Computational Excursions in Analysis and Number Theory / by Peter Borwein
(CMS Books in Mathematics / Ouvrages de mathématiques de la SMC)
| データ種別 | 電子ブック |
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| 出版情報 | New York, NY : Springer New York , 2002 |
| 本文言語 | 英語 |
| 大きさ | X, 220 p. 4 illus : online resource |
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| 内容注記 | 1 Introduction 2 LLL and PSLQ 3 Pisot and Salem Numbers 4 Rudin-Shapiro Polynomials 5 Fekete Polynomials 6 Products of Cyclotomic Polynomials 7 Location of Zeros 8 Maximal Vanishing 9 Diophantine Approximation of Zeros 10 The Integer Chebyshev Problem 11 The Prouhet-Tarry-Escott Problem 12 The Easier Waring Problem 13 The Erd?s-Szekeres Problem 14 Barker Polynomials and Golay Pairs 15 The Littlewood Problem 16 Spectra A A Compendium of Inequalities B Lattice Basis Reduction and Integer Relations C Explicit Merit Factor Formulae D Research Problems |
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| 一般注記 | 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 |
| 著者標目 | *Borwein, Peter author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Computer science -- Mathematics 全ての件名で検索 LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Number theory FREE:Mathematics FREE:Number Theory FREE:Analysis FREE:Symbolic and Algebraic Manipulation |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9780387216522 
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| ISBN | 9780387216522 |
| URL | http://dx.doi.org/10.1007/978-0-387-21652-2 |
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