ENGLISH

Lessons in play : an introduction to combinatorial game theory

By Richard J. Nowakowski; Michael H. Albert; David Wolfe

Book information

Year
2019
ISBN
9780429524097, 0429524099, 9780429537561, 0429537565
Language
english
Format
PDF
Filesize
8 MB (8061267 bytes)
Edition
Second
Pages
\346
Time added
2020-08-28 07:02:54

Description

Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface 0: 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 Case Study: 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 8.6 Domineering Snakes 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 Maze 10.5 Ordinal Sum 10.6 Stirling-Shave 10.7 Even More Toppling Dominoes Problems ω: Further Directions ω.1 Transfinite Games ω.2 Algorithms and Complexity ω.3 Loopy Games ω.4 Kos: Repeated Local Positions ω.5 Top-Down Thermography ω.6 Enriched Environments ω.7 Idempotents ω.8 Misère Play ω.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 Bibliography Index

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