Asymptopia
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the landscape for every mathematician. The objective of this book is to
present the ideas of how to approach asymptotic problems that arise in
discrete mathematics, analysis of algorithms, and number theory. A
broad range of topics is covered, including distribution of prime
integers, Erdős Magic, random graphs, Ramsey numbers, and asymptotic
geometry.
The author is a disciple of Paul Erdős, who taught him about Asymptopia. Primes less than , graphs with
vertices, random walks of
steps--Erdős was fascinated by the limiting behavior as the variables
approached, but never reached, infinity. Asymptotics is very much an
art. The various functions ,
,
,
,
all have distinct personalities. Erdős knew these functions as
personal friends. It is the author's hope that these insights may be
passed on, that the reader may similarly feel which function has the
right temperament for a given task. This book is aimed at strong
undergraduates, though it is also suitable for particularly good high
school students or for graduates wanting to learn some basic
techniques.
Asymptopia is a beautiful world. Enjoy!
