Peter Swinnerton-Dyer's Books

Arithmetic Geometry

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007

By: Jean-Louis Colliot-Thélène,Peter Swinnerton-Dyer,Paul Vojta

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Arithmetic Geometry

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007

By: Jean-Louis Colliot-Thélène,Peter Swinnerton-Dyer,Paul Vojta

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

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Page Count

251

Publisher

Springer

Published Date

ISBN 10

3642159451

ISBN 13

9783642159459

Modular Forms: A Classical And Computational Introduction (2nd Edition)

By: Lloyd James Peter Kilford

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Modular Forms: A Classical And Computational Introduction (2nd Edition)

By: Lloyd James Peter Kilford

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

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252

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1783265477

ISBN 13

9781783265473

Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

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Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

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Page Count

166

Publisher

Springer

Published Date

ISBN 10

3540697020

ISBN 13

9783540697022

The Royal Society and the Promotion of Science since 1960

By: Peter Collins

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The Royal Society and the Promotion of Science since 1960

By: Peter Collins

The first synoptic history of how the Royal Society faced up to the challenges of continued relevance from 1960 onwards.

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Page Count

357

Publisher

Cambridge University Press

Published Date

ISBN 10

1107029260

ISBN 13

9781107029262

Convex and Discrete Geometry

By: Peter M. Gruber

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Convex and Discrete Geometry

By: Peter M. Gruber

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.

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Page Count

590

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540711333

ISBN 13

9783540711339

Continued Fractions

By: Andrew M Rockett,Peter Szusz

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Continued Fractions

By: Andrew M Rockett,Peter Szusz

This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.

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Page Count

200

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813103418

ISBN 13

9789813103412

Special Values of Dirichlet Series, Monodromy, and the Periods of Automorphic Forms

By: Peter Stiller

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Special Values of Dirichlet Series, Monodromy, and the Periods of Automorphic Forms

By: Peter Stiller

In this paper we explore a relationship that exists between the classical cusp form for subgroups of finite index in [italic]SL2([double-struck capital]Z) and certain differential equations, and we develop a connection between the equation's monodromy representation and the special values in the critical strip of the Dirichlet series associated to the cusp form.

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Page Count

123

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821823000

ISBN 13

9780821823002

Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

By: Deniz Bilman,Peter D. Miller

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Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

By: Deniz Bilman,Peter D. Miller

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Page Count

102

Publisher

American Mathematical Society

Published Date

ISBN 10

1470471213

ISBN 13

9781470471217

The Meanings Of Mass Higher Education

By: Scott, Peter

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The Meanings Of Mass Higher Education

By: Scott, Peter

This book is the first systematic attempt to analyse the growth of mass higher education in a specifically British context, while seeking to develop more theoretical perspectives on this transformation of elite university systems into open post-secondary education systems. It is divided into three main sections. The first examines the evolution of British higher education and the development of universities and other institutions. The second explores the political, social and economic context within which mass systems are developing. What are the links between post-industrial society, a post-Fordist economy and the mass university? The third section discusses the links between massification and wider currents in intellectual and scientific culture.

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Page Count

210

Publisher

McGraw-Hill Education (UK)

Published Date

ISBN 10

0335194427

ISBN 13

9780335194421

Research Problems in Discrete Geometry

By: Peter Brass,William O. J. Moser,János Pach

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Research Problems in Discrete Geometry

By: Peter Brass,William O. J. Moser,János Pach

This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

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Page Count

507

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387238158

ISBN 13

9780387238159

Finite Fields: Theory, Applications, and Algorithms

Theory, Applications, and Algorithms

By: Gary L. Mullen,Peter Jau-Shyong Shiue

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Finite Fields: Theory, Applications, and Algorithms

Theory, Applications, and Algorithms

By: Gary L. Mullen,Peter Jau-Shyong Shiue

Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.

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Page Count

434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851837

ISBN 13

9780821851838

Chaotic Numerics

An International Workshop on the Approximation and Computation of Complicated Dynamical Behavior, Deakin University, Geelong, Australia, July 12-16, 1993

By: Peter E. Kloeden

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Chaotic Numerics

An International Workshop on the Approximation and Computation of Complicated Dynamical Behavior, Deakin University, Geelong, Australia, July 12-16, 1993

By: Peter E. Kloeden

Much of what is known about specific dynamical systems is obtained from numerical experiments. Although the discretization process usually has no significant effect on the results for simple, well-behaved dynamics, acute sensitivity to changes in initial conditions is a hallmark of chaotic behavior. How confident can one be that the numerical dynamics reflects that of the original system? Do numerically calculated trajectories always shadow a true one? What role does numerical analysis play in the study of dynamical systems? And conversely, can advances in dynamical systems provide new insights into numerical algorithms? These and related issues were the focus of the workshop on Chaotic Numerics, held at Deakin University in Geelong, Australia, in July 1993. The contributions to this book are based on lectures presented during the workshop and provide a broad overview of this area of research.

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290

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851845

ISBN 13

9780821851845

The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations

By: Robert M. Guralnick,Peter Müller,Jan Saxl

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The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations

By: Robert M. Guralnick,Peter Müller,Jan Saxl

Investigates the analogous question for rational functions. This book describes the Galois theoretic translation, based on Chebotarev's density theorem, leads to a certain property of permutation groups, called exceptionality.

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American Mathematical Soc.

Published Date

ISBN 10

0821832883

ISBN 13

9780821832882

Retreat Or Resolution?

Tackling the Crisis of Mass Higher Education

By: Peter Scott

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Retreat Or Resolution?

Tackling the Crisis of Mass Higher Education

By: Peter Scott

Peter Scott examines the development of mass higher education and calls for robust action to secure fair access at all levels and changes in the governance and management at both system and institutional levels to ensure more democratic accountability.

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Page Count

228

Publisher

Policy Press

Published Date

ISBN 10

1447363280

ISBN 13

9781447363286

Random Matrices, Frobenius Eigenvalues, and Monodromy

By: Nicholas M. Katz,Peter Sarnak

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Random Matrices, Frobenius Eigenvalues, and Monodromy

By: Nicholas M. Katz,Peter Sarnak

The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.

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Page Count

441

Publisher

American Mathematical Society

Published Date

ISBN 10

1470475073

ISBN 13

9781470475079

Geometry of the Spectrum

1993 Joint Summer Research Conference on Spectral Geometry, July 17-23, 1993, University of Washington, Seattle

By: Robert Brooks,Carolyn Gordon,Peter A. Perry

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Geometry of the Spectrum

1993 Joint Summer Research Conference on Spectral Geometry, July 17-23, 1993, University of Washington, Seattle

By: Robert Brooks,Carolyn Gordon,Peter A. Perry

Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.

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Page Count

314

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851853

ISBN 13

9780821851852

Extremal Riemann Surfaces

From the Proceedings of the AMS Special Session with Related Papers January 4-5, 1995, San Francisco, California

By: John R. Quine,Peter Sarnak

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Extremal Riemann Surfaces

From the Proceedings of the AMS Special Session with Related Papers January 4-5, 1995, San Francisco, California

By: John R. Quine,Peter Sarnak

Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal metric.

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Page Count

258

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821805142

ISBN 13

9780821805145

Pi: A Source Book

By: J.L. Berggren,Jonathan M. Borwein,Peter Borwein

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Pi: A Source Book

By: J.L. Berggren,Jonathan M. Borwein,Peter Borwein

This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.

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Page Count

832

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387205713

ISBN 13

9780387205717

Frontiers of Complexity

The Search for Order in a Choatic World

By: Peter Coveney,Roger Highfield

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Frontiers of Complexity

The Search for Order in a Choatic World

By: Peter Coveney,Roger Highfield

SCIENCE JOURNALISM AT ITS BEST. . . An impeccably researched, amazingly up-to-date, crisply written and well-illustrated survey." --Nature At the cutting edge of the sciences, a dynamic new concept is emerging: complexity. In this groundbreaking new book, Peter Coveney and Roger Highfield explore how complexity in mathematics, physics, biology, chemistry, and even the social sciences is transforming not only the way we think about the universe, but also the very assumptions that underlie conventional science. Complexity is a watchword for a new way of thinking about the behavior of interacting units, whether they are atoms, ants in a colony, or neurons firing in a human brain. The rise of the electronic computer provided both the key and the catalyst to our exploration of complexity. A new generation of computers that runs on light and exploits the bizarre properties of quantum mechanics promises to deepen our understanding still further. The advances we have already witnessed are spectacular. The authors take us inside laboratories where scientists are evolving the genetic molecules that enabled life to emerge on earth and generating universes teeming with virtual creatures in cyber-space. We witness the utterly realistic behavior of a school of virtual fish--computer-generated replicas that have been trained to swim gracefully, hunt for food, and scatter at the approach of a leopard shark. Compelling in its clarity, far-reaching in its implications, vibrant with the excitement of new discovery, Frontiers of Complexity is an arresting account of how far science has come in the past fifty years and an essential guide to the rapidly approaching future. "[A] MARVELOUS AND COMPREHENSIVE WORK . . . Virtually any scientist or interested lay reader will find this book engrossing, edifying and inspiring." --Publishers Weekly (starred review)

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Page Count

492

Publisher

Ballantine Books

Published Date

ISBN 10

0449910814

ISBN 13

9780449910818

Book's by Peter Swinnerton-Dyer

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