Preface to the First

Edition

Ramsey Theory on the Integers covers a variety of topics from the

field of Ramsey theory, limiting its focus to the set of integers – an

area that has seen a remarkable burst of research activity during the

past twenty years.

The book has two primary purposes: (1) to provide students with

a gentle, but meaningful, introduction to mathematical research – to

give them an appreciation for the essence of mathematical research

and its inescapable allure and also to get them started on their own

research work; (2) to be a resource for all mathematicians who are

interested in combinatorial or number theoretical problems, particu-

larly “Erd˝ os-type” problems.

Many results in Ramsey theory sound rather complicated and

can be hard to follow; they tend to have a lot of quantifiers and may

well involve objects whose elements are sets whose elements are sets

(that is not a misprint). However, when the objects under consider-

ation are sets of integers, the situation is much simpler. The student

need not be intimidated by the words “Ramsey theory,” thinking that

the subject matter is too deep or complex – it is not! The material

in this book is, in fact, quite accessible. This accessibility, together

with the fact that scores of questions in the subject are still to be

answered, makes Ramsey theory on the integers an ideal subject for

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