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CMS Books in Mathematics

Computational Excursions in Analysis and Number Theory

Authors: Borwein, Peter

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eBook 101,14 €
price for Spain (gross)
  • ISBN 978-0-387-21652-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-0-387-95444-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4419-3000-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book is designed for a computationally intensive graduate course based around a collection of classical unsolved extremal problems for polynomials. These problems, all of which lend themselves to extensive computational exploration, live at the interface of analysis, combinatorics and number theory so the techniques involved are diverse. A main computational tool used is the LLL algorithm for finding small vectors in a lattice.

Many exercises and open research problems are included. Indeed one aim of the book is to tempt the able reader into the rich possibilities for research in this area.

Peter Borwein is Professor of Mathematics at Simon Fraser University and the Associate Director of the Centre for Experimental and Constructive Mathematics. He is also the recipient of the Mathematical Association of Americas Chauvenet Prize and the Merten M. Hasse Prize for expository writing in mathematics.

Reviews

From the reviews of the first edition:

MAA ONLINE

"Explanations are thorough but not easy to understand. Nevertheless, they can be understood by the determined graduate student in mathematics. However, the ideal mix would be a collection of mathematics and computer science students, as the level of computer expertise needed to code the solutions to the problems is at the upper division level…Research mathematicians often need to be able to write code to attack specific problems when no appropriate software tool is available. This book is ideal for a course designed to teach graduate students how to do that as long as they have or can obtain the necessary programming knowledge."

P. Borwein

Computational Excursions in Analysis and Number Theory

"Borwein has collected known results in the direction of several related, appealing, old, open problems (Integer Chebyshev, Prouhet-Tarry-Escott, Erdos-Szekeres, Littlewood). Far from narrow, this interdisciplinary book draws on Diophantine, analytic, and probabilistic techniques. Also, by dint of the celebrated lattice reduction algorithm, some aspects of these problems admit attack by computer; a handful of intriguing computer graphics offer visceral evidence of the intrinsic complexity of the underlying phenomena. Pisot and Salam numbers make terrific enrichment material for undergraduates. As in all Borwein's books, we get beautiful mathematics gracefully explained."—CHOICE

"This extraordinary book brings together a variety of old problems – old, but very much alive - about polynomials with integer co-efficients. … The necessary background is also presented, which makes the book self-contained … . this book is suitable for advanced students of analysis and analytic number theory. It is very well written, rather concise and to the point. … Strongly recommended for specialists in computational analysis and number theory." (R. Stroeker, Nieuw Archief voor Wiskunde, Vol. 7 (3), 2006)


Table of contents (16 chapters)

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-0-387-21652-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-0-387-95444-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4419-3000-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Computational Excursions in Analysis and Number Theory
Authors
Series Title
CMS Books in Mathematics
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-21652-2
DOI
10.1007/978-0-387-21652-2
Hardcover ISBN
978-0-387-95444-8
Softcover ISBN
978-1-4419-3000-2
Series ISSN
1613-5237
Edition Number
1
Number of Pages
X, 220
Number of Illustrations and Tables
4 b/w illustrations
Topics