Computational Excursions in analysis and number theory /

Computational Excursions in analysis and number theory / Peter Borwein.

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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 th...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Borwein, Peter B.
Format: eBook
Language:English
Published: New York : Springer, ©2002.
Series:CMS books in mathematics ; 10.
Subjects:
Number theory.
Diophantine analysis.
Table of Contents:
  • Preface
  • Introduction
  • LLL and PSLQ
  • Pisot and Salem Numbers
  • Rudin-Shapiro Polynomials
  • Fekete Polynomials
  • Products of Cyclotomic Polynomials
  • Location of Zeros
  • Maximal Vanishing
  • Diophantine Approximation of Zeros
  • The Integer-Chebyshev Problem
  • The Prouhet-Tarry-Escott Problem
  • The Easier Waring Problem
  • The Erdös-Szekeres Problem
  • Barker Polynomials and Golay Pairs
  • The Littlewood Problem
  • Spectra
  • Appendix A: A Compendium of Inequalities
  • B: Lattice Basis Reduction and Integer Relations
  • C: Explicit Merit Factor Formulae
  • D: Research Problems
  • References
  • Index.

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