Number Theory And Its Applications Ii

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Number Theory And Its Applications Ii

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Author : Hailong Li
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-11-29

Number Theory And Its Applications Ii written by Hailong Li and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.

The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applications.Number theory used to be described as the queen of mathematics, that is, there is no practical use. However, with the development of computers and the security of internet communications, the importance of number theory has been exponentially increasing daily. The raison d'être of the present book in this situation is that it is extremely reader-friendly while keeping the rigor of serious mathematics and in-depth analysis of practical applications to various subjects including control theory and pseudo-random number generation. The use of operators is prevailing rather abundantly in anticipation of applications to electrical engineering, allowing the reader to master these skills without much difficulty. It also delivers a very smooth bridging between elementary subjects including linear algebra and group theory (and algebraic number theory) for the reader to be well-versed in an efficient and effortless way. One of the main features of the book is that it gives several different approaches to the same topic, helping the reader to gain deeper insight and comprehension. Even just browsing through the materials would be beneficial to the reader.

Number Theory With Applications

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Author : Wen-ching Li
language : en
Publisher: World Scientific Publishing Company
Release Date : 1996-02-16

Number Theory With Applications written by Wen-ching Li and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-16 with Mathematics categories.

Novel and important applications of number theory to graph theory and vice versa had been made in the past decade. The two main tools used are based on the estimates of character sums and the estimates of the eigenvalues of Hecke operators, both are rooted in the celebrated Weil conjectures settled by Deligne in 1973. The purpose of this book is to give, from scratch, a coherent and comprehensive introduction to the topics in number theory related to the central tools, with the ultimate goal of presenting their applications. This book includes many important subjects in number theory, such as Weil conjectures, Riemann-Roch theorem, L-functions, character sum estimates, modular forms, and representation theory.

Number Theory And Its Applications

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Author : Satyabrota Kundu
language : en
Publisher: CRC Press
Release Date : 2022-01-31

Number Theory And Its Applications written by Satyabrota Kundu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-31 with Mathematics categories.

Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses. Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

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.

Discrete Mathematics And Its Applications

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Author : Kenneth Rosen
language : en
Publisher: McGraw-Hill Education
Release Date : 2006-07-26

Discrete Mathematics And Its Applications written by Kenneth Rosen and has been published by McGraw-Hill Education this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-26 with Mathematics categories.

Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.

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.

Number Theory And Its Applications In China

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Author : Yuan Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Number Theory And Its Applications In China written by Yuan Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.

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.

Introduction To Number Theory

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Author : Richard Michael Hill
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-12-04

Introduction To Number Theory written by Richard Michael Hill and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with Mathematics categories.

'Probably its most significant distinguishing feature is that this book is more algebraically oriented than most undergraduate number theory texts.'MAA ReviewsIntroduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p-adic powers series such as exp(px) and log(1+px), the Euclidean property of some quadratic rings, representation of integers as norms from quadratic rings, and Pell's equation via continued fractions.Throughout the five chapters and more than 100 exercises and solutions, readers gain the advantage of a number theory book that focuses on doing calculations. This textbook is a valuable resource for undergraduates or those with a background in university level mathematics.

Computational Number Theory

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Author : Abhijit Das
language : en
Publisher: CRC Press
Release Date : 2013-03-18

Computational Number Theory written by Abhijit Das and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-18 with Computers categories.

Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry. Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography. With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.