Nigel Cutland's Books

Computability

An Introduction to Recursive Function Theory

By: Nigel Cutland

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Computability

An Introduction to Recursive Function Theory

By: Nigel Cutland

What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.

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Page Count

268

Publisher

Cambridge University Press

Published Date

ISBN 10

1139935607

ISBN 13

9781139935609

Derivative Pricing in Discrete Time

By: Nigel J. Cutland,Alet Roux

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Derivative Pricing in Discrete Time

By: Nigel J. Cutland,Alet Roux

Derivatives are financial entities whose value is derived from the value of other more concrete assets such as stocks and commodities. They are an important ingredient of modern financial markets. This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.

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Page Count

329

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447144074

ISBN 13

9781447144076

Nonstandard Methods For Stochastic Fluid Mechanics

By: Marek Capinski,Nigel J Cutland

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Nonstandard Methods For Stochastic Fluid Mechanics

By: Marek Capinski,Nigel J Cutland

This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations.The authors provide a self-contained introduction to nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.

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Page Count

246

Publisher

World Scientific

Published Date

ISBN 10

9814502200

ISBN 13

9789814502207

Developments in Nonstandard Mathematics

By: Nigel J Cutland,Vitor Neves,A F Oliveira,Jose Sousa-Pinto

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Developments in Nonstandard Mathematics

By: Nigel J Cutland,Vitor Neves,A F Oliveira,Jose Sousa-Pinto

This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.

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Page Count

278

Publisher

CRC Press

Published Date

ISBN 10

1000724646

ISBN 13

9781000724646

Annotated Companies Legislation

By: Nigel Boardman

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Annotated Companies Legislation

By: Nigel Boardman

A comprehensive guide to companies legislation in a convenient paperback volume. Written from the perspective of the 2006 regime, it gives detailed section-by-section commentary alongside the Companies Act 2006 and surviving parts of the previous legislation as well as including the text of relevant statutory instruments.

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Page Count

2314

Publisher

Oxford University Press, USA

Published Date

ISBN 10

0199593922

ISBN 13

9780199593927

Loeb Measures in Practice: Recent Advances

EMS Lectures 1997

By: Nigel J. Cutland

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Loeb Measures in Practice: Recent Advances

EMS Lectures 1997

By: Nigel J. Cutland

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.

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Page Count

118

Publisher

Springer

Published Date

ISBN 10

3540445315

ISBN 13

9783540445319

Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

By: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

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Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

By: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

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Page Count

364

Publisher

Springer

Published Date

ISBN 10

3540397027

ISBN 13

9783540397021

Computability

An Introduction to Recursive Function Theory

By: Nigel Cutland

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Computability

An Introduction to Recursive Function Theory

By: Nigel Cutland

What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.

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