Finite Fields - 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 Finite Fields write by Rudolf Lidl. This book was released on 1997. Finite Fields available in PDF, EPUB and Kindle. This book is devoted entirely to the theory of finite fields.
Lectures on Finite Fields
Lectures on Finite Fields - 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 Lectures on Finite Fields write by Xiang-dong Hou. This book was released on 2018-06-07. Lectures on Finite Fields available in PDF, EPUB and Kindle. The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.
Finite Fields: Theory and Computation
Finite Fields: Theory and Computation - 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 Finite Fields: Theory and Computation write by Igor Shparlinski. This book was released on 2013-03-09. Finite Fields: Theory and Computation available in PDF, EPUB and Kindle. This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Applications of Finite Fields
Applications of Finite Fields - 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 Finite Fields write by Alfred J. Menezes. This book was released on 2013-04-17. Applications of Finite Fields available in PDF, EPUB and Kindle. The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.
Handbook of Finite Fields
Handbook of Finite Fields - 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 Handbook of Finite Fields write by Gary L. Mullen. This book was released on 2013-06-17. Handbook of Finite Fields available in PDF, EPUB and Kindle. Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
