Download or read book Recent Advances in Polynomials written by Kamal Shah and published by BoD – Books on Demand. This book was released on 2022-05-18 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad overview of recent developments in polynomials and their applications. It includes eight chapters that address such topics as characteristic functions of polynomials, permutations, Gon?arov polynomials, irreducible factors, polynomial regression algorithms, and the use of polynomials in fractional calculus, and much more.
Download or read book Computational and Algorithmic Problems in Finite Fields written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, 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 araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Download or read book Arithmetic of Finite Fields written by Claude Carlet and published by Springer. This book was released on 2007-09-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, held in Madrid, Spain in June 2007. It covers structures in finite fields, efficient implementation and architectures, efficient finite field arithmetic, classification and construction of mappings over finite fields, curve algebra, cryptography, codes, and discrete structures.
Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Finite Fields and Applications written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 2007 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Download or read book Finite Fields Theory and Computation written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorics and Finite Fields written by Kai-Uwe Schmidt and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
Download or read book Open Problems in Mathematics and Computational Science written by Çetin Kaya Koç and published by Springer. This book was released on 2015-03-25 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.
Download or read book Orthomorphism Graphs of Groups written by Anthony B. Evans and published by Springer. This book was released on 2006-11-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about orthomorphisms and complete mappings of groups, and related constructions of orthogonal latin squares. It brings together, for the first time in book form, many of the results in this area. The aim of this book is to lay the foundations for a theory of orthomorphism graphsof groups, and to encourage research in this area. To this end, many directions for future research are suggested. The material in this book should be accessible to any graduate student who has taken courses in algebra (group theory and field theory). It will mainly be useful in research on combinatorial design theory, group theory and field theory.
Download or read book Elementary Number Theory written by Gove Effinger and published by CRC Press. This book was released on 2021-09-08 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Number Theory, Gove Effinger, Gary L. Mullen This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject. Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter. The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.
Download or read book Finite Fields and Applications written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 2008 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.
Download or read book Topics in Finite Fields written by Gohar Kyureghyan and published by American Mathematical Soc.. This book was released on 2015-01-29 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 11th International Conference on Finite Fields and their Applications (Fq11), held July 22-26, 2013, in Magdeburg, Germany. Finite Fields are fundamental structures in mathematics. They lead to interesting deep problems in number theory, play a major role in combinatorics and finite geometry, and have a vast amount of applications in computer science. Papers in this volume cover these aspects of finite fields as well as applications in coding theory and cryptography.
Download or read book Finite Fields and Applications written by Dieter Jungnickel and published by Springer Science & Business Media. This book was released on 2001-03-20 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.
Download or read book Algebra of Polynomials written by and published by Elsevier. This book was released on 2000-04-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra of Polynomials
Download or read book Women in Numbers Europe II written by Irene I. Bouw and published by Springer. This book was released on 2018-06-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work.
Download or read book Contemporary Developments In Finite Fields And Applications written by Gove Effinger and published by World Scientific. This book was released on 2016-06-15 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a collection of 20 refereed articles written in connection with lectures presented at the 12th International Conference on Finite Fields and Their Applications ('Fq12') at Skidmore College in Saratoga Springs, NY in July 2015. Finite fields are central to modern cryptography and secure digital communication, and hence must evolve rapidly to keep pace with new technologies. Topics in this volume include cryptography, coding theory, structure of finite fields, algorithms, curves over finite fields, and further applications.Contributors will include: Antoine Joux (Fondation Partenariale de l'UPMC, France); Gary Mullen (Penn State University, USA); Gohar Kyureghyan (Otto-von-Guericke Universität, Germany); Gary McGuire (University College Dublin, Ireland); Michel Lavrauw (Università degli Studi di Padova, Italy); Kirsten Eisentraeger (Penn State University, USA); Renate Scheidler (University of Calgary, Canada); Michael Zieve (University of Michigan, USA).
Download or read book Sequences Subsequences and Consequences written by Solomon W. Golomb and published by Springer Science & Business Media. This book was released on 2007-12-13 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interested readers will find here the thoroughly refereed post-proceedings of the International Workshop of Sequences, Subsequences and Consequences, SSC 2007, held in Los Angeles, USA, in 2007. The 16 revised invited full papers and one revised contributed paper are presented together with three keynote lectures and were carefully reviewed and selected for the book. The theory of sequences has found practical applications in many areas of coded communications and in cryptography.
