Applications of Number Theory to Numerical Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applications of Number Theory to Numerical Analysis write by L.-K. Hua. This book was released on 2012-12-06. Applications of Number Theory to Numerical Analysis available in PDF, EPUB and Kindle. 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.
Applications of Number Theory to Numerical Analysis
Applications of Number Theory to Numerical Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applications of Number Theory to Numerical Analysis write by S. K. Zaremba. This book was released on 2014-05-10. Applications of Number Theory to Numerical Analysis available in PDF, EPUB and Kindle. Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.
Theory and Applications of Numerical Analysis
Theory and Applications of Numerical Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory and Applications of Numerical Analysis write by G. M. Phillips. This book was released on 1996-07-05. Theory and Applications of Numerical Analysis available in PDF, EPUB and Kindle. Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. a unique blend of theory and applications two brand new chapters on eigenvalues and splines inclusion of formal algorithms numerous fully worked examples a large number of problems, many with solutions
Number Theory for Computing
Number Theory for Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Number Theory for Computing write by Song Y. Yan. This book was released on 2013-03-09. Number Theory for Computing available in PDF, EPUB and Kindle. Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.
From Great Discoveries in Number Theory to Applications
From Great Discoveries in Number Theory to Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook From Great Discoveries in Number Theory to Applications write by Michal Křížek. This book was released on 2021-09-21. From Great Discoveries in Number Theory to Applications available in PDF, EPUB and Kindle. 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.
