Hardback
ISBN 9781032213613
Paperback
ISBN 9781032213057
134 Pages 165 Color Illustrations
December 14, 2023 by A K Peters/CRC Press
Mathematicians Playing Games explores a wide variety of popular mathematical games, including their historical beginnings and the mathematical theories that underpin them. Its academic level is suitable for high school students and higher, but people of any age or level will find something to entertain them, and something new to learn. It would be a fantastic resource for high school mathematics classrooms or undergraduate mathematics for liberal arts course, and belongs on the shelf of anyone with an interest in recreational mathematics.
Suitable for anyone with an interest in games and mathematics. Could be especially useful to middle and high school students and their teachers
Includes various exercises for fun for readers.
1. 15 Puzzle: A Tile Matching Game That Is Difficult Even for Computers.
2. Peg Solitaire: Jumping Game Where We Meet Algebra.
3. Chomp Game: Avoid a Poisoned Chocolate.
4. Super Tic-Tac-Toe: Five Stone Game over a Donut.
5. Mastermind: A Cryptographic Game.
6. Ramsey Theorem and Sim Game: Don’t Draw a Red Triangle.
7. Nine Men’s Morris: Three Soldiers' Side by Side.
8. The Game of Quatrainment: Flip Neighbor Stones.
9. n-Queens Game and Puzzle: Playing Chess Only with Queens.
10. Light Out: Turn Off Lights by Linear Equations.
11. 1258 Board Game: Magic Square and Orthogonal Latin Square.
12. Switching Game: Shannon’s Network Game.
13. Dots and Boxes: Occupy More Boxes.
14. Matricking: Factorization and Cube Net Game.
15. SET Game: Steiner Triple System Game.
16. Dobble Game: Finite Projective Plane Game.
17. Find-a-Best-Friend Game: A Game of the Perfect Hamming Code.
Softcover
Softcover ISBN: 978-1-4704-7553-6
Product Code: SURV/40.10
Mathematical Surveys and Monographs Volume: 40;
2023; 570 pp
MSC: Primary 20;
This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see Mathematical Surveys and Monographs, Volume 40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.
Graduate students and researchers interested in the theory of finite groups.
General group-theoretic lemmas
Theorem C6
and C?6
Theorems C4
and C?4
: Introduction
Theorem C?4
: Stage A1. First steps
Theorem C?4
: Stage A2. Nonconstrained p
-rank 3 centralizers
Theorem C?4
: Stage A3. KM
-singularities
Theorem C?4
: Stage A4. Setups for recognizing G
Theorem C?4
: Stage A5. Recognition
Properties of K
-groups
Hardcover ISBN: 978-1-4704-6796-8
Product Code: GSM/238
Expected availability date: December 26, 2023
Graduate Studies in Mathematics Volume: 238;
2023; 415 pp
MSC: Primary 91;
Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises.
The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented.
In this second edition, the content on cooperative games is considerably strengthened, with a new chapter on applications of cooperative games and operations research, including some material on computational aspects and applications outside academia.
This book is published in cooperation with Real Sociedad Matematica Espanola.
Graduate students and researchers interested in game theory.
Introduction to decision theory
Strategic games
Extensive games
Games with incomplete information
Fundamentals of cooperative games
Applications of cooperative games
Softcover ISBN: 978-1-4704-7210-8
Product Code: ULECT/78
University Lecture Series Volume: 78;
2023; 165 pp
MSC: Primary 03;
Description
This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system AD+
and presents his initial analysis of these axioms. These results include the consistency of AD+
from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, AD+
, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of AD+
is an active area of contemporary research in set theory.
The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
Graduate students and researchers interested in logic.
Preliminaries
Determinacy
The Wadge hierarchy
Coding lemmas
Properties of pointclasses
Strong partition cardinals
Suslin sets and uniformization
AD+
Ordinal determinacy
Infinity-Borel sets
Cone measure ultraproducts
Vop?nka algebras
Suslin sets and strong codes
Scales from uniformization
Real determinacy from scales
Questions
Hardcover ISBN: 978-1-4704-6796-8
Product Code: GSM/238
Expected availability date: December 26, 2023
Graduate Studies in Mathematics Volume: 238;
2023; 415 pp
MSC: Primary 91;
Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises.
The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented.
In this second edition, the content on cooperative games is considerably strengthened, with a new chapter on applications of cooperative games and operations research, including some material on computational aspects and applications outside academia.
This book is published in cooperation with Real Sociedad Matematica Espanola.
Graduate students and researchers interested in game theory.
Introduction to decision theory
Strategic games
Extensive games
Games with incomplete information
Fundamentals of cooperative games
Applications of cooperative games
Softcover ISBN: 978-1-4704-6010-5
Expected availability date: January 20, 2024
MSRI Mathematical Circles Library Volume: 29;
2023
MSC: Primary 00; 05; 52; 60; 94; 97;
This book is a translation from Russian of Part III of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. Part I, Algebra (Mathematical Circles Library, Volume 25), and Part II, Geometry (Mathematical Circles Library, Volume 26), have been published in the same series.
The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover such topics in combinatorics as counting, graphs, constructions and invariants in combinatorics, games and algorithms, probabilistic aspects of combinatorics, and combinatorial geometry.
Definitions and/or references for material that is not standard in the school curriculum are included. To help students that might be unfamiliar with new material, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions.
The book is based on classes taught by the authors at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
High school students and their mentors and teachers.