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Produktbild: Lessons in Play

Lessons in Play An Introduction to Combinatorial Game Theory, Second Edition

119,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

22.04.2019

Abbildungen

farbige, schwarzweisse Abbildungen

Verlag

Taylor and Francis

Seitenzahl

346

Maße (L/B/H)

23,9/15,7/2,3 cm

Gewicht

748 g

Auflage

2nd edition

Sprache

Englisch

ISBN

978-1-4822-4303-1

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

22.04.2019

Abbildungen

farbige, schwarzweisse Abbildungen

Verlag

Taylor and Francis

Seitenzahl

346

Maße (L/B/H)

23,9/15,7/2,3 cm

Gewicht

748 g

Auflage

2nd edition

Sprache

Englisch

ISBN

978-1-4822-4303-1

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Lessons in Play

  • 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