Numbers 5.2 Case Study: Shove 5.3 Stops 5.4 A Few All-Smalls: Up, Down, and Stars 5.5 Switches 5.6 Case Study: Elephants & Rhinos 5.7 Tiny and Miny 5.8 Toppling Dominoes 5.9 Proofs of Equivalence of Games and Numbers Problems 6 Structure 6.1 Games Born by Day 2 6.2 Extremal Games Born By Day n 6.3 More About Numbers 6.4 The Distributive Lattice of Games Born by Day n 6.5 Group Structure Problems 7 Impartial Games 7.1 A Star-Studded Game 7.2 The Analysis of Nim 7.3 Adding Stars 7.4 A More Succinct Notation 7.5 Taking-and-Breaking Games 7.6 Subtraction Games 7.7 Keypad Games Problems 8 Hot Games 8.1 Comparing Games and Numbers 8.2 Coping with Confusion 8.3 Cooling Things Down 8.4 Strategies for Playing Hot Games 8.5 Norton Products Problems 9 All-Small Games 9.1 Cast of Characters 9.2 Motivation: The Scale of Ups 9.3 Equivalence Under 9.4 Atomic Weight 9.5 All-Small Shove 9.6 More Toppling Dominoes 9.7 Clobber Problems 10 Trimming Game Trees 10.1 Introduction 10.2 Reduced Canonical Form 10.3 Hereditary-Transitive Games 10.4 Ordinal Sum 10.5 Stirling-Shave 10.6 Even More Toppling Dominoes Problems Further Directions 1 Transfinite Games 2 Algorithms and Complexity 3 Loopy Games 4 Kos: Repeated Local Positions 5 Top-Down Thermography 6 Enriched Environments 7 Idempotents 8 Mis`ere Play 9 Scoring Games A Top-Down Induction A.1 Top-Down Induction A.2 Examples A.3 Why is Top-Down Induction Better? A.4 Strengthening the Induction Hypothesis A.5 Inductive Reasoning Problems B CGSuite B.1 Installing CGSuite B.2 Worksheet Basics B.3 Programming in CGSuite's Language C Solutions to Exercises D Rulesets

Informations sur le produit

Titre: Lessons in Play
Code EAN: 9781482243031
ISBN: 978-1-4822-4303-1
Format: Livre Relié
Editeur: Taylor and Francis
Genre: Mathématique
nombre de pages: 344
Poids: 671g
Taille: H235mm x B156mm
Année: 2019
Auflage: 2. A.