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| Author | : Gary L. Mullen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 190 |
| Release | : 2007 |
| Genre | : Computers |
| ISBN | : 0821844180 |
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
| Author | : Kai-Uwe Schmidt |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 459 |
| Release | : 2019-07-08 |
| Genre | : Mathematics |
| ISBN | : 3110641968 |
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 | : Rudolf Lidl |
| Publisher | : Cambridge University Press |
| Total Pages | : 784 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780521392310 |
This book is devoted entirely to the theory of finite fields.
| Author | : Kannan Soundararajan |
| Publisher | : American Mathematical Society |
| Total Pages | : 100 |
| Release | : 2022-11-09 |
| Genre | : Mathematics |
| ISBN | : 1470469308 |
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 | : Gary L. Mullen |
| Publisher | : CRC Press |
| Total Pages | : 1048 |
| Release | : 2013-06-17 |
| Genre | : Computers |
| ISBN | : 1439873828 |
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 | : Xiang-dong Hou |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 242 |
| Release | : 2018-06-07 |
| Genre | : Mathematics |
| ISBN | : 1470442892 |
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 | : Gary L. Mullen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 278 |
| Release | : 2008 |
| Genre | : Computers |
| ISBN | : 0821843095 |
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 | : Larry Guth |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 287 |
| Release | : 2016-06-10 |
| Genre | : Mathematics |
| ISBN | : 1470428903 |
This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.
| Author | : Jonathan L. Gross |
| Publisher | : CRC Press |
| Total Pages | : 664 |
| Release | : 2016-04-19 |
| Genre | : Computers |
| ISBN | : 1584887443 |
This combinatorics text provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. It presents the computer and software algorithms in pseudo-code and incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition. Numerous problems, solutions, and hints reinforce basic skills and assist with creative problem solving. The author also offers a website with extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises.
