Author	Borwein, Peter. author
Title	Computational Excursions in Analysis and Number Theory [electronic resource] / by Peter Borwein
Imprint	New York, NY : Springer New York, 2002
Connect to	http://dx.doi.org/10.1007/978-0-387-21652-2
Descript	X, 220 p. 4 illus. online resource

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

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

1. Mathematics
2. Computer science -- Mathematics
3. Mathematical analysis
4. Analysis (Mathematics)
5. Number theory
6. Mathematics
7. Number Theory
8. Analysis
9. Symbolic and Algebraic Manipulation