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Fundamentals of Ramsey Theory (Hardcover)
Loot Price: R2,652
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Fundamentals of Ramsey Theory (Hardcover)
Series: Discrete Mathematics and Its Applications
Expected to ship within 12 - 17 working days
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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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