A Course in Computational Algebraic Number Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3662029456
Total Pages : 556 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis A Course in Computational Algebraic Number Theory by : Henri Cohen

Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Problems in Algebraic Number Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 0387269983
Total Pages : 354 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Problems in Algebraic Number Theory by : M. Ram Murty

Download or read book Problems in Algebraic Number Theory written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2005-09-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

Computational Problems, Methods, and Results in Algebraic Number Theory

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Publisher : Springer
ISBN 13 : 3540374663
Total Pages : 108 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Computational Problems, Methods, and Results in Algebraic Number Theory by : H. G. Zimmer

Download or read book Computational Problems, Methods, and Results in Algebraic Number Theory written by H. G. Zimmer and published by Springer. This book was released on 2006-11-15 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

SOME COMPUTATIONAL PROBLEMS IN ALGEBRAIC NUMBER THEORY

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Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis SOME COMPUTATIONAL PROBLEMS IN ALGEBRAIC NUMBER THEORY by : United States. National Bureau of Standards

Download or read book SOME COMPUTATIONAL PROBLEMS IN ALGEBRAIC NUMBER THEORY written by United States. National Bureau of Standards and published by . This book was released on 1954 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Topics in Computational Number Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1441984895
Total Pages : 591 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Advanced Topics in Computational Number Theory by : Henri Cohen

Download or read book Advanced Topics in Computational Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2012-10-29 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.

An Illustrated Theory of Numbers

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Publisher : American Mathematical Soc.
ISBN 13 : 9781470434939
Total Pages : 0 pages
Book Rating : 4.4/5 (349 download)

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Book Synopsis An Illustrated Theory of Numbers by : Martin H. Weissman

Download or read book An Illustrated Theory of Numbers written by Martin H. Weissman and published by American Mathematical Soc.. This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seeing arithmetic -- Foundations -- The Euclidean algorithm -- Prime factorization -- Rational and constructible numbers -- Gaussian and Eisenstein integers -- Modular arithmetic -- The modular worlds -- Modular dynamics -- Assembling the modular worlds -- Quadratic residues -- Quadratic forms -- The topograph -- Definite forms -- Indefinite forms

Computational Problems, Methods, and Results in Algebraic Number Theory

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Publisher : Springer
ISBN 13 : 9780387058221
Total Pages : 103 pages
Book Rating : 4.0/5 (582 download)

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Book Synopsis Computational Problems, Methods, and Results in Algebraic Number Theory by : Horst G. Zimmer

Download or read book Computational Problems, Methods, and Results in Algebraic Number Theory written by Horst G. Zimmer and published by Springer. This book was released on 1972-01-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Brief Guide to Algebraic Number Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521004237
Total Pages : 164 pages
Book Rating : 4.0/5 (42 download)

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Book Synopsis A Brief Guide to Algebraic Number Theory by : H. P. F. Swinnerton-Dyer

Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Algebraic Number Theory and Fermat's Last Theorem

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Publisher : CRC Press
ISBN 13 : 143986408X
Total Pages : 334 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Algebraic Number Theory and Fermat's Last Theorem by : Ian Stewart

Download or read book Algebraic Number Theory and Fermat's Last Theorem written by Ian Stewart and published by CRC Press. This book was released on 2001-12-12 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it

Computer Algebra and Polynomials

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Publisher : Springer
ISBN 13 : 3319150812
Total Pages : 222 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Computer Algebra and Polynomials by : Jaime Gutierrez

Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Computer Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 3709134064
Total Pages : 282 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Computer Algebra by : R. Albrecht

Download or read book Computer Algebra written by R. Albrecht and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as "symbolic and algebraic computation" or "formula manipulation". Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms.

A Course in Computational Number Theory

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Publisher : Wiley
ISBN 13 : 9780470412152
Total Pages : 0 pages
Book Rating : 4.4/5 (121 download)

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Book Synopsis A Course in Computational Number Theory by : David Bressoud

Download or read book A Course in Computational Number Theory written by David Bressoud and published by Wiley. This book was released on 2008-06-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell’s equation, and the Gaussian primes.

Mathematics and Computation

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Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Fundamental Problems of Algorithmic Algebra

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Publisher : Oxford University Press on Demand
ISBN 13 : 9780195125160
Total Pages : 511 pages
Book Rating : 4.1/5 (251 download)

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Book Synopsis Fundamental Problems of Algorithmic Algebra by : Chee-Keng Yap

Download or read book Fundamental Problems of Algorithmic Algebra written by Chee-Keng Yap and published by Oxford University Press on Demand. This book was released on 2000 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics. Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features · Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system · Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor · Aims to be self-contained in its mathematical development · Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students

Topics in Computational Number Theory Inspired by Peter L. Montgomery

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Publisher : Cambridge University Press
ISBN 13 : 1107109353
Total Pages : 281 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Topics in Computational Number Theory Inspired by Peter L. Montgomery by : Joppe W. Bos

Download or read book Topics in Computational Number Theory Inspired by Peter L. Montgomery written by Joppe W. Bos and published by Cambridge University Press. This book was released on 2017-10-12 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the many ideas and algorithms that Peter L. Montgomery has contributed to computational number theory and cryptography.

Number Theory for Computing

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Publisher : Springer Science & Business Media
ISBN 13 : 366204773X
Total Pages : 454 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Number Theory for Computing by : Song Y. Yan

Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.

Algorithmic Number Theory: Efficient algorithms

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Publisher : MIT Press
ISBN 13 : 9780262024051
Total Pages : 536 pages
Book Rating : 4.0/5 (24 download)

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Book Synopsis Algorithmic Number Theory: Efficient algorithms by : Eric Bach

Download or read book Algorithmic Number Theory: Efficient algorithms written by Eric Bach and published by MIT Press. This book was released on 1996 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1.