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Neverending Fractions
This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.
Notes on Fermat's Last Theorem
Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof he claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated only recently with the proof of the theorem by Andrew Wiles. This book offers the first serious treatment of Fermat's Last Theorem since Wiles's proof. It is based on a series of lectures given by ...
Number Theory
These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.
High Primes and Misdemeanours
This volume consists of a selection of papers based on presentations made at the international conference on number theory held in honor of Hugh Williams' sixtieth birthday. The papers address topics in the areas of computational and explicit number theory and its applications. The material is suitable for graduate students and researchers interested in number theory.
Algorithmic Number Theory
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Constructive, Experimental, and Nonlinear Analysis
"This volume presents twenty original refereed papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in nonsmooth and functional analysis with applications to control theory. These papers originated largely from a conference held in conjunction with a 1999 Doctorate Honoris Causa awarded to Jonathan Borwein at Limoges. As such they reflect the areas in which Dr. Borwein has worked. In addition to providing a snapshot of research in the field of modern analysis, the papers suggest some of the directions this research is following at the beginning of the millennium."--BOOK JACKET.
Number Theory in Progress
Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.
Integration in Finite Terms: Fundamental Sources
This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
