Lessons in Play
An Introduction to Combinatorial Game Theory, Second Edition
by Michael Albert, Richard Nowakowski, David Wolfe
2nd Edition
Publisher: A K Peters/CRC Press (T&F)
Book Details
| Print ISBN | 9781482243031 |
| eText ISBN | 9780429537561 |
| Publisher | A K Peters/CRC Press (T&F) |
| Publishing Year | 2019 |
| Edition | 2nd Edition |
| Language | English |
| Pages | 346 |
Lessons in Play: An Introduction to Combinatorial Game Theory, Second Edition, 2nd Edition, presents the mathematical analysis of games through foundational principles and concrete applications. The 2019 edition reorganizes the original text to make its core ideas accessible to students and instructors.
Coverage introduces fundamental strategies, outcome classes, sums of games, and algebraic frameworks where games form a group with a partial order. The textbook also explores impartial games such as Nim, hot games requiring cooling methods, and all-small games.
Structured with mathematical proofs, exercises, and illustrative examples, the work employs a two-step pedagogical approach that establishes basic results before proceeding to deeper abstract theory.
Table of Contents
Chapter 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
Chapter 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
Chapter 3: Motivational Interlude: Sums of Games
- • 3.1 Sums
- • 3.2 Comparisons
- • 3.3 Equality and Identity
- • 3.4 Case Study: Domineering Rectangles
- • Problems
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter A: Top-Down Induction
- • A.1 Top-Down Induction
- • A.2 Examples
Customer Reviews
0.0
0 reviews
No reviews yet. Be the first to review this book!
Write a Review
Reviewed by GradeFocus Editorial Team
