H. Niederreiter's Books

Finite Fields

By: Lidl,H. Niederreiter

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The theory of finite fields is a branch of modern algebra that has come to the fore in the last fifty years because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching circuits. This book, the first one devoted entirely to this theory, provides comprehensive coverage of the literature on finite fields and their applications. Extensive bibliographical notes at the end of each chapter give a historical survey of the development of the subject. Worked examples and lists of exercises found throughout the book make it useful as a text for advanced level courses.

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660

Publisher

Cambridge University Press

Published Date

ISBN 10

0521302404

ISBN 13

9780521302401

Introduction to Finite Fields and Their Applications

By: Rudolf Lidl,Harald Niederreiter

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Introduction to Finite Fields and Their Applications

By: Rudolf Lidl,Harald Niederreiter

The first part of this book presents an introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications. The second part is devoted to a discussion of the most important applications of finite fields especially information theory, algebraic coding theory and cryptology (including some very recent material that has never before appeared in book form). There is also a chapter on applications within mathematics, such as finite geometries. combinatorics. and pseudorandom sequences. Worked-out examples and list of exercises found throughout the book make it useful as a textbook.

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407

Published Date

ISBN 10

0521307066

ISBN 13

9780521307062

Finite Fields and Applications

Proceedings of The Fifth International Conference on Finite Fields and Applications Fq 5, held at the University of Augsburg, Germany, August 2–6, 1999

By: Dieter Jungnickel,H. Niederreiter

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Finite Fields and Applications

Proceedings of The Fifth International Conference on Finite Fields and Applications Fq 5, held at the University of Augsburg, Germany, August 2–6, 1999

By: Dieter Jungnickel,H. Niederreiter

This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.

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514

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540411097

ISBN 13

9783540411093

Random and Quasi-Random Point Sets

By: Peter Hellekalek,Gerhard Larcher

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Random and Quasi-Random Point Sets

By: Peter Hellekalek,Gerhard Larcher

This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical ("a priori") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "random" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These "quasi-random" points are produced by deterministic algorithms and should be as "super" uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets.

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Page Count

345

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461217024

ISBN 13

9781461217022

Book's by H. Niederreiter

Finite Fields

Finite Fields

Introduction to Finite Fields and Their Applications

Introduction to Finite Fields and Their Applications

Finite Fields and Applications

Finite Fields and Applications

Random and Quasi-Random Point Sets

Random and Quasi-Random Point Sets

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