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Author: Kai-Uwe Schmidt Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110641968 Category : Mathematics Languages : en Pages : 459
Book Description
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: Kai-Uwe Schmidt Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110641968 Category : Mathematics Languages : en Pages : 459
Book Description
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. ISBN: 1470442892 Category : Mathematics Languages : en Pages : 242
Book Description
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: CRC Press ISBN: 1439873828 Category : Computers Languages : en Pages : 1048
Book Description
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: Kai-Uwe Schmidt Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110642093 Category : Mathematics Languages : en Pages : 354
Book Description
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: Dirk Hachenberger Publisher: Springer Nature ISBN: 3030608069 Category : Mathematics Languages : en Pages : 785
Book Description
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.
Author: Gary L. Mullen Publisher: American Mathematical Soc. ISBN: 0821844180 Category : Computers Languages : en Pages : 190
Book Description
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Author: David J. Covert Publisher: American Mathematical Soc. ISBN: 1470460319 Category : Education Languages : en Pages : 181
Book Description
Erdős asked how many distinct distances must there be in a set of n n points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of a compact set in order to guarantee that the set of distinct distances has positive Lebesgue measure in R R. The finite field distance problem poses the analogous question in a vector space over a finite field. The problem is relatively new but remains tantalizingly out of reach. This book provides an accessible, exciting summary of known results. The tools used range over combinatorics, number theory, analysis, and algebra. The intended audience is graduate students and advanced undergraduates interested in investigating the unknown dimensions of the problem. Results available until now only in the research literature are clearly explained and beautifully motivated. A concluding chapter opens up connections to related topics in combinatorics and number theory: incidence theory, sum-product phenomena, Waring's problem, and the Kakeya conjecture.
Author: Larry Guth Publisher: American Mathematical Soc. ISBN: 1470428903 Category : Mathematics Languages : en Pages : 287
Book Description
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: Kai-Uwe Schmidt
Author: Kai-Uwe Schmidt
Author: Rudolf Lidl
Author: Xiang-dong Hou
Author: Gary L. Mullen
Author: Kai-Uwe Schmidt
Author: Dirk Hachenberger
Author: Gary L. Mullen
Author: Richard P. Stanley
Author: David J. Covert
Author: Larry Guth