Preface to the First
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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