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Elwyn Berlekamp, John Conway, and Richard Guy wrote 'Winning Ways
for your Mathematical Plays' and turned a recreational mathematics
topic into a full mathematical fi eld. They combined set theory,
combinatorics, codes, algorithms, and a smattering of other fi
elds, leavened with a liberal dose of humor and wit. Their legacy
is a lively fi eld of study that still produces many surprises.
Despite being experts in other areas of mathematics, in the 50
years since its publication, they also mentored, talked, and played
games, giving their time, expertise, and guidance to several
generations of mathematicians. This volume is dedicated to Elwyn
Berlekamp, John Conway, and Richard Guy. It includes 20
contributions from colleagues that refl ect on their work in
combinatorial game theory.
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Combinatorial Number Theory - Proceedings of the 'Integers Conference 2007', Carrollton, Georgia, USA, October 24-27, 2007 (Hardcover)
Bruce Landman, Melvyn B Nathanson, Jaroslav Nesetril, Richard J. Nowakowski, Carl Pomerance, …
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R9,852
Discovery Miles 98 520
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Ships in 10 - 15 working days
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This volume contains selected refereed papers based on lectures
presented at the 'Integers Conference 2007', an international
conference in combinatorial number theory that was held in
Carrollton, Georgia in October 2007. The proceedings include
contributions from many distinguished speakers, including George
Andrews, Neil Hindman, Florian Luca, Carl Pomerance, Ken Ono and
Igor E. Shparlinski. Among the topics considered in these papers
are additive number theory, multiplicative number theory,
sequences, elementary number theory, theory of partitions, and
Ramsey theory.
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Combinatorial Number Theory - Proceedings of the 'Integers Conference 2005' in Celebration of the 70th Birthday of Ronald Graham, Carrollton, Georgia, October 27-30, 2005 (Hardcover, Reprint 2012)
Bruce Landman, Melvyn B Nathanson, Jaroslav Nesetril, Richard J. Nowakowski, Carl Pomerance
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R8,137
Discovery Miles 81 370
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Ships in 10 - 15 working days
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This carefully edited volume contains selected refereed papers
based on lectures presented by many distinguished speakers at the
"Integers Conference 2005," an international conference in
combinatorial number theory. The conference was held in celebration
of the 70th birthday of Ronald Graham, a leader in several fields
of mathematics.
This book is the first and only one of its kind on the topic of
Cops and Robbers games, and more generally, on the field of vertex
pursuit games on graphs. The book is written in a lively and highly
readable fashion, which should appeal to both senior undergraduates
and experts in the field (and everyone in between). One of the main
goals of the book is to bring together the key results in the
field; as such, it presents structural, probabilistic, and
algorithmic results on Cops and Robbers games. Several recent and
new results are discussed, along with a comprehensive set of
references. The book is suitable for self-study or as a textbook,
owing in part to the over 200 exercises. The reader will gain
insight into all the main directions of research in the field and
will be exposed to a number of open problems.
Combinatorial games are the strategy games that people like to
play, for example chess, Hex, and Go. They differ from economic
games in that there are two players who play alternately with no
hidden cards and no dice. These games have a mathematical structure
that allows players to analyse them in the abstract. Games of No
Chance 4 contains the first comprehensive explorations of misere
(last player to move loses) games, extends the theory for some
classes of normal-play (last player to move wins) games and extends
the analysis for some specific games. It includes a tutorial for
the very successful approach to analysing misere impartial games
and the first attempt at using it for misere partisan games. Hex
and Go are featured, as well as new games: Toppling Dominoes and
Maze. Updated versions of Unsolved Problems in Combinatorial Game
Theory and the Combinatorial Games Bibliography complete the
volume.
This fascinating look at combinatorial games, that is, games not
involving chance or hidden information, offers updates on standard
games such as Go and Hex, on impartial games such as Chomp and
Wythoff's Nim, and on aspects of games with infinitesimal values,
plus analyses of the complexity of some games and puzzles and
surveys on algorithmic game theory, on playing to lose, and on
coping with cycles. The volume is rounded out with an up-to-date
bibliography by Fraenkel and, for readers eager to get their hands
dirty, a list of unsolved problems by Guy and Nowakowski.
Highlights include some of Siegel's groundbreaking work on loopy
games, the unveiling by Friedman and Landsberg of the use of
renormalization to give very intriguing results about Chomp, and
Nakamura's 'Counting Liberties in Capturing Races of Go'. Like its
predecessors, this book should be on the shelf of all serious games
enthusiasts.
Is Nine-Men's Morris, in the hands of perfect players, a win for white or for black--or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full anlaysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men's Morris and Pentominoes; and new theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.
Is Nine-Men's Morris, in the hands of perfect players, a win for white or for black--or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full anlaysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men's Morris and Pentominoes; and new theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.
This fascinating look at combinatorial games, that is, games not
involving chance or hidden information, offers updates on standard
games such as Go and Hex, on impartial games such as Chomp and
Wythoff's Nim, and on aspects of games with infinitesimal values,
plus analyses of the complexity of some games and puzzles and
surveys on algorithmic game theory, on playing to lose, and on
coping with cycles. The volume is rounded out with an up-to-date
bibliography by Fraenkel and, for readers eager to get their hands
dirty, a list of unsolved problems by Guy and Nowakowski.
Highlights include some of Siegel's groundbreaking work on loopy
games, the unveiling by Friedman and Landsberg of the use of
renormalization to give very intriguing results about Chomp, and
Nakamura's 'Counting Liberties in Capturing Races of Go'. Like its
predecessors, this book should be on the shelf of all serious games
enthusiasts.
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