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Computational Excursions in Analysis and Number Theory (CMS Books in Mathematics)

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Computational Excursions in Analysis and Number Theory (CMS Books in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

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

Product Details

ISBN:
9781441930002
Author:
Borwein, Peter
Publisher:
Springer
Location:
Y
Subject:
Number Theory
Subject:
computational number theory
Subject:
Analysis
Subject:
Symbolic and Algebraic Manipulation
Subject:
Mathematics-Number Theory
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Subject:
Algebra_xData processing
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2002
Series:
CMS Books in Mathematics
Publication Date:
20101203
Binding:
TRADE PAPER
Language:
English
Pages:
230
Dimensions:
235 x 155 mm 730 gr

Related Subjects

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Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Computational Excursions in Analysis and Number Theory (CMS Books in Mathematics) New Trade Paper
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Product details 230 pages Not Avail - English 9781441930002 Reviews:
"Synopsis" by , This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
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