Advanced Topics in Computational Number Theory, Henri Cohen

Автор: Peter Borwein
Название: Computational Excursions in Analysis and Number Theory
ISBN: 1441930000 ISBN-13(EAN): 9781441930002
Издательство: Springer
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Описание: This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

Автор: Borwein Peter
Название: Computational Excursions in Analysis and Number Theory
ISBN: 0387954449 ISBN-13(EAN): 9780387954448
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

Автор: Kaczynski
Название: Computational Homology
ISBN: 0387408533 ISBN-13(EAN): 9780387408538
Издательство: Springer
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Описание: Uses the computer to take a combinatorial computational approach to homological problems. This interdisciplinary book is aimed at researchers and students in mathematics, computer science, nonlinear dynamics, and engineering.

Автор: Edelsbrunner , Herbe
Название: Computational topology
ISBN: 0821849255 ISBN-13(EAN): 9780821849255
Издательство: Mare Nostrum (Eurospan)
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Описание: Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. It covers motivating problems in both mathematics and computer science. Building up from classic topics in geometric and algebraic topology, it covers persistent homology.

Автор: Scott D. Ahlgren; George E. Andrews; Ken Ono
Название: Topics in Number Theory
ISBN: 1461379881 ISBN-13(EAN): 9781461379881
Издательство: Springer
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Цена: 13275.00 р.
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Описание: From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. " The papers in this volume provide an accurate picture of many of the topics presented at the conference including contributions from four of the plenary lectures.

Автор: Henri Cohen
Название: Advanced Topics in Computational Number Theory
ISBN: 1461264197 ISBN-13(EAN): 9781461264194
Издательство: Springer
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Цена: 9083.00 р.
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Описание: The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations. The practical com- pletion of this task (sometimes known as the Dedekind program) has been one of the major achievements of computational number theory in the past ten years, thanks to the efforts of many people. Even though some practical problems still exist, one can consider the subject as solved in a satisfactory manner, and it is now routine to ask a specialized Computer Algebra Sys- tem such as Kant/Kash, liDIA, Magma, or Pari/GP, to perform number field computations that would have been unfeasible only ten years ago. The (very numerous) algorithms used are essentially all described in A Course in Com- putational Algebraic Number Theory, GTM 138, first published in 1993 (third corrected printing 1996), which is referred to here as CohO]. That text also treats other subjects such as elliptic curves, factoring, and primality testing. Itis important and natural to generalize these algorithms. Several gener- alizations can be considered, but the most important are certainly the gen- eralizations to global function fields (finite extensions of the field of rational functions in one variable overa finite field) and to relative extensions ofnum- ber fields. As in CohO], in the present book we will consider number fields only and not deal at all with function fields.

Автор: M.E. Pohst
Название: Computational Algebraic Number Theory
ISBN: 3764329130 ISBN-13(EAN): 9783764329136
Издательство: Springer
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Цена: 4186.00 р.
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Описание: Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. This book emphasizes practical algorithms for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields.

Автор: Henri Cohen
Название: A Course in Computational Algebraic Number Theory
ISBN: 3642081428 ISBN-13(EAN): 9783642081422
Издательство: Springer
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Цена: 9077.00 р.
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Описание: With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al- gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli- cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.

Автор: Kwok Y. Lam; Igor Shparlinski; Huaxiong Wang; Chao
Название: Cryptography and Computational Number Theory
ISBN: 3034895070 ISBN-13(EAN): 9783034895071
Издательство: Springer
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Описание: This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT`99, which has been held in Singapore during the week of November 22-26, 1999.

Автор: Yan Song Y
Название: Computational Number Theory and Modern Cryptography
ISBN: 1118188586 ISBN-13(EAN): 9781118188583
Издательство: Wiley
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Цена: 13139.00 р.
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Описание: * Makes deep mathematical problems accessible to computer scientists and engineers * Based on classroom tested materials used in the US, UK and China * Exercises included in every chapter * Instructor resources available on the book s Companion Website .

Автор: Rassias, Michael Th.
Название: Problem-solving and selected topics in number theory
ISBN: 1489981942 ISBN-13(EAN): 9781489981943
Издательство: Springer
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Цена: 7685.00 р.
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Описание: This self-contained introduction to classical number theory is written for undergraduate and graduate students, alike. Proofs of the theorems and solutions of the exercises are presented step-by-step.

Автор: Hugh L. Montgomery
Название: Topics in Multiplicative Number Theory
ISBN: 3540056416 ISBN-13(EAN): 9783540056416
Издательство: Springer
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Цена: 3487.00 р.
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