Application Of Number
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Applications Of Number Theory To Numerical Analysis
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Author : L.-K. Hua
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Number Theory To Numerical Analysis written by L.-K. Hua and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num ber theory to construct a sequence of uniformly distributed sets in the s dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis fies certain conditions.
From Great Discoveries In Number Theory To Applications
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Author : Michal Křížek
language : en
Publisher: Springer Nature
Release Date : 2021-09-21
From Great Discoveries In Number Theory To Applications written by Michal Křížek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Mathematics categories.
This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Key Skills
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Author : Jill Gask
language : en
Publisher:
Release Date : 2005
Key Skills written by Jill Gask and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Manual Of Patent Examining Procedure
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Author : United States. Patent and Trademark Office
language : en
Publisher:
Release Date : 1998
Manual Of Patent Examining Procedure written by United States. Patent and Trademark Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Patent practice categories.
Number Theory For Computing
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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Number Theory For Computing written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Computers categories.
Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping Ralph Merkle receive the credit he deserves. Diffie, Rivest, Shamir, Adleman and I had the good luck to get expedited review of our papers, so that they appeared before Merkle's seminal contribu tion. Your noting his early submission date and referring to what has come to be called "Diffie-Hellman key exchange" as it should, "Diffie-Hellman-Merkle key exchange", is greatly appreciated. It has been gratifying to see how cryptography and number theory have helped each other over the last twenty-five years. :'-Jumber theory has been the source of numerous clever ideas for implementing cryptographic systems and protocols while cryptography has been helpful in getting funding for this area which has sometimes been called "the queen of mathematics" because of its seeming lack of real world applications. Little did they know! Stanford, 30 July 2001 Martin E. Hellman Preface to the Second Edition Number theory is an experimental science.
Uspto Image File Wrapper Petition Decisions 0293
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Author :
language : en
Publisher: USPTO
Release Date :
Uspto Image File Wrapper Petition Decisions 0293 written by and has been published by USPTO this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Federal Register
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Author :
language : en
Publisher:
Release Date : 2013-04
Federal Register written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04 with Delegated legislation categories.
Export Administration Regulations
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Author : United States. Office of Export Administration
language : en
Publisher:
Release Date :
Export Administration Regulations written by United States. Office of Export Administration and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Export controls categories.
Code Of Federal Regulations
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Author :
language : en
Publisher:
Release Date : 2001
Code Of Federal Regulations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Administrative law categories.
The Code Of Federal Regulations Of The United States Of America
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Author :
language : en
Publisher:
Release Date : 2001
The Code Of Federal Regulations Of The United States Of America written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Administrative law categories.
The Code of Federal Regulations is the codification of the general and permanent rules published in the Federal Register by the executive departments and agencies of the Federal Government.