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Synopsis
This book is designed for a course in computational number theory. It is based around a number of difficult old problems that live at the interface of analytic, computational and Diophantine number theory. The techniques for tackling these problems are various and include probabilistic methods, combinatorial methods, Diophantine and analytic techniques. The main computational tool used is the LLL algorithm for finding small vectors in a lattice. The book is intended as an introduction to a diverse collection of techniques for solving number- theoretic problems. For all chapters, the author has suggested related research papers where additional details may be pursued. There are many exercises and open research problems included. Indeed
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From the Back Cover
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.
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Computational Excursions in Analysis and Number Theory
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