Combinatorics And Finite Fields PDF Download
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Author | : Kannan Soundararajan |
Publisher | : American Mathematical Society |
Total Pages | : 100 |
Release | : 2022-11-09 |
Genre | : Mathematics |
ISBN | : 1470469308 |
Download Finite Fields, with Applications to Combinatorics Book in PDF, ePub and Kindle
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Author | : Kai-Uwe Schmidt |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 506 |
Release | : 2019-07-08 |
Genre | : Mathematics |
ISBN | : 3110641968 |
Download Combinatorics and Finite Fields Book in PDF, ePub and Kindle
The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansj rg Albrecher, University of Lausanne, SwitzerlandRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria
Author | : Kai-Uwe Schmidt |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 354 |
Release | : 2019-07-08 |
Genre | : Mathematics |
ISBN | : 3110642093 |
Download Combinatorics and Finite Fields Book in PDF, ePub and Kindle
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.
Author | : Xiang-dong Hou |
Publisher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 2018-06-07 |
Genre | : Finite fields (Algebra) |
ISBN | : 1470442892 |
Download Lectures on Finite Fields Book 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.
Author | : Rudolf Lidl |
Publisher | : Cambridge University Press |
Total Pages | : 784 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780521392310 |
Download Finite Fields Book in PDF, ePub and Kindle
This book is devoted entirely to the theory of finite fields.
Author | : Gary L. Mullen |
Publisher | : CRC Press |
Total Pages | : 1048 |
Release | : 2013-06-17 |
Genre | : Computers |
ISBN | : 1439873828 |
Download Handbook of Finite Fields Book 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
Author | : James A. Davis |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 214 |
Release | : 2020-10-26 |
Genre | : Mathematics |
ISBN | : 3110621738 |
Download Finite Fields and their Applications Book in PDF, ePub and Kindle
The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.
Author | : Gary L. Mullen |
Publisher | : American Mathematical Soc. |
Total Pages | : 278 |
Release | : 2008 |
Genre | : Computers |
ISBN | : 0821843095 |
Download Finite Fields and Applications Book in PDF, ePub and Kindle
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.
Author | : Gary L. Mullen |
Publisher | : American Mathematical Soc. |
Total Pages | : 190 |
Release | : 2007 |
Genre | : Computers |
ISBN | : 0821844180 |
Download Finite Fields and Applications Book in PDF, ePub and Kindle
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Author | : Dirk Hachenberger |
Publisher | : Springer Nature |
Total Pages | : 785 |
Release | : 2020-09-29 |
Genre | : Mathematics |
ISBN | : 3030608069 |
Download Topics in Galois Fields Book in PDF, ePub and Kindle
This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.