Computational Excursions in Analysis and Number Theory

  • Peter Borwein
Part of the CMS Books in Mathematics / Ouvrages de mathématiques de la SMC book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Peter Borwein
    Pages 1-9
  3. Peter Borwein
    Pages 11-13
  4. Peter Borwein
    Pages 15-26
  5. Peter Borwein
    Pages 27-35
  6. Peter Borwein
    Pages 37-42
  7. Peter Borwein
    Pages 43-52
  8. Peter Borwein
    Pages 53-58
  9. Peter Borwein
    Pages 59-66
  10. Peter Borwein
    Pages 67-74
  11. Peter Borwein
    Pages 75-84
  12. Peter Borwein
    Pages 85-95
  13. Peter Borwein
    Pages 97-101
  14. Peter Borwein
    Pages 103-107
  15. Peter Borwein
    Pages 109-119
  16. Peter Borwein
    Pages 121-132
  17. Peter Borwein
    Pages 133-139
  18. Back Matter
    Pages 141-220

About this book

Introduction

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.

Keywords

Diophantine approximation Maxima algorithms calculus combinatorics computational number theory extrema maximum number theory

Authors and affiliations

  • Peter Borwein
    • 1
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-21652-2
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3000-2
  • Online ISBN 978-0-387-21652-2
  • Series Print ISSN 1613-5237
  • About this book