Spencer, Joel
Asymptopia - Providence American Mathematical Society 2014 - xiv, 183p. - Student Mathematical Library 71 .
Includes Bibliography (179-180) and Index
Chapter 0. An infinity of primes Chapter 1. Stirling's formula Chapter 2. Big Oh, little oh and all that Chapter 3. Integration in Asymptopia Chapter 4. From integrals to sums Chapter 5. Asymptotics of binomial coefficients $\binom $ Chapter 6. Unicyclic graphs Chapter 7. Ramsey numbers Chapter 8. Large deviations Chapter 9. Primes Chapter 10. Asymptotic geometry Chapter 11. Algorithms Chapter 12. Potpourri Chapter 13. Really Big Numbers!
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, 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 n
, graphs with v vertices, random walks of t steps—Erdős was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. 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.
9781470438432 (PB)
Combinatorial analysis
Number theory -- Elementary number theory -- Primes
511 / SPE
Asymptopia - Providence American Mathematical Society 2014 - xiv, 183p. - Student Mathematical Library 71 .
Includes Bibliography (179-180) and Index
Chapter 0. An infinity of primes Chapter 1. Stirling's formula Chapter 2. Big Oh, little oh and all that Chapter 3. Integration in Asymptopia Chapter 4. From integrals to sums Chapter 5. Asymptotics of binomial coefficients $\binom $ Chapter 6. Unicyclic graphs Chapter 7. Ramsey numbers Chapter 8. Large deviations Chapter 9. Primes Chapter 10. Asymptotic geometry Chapter 11. Algorithms Chapter 12. Potpourri Chapter 13. Really Big Numbers!
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, 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 n
, graphs with v vertices, random walks of t steps—Erdős was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. 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.
9781470438432 (PB)
Combinatorial analysis
Number theory -- Elementary number theory -- Primes
511 / SPE