Asymptotics in one form or another are part of 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, Erdos Magic, random graphs, Ramsey numbers, and
asymptotic geometry. The author is a disciple of Paul Erdos, who
taught him about Asymptopia. Primes less than n , graphs with v
vertices, random walks of t steps - Erdos was fascinated by the
limiting behavior as the variables approached, but never reached,
infinity. Asymptotics is very much an art. The various functions
nlnn , n 2 , lnn n , lnn ? ? ? ? , 1 nlnn all have distinct
personalities. Erdos 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!
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