finite fields encyclopedia of mathematics and its applications

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Finite Fields

Author : Rudolf Lidl
ISBN : 0521392314
Genre : Mathematics
File Size : 58. 76 MB
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This book is devoted entirely to the theory of finite fields.

Handbook Of Finite Fields

Author : Gary L. Mullen
ISBN : 9781439873823
Genre : Computers
File Size : 24. 17 MB
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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 each chapter is self contained and peer reviewed. The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials, special functions, sequences, algorithms, curves, and related computational aspects. The final part describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas. The book provides a comprehensive index and easy access to over 3,000 references, enabling you to quickly locate up-to-date facts and results regarding finite fields.

Finite Fields And Applications

Author : Dieter Jungnickel
ISBN : 9783642567551
Genre : Mathematics
File Size : 58. 30 MB
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Skew Fields

Author : Paul Moritz Cohn
ISBN : 0521432170
Genre : Mathematics
File Size : 76. 21 MB
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This work offers a comprehensive account of skew fields and related mathematics.

Finite Fields And Applications

Author : Gary L. Mullen
ISBN : 9783540246336
Genre : Mathematics
File Size : 74. 87 MB
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Finite Precision Number Systems And Arithmetic

Author : Peter Kornerup
ISBN : 9781139643559
Genre : Mathematics
File Size : 51. 44 MB
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Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.

Random Graphs

Author : Valentin Fedorovich Kolchin
ISBN : 0521440815
Genre : Mathematics
File Size : 78. 62 MB
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Results of research on classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields.

Computation With Finitely Presented Groups

Author : Charles C. Sims
ISBN : 0521432138
Genre : Mathematics
File Size : 20. 73 MB
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Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Applied Abstract Algebra

Author : Rudolf Lidl
ISBN : 9781475729412
Genre : Mathematics
File Size : 63. 27 MB
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Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.

Finite Fields For Computer Scientists And Engineers

Author : Robert J. McEliece
ISBN : 9781461319832
Genre : Technology & Engineering
File Size : 21. 94 MB
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This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.

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