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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.
Over a career that spanned 60 years, Ronald L. Graham (known to all
as Ron) made significant contributions to the fields of discrete
mathematics, number theory, Ramsey theory, computational geometry,
juggling and magical mathematics, and many more. Ron also was a
mentor to generations of mathematicians, he gave countless talks
and helped bring mathematics to a wider audience, and he held
signifi cant leadership roles in the mathematical community. This
volume is dedicated to the life and memory of Ron Graham, and
includes 20-articles by leading scientists across a broad range of
subjects that refl ect some of the many areas in which Ron worked.
Ramsey theory is a fascinating topic. The author shares his view of
the topic in this contemporary overview of Ramsey theory. He
presents from several points of view, adding intuition and detailed
proofs, in an accessible manner unique among most books on the
topic. This book covers all of the main results in Ramsey theory
along with results that have not appeared in a book before. The
presentation is comprehensive and reader friendly. The book covers
integer, graph, and Euclidean Ramsey theory with many proofs being
combinatorial in nature. The author motivates topics and
discussion, rather than just a list of theorems and proofs. In
order to engage the reader, each chapter has a section of
exercises. This up-to-date book introduces the field of Ramsey
theory from several different viewpoints so that the reader can
decide which flavor of Ramsey theory best suits them. Additionally,
the book offers: A chapter providing different approaches to Ramsey
theory, e.g., using topological dynamics, ergodic systems, and
algebra in the Stone-Cech compactification of the integers. A
chapter on the probabilistic method since it is quite central to
Ramsey-type numbers. A unique chapter presenting some applications
of Ramsey theory. Exercises in every chapter The intended audience
consists of students and mathematicians desiring to learn about
Ramsey theory. An undergraduate degree in mathematics (or its
equivalent for advanced undergraduates) and a combinatorics course
is assumed. TABLE OF CONENTS Preface List of Figures List of Tables
Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey
Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey
Theory 6. The Probabilistic Method 7. Applications Bibliography
Index Biography Aaron Robertson received his Ph.D. in mathematics
from Temple University under the guidance of his advisor Doron
Zeilberger. Upon finishing his Ph.D. he started at Colgate
University in upstate New York where he is currently Professor of
Mathematics. He also serves as Associate Managing editor of the
journal Integers. After a brief detour into the world of
permutation patterns, he has focused most of his research on Ramsey
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.
From the nationally recognized Educational Theatre Association's
Thespian Playworks competition come four short scripts - all
created by high school-aged playwrights! Included in this volume
are: The Actuality of Henri by Jacob Sellars The Christian
Soothsayer by Aaron Robertson The Crib by Steve Rathje Houdini Will
Die by Sage Voorhees
Three brothers, from a privileged Spanish family, must face the
challenges of a political collapse among a diverse and hostile
climate. Will the challenge bring them together or drive them
apart?
Ramsey theory is the study of the structure of mathematical objects
that is preserved under partitions. In its full generality, Ramsey
theory is quite powerful, but can quickly become complicated. By
limiting the focus of this book to Ramsey theory applied to the set
of integers, the authors have produced a gentle, but meaningful,
introduction to an important and enticing branch of modern
mathematics. Ramsey Theory on the Integers offers students a
glimpse into the world of mathematical research and the opportunity
for them to begin pondering unsolved problems. For this new
edition, several sections have been added and others have been
significantly updated. Among the newly introduced topics are:
rainbow Ramsey theory, an "inequality" version of Schur's theorem,
monochromatic solutions of recurrence relations, Ramsey results
involving both sums and products, monochromatic sets avoiding
certain differences, Ramsey properties for polynomial progressions,
generalizations of the Erdos-Ginzberg-Ziv theorem, and the number
of arithmetic progressions under arbitrary colorings. Many new
results and proofs have been added, most of which were not known
when the first edition was published. Furthermore, the book's
tables, exercises, lists of open research problems, and
bibliography have all been significantly updated. This innovative
book also provides the first cohesive study of Ramsey theory on the
integers. It contains perhaps the most substantial account of
solved and unsolved problems in this blossoming subject. This
breakthrough book will engage students, teachers, and researchers
alike.
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