Lectures On Finite Fields PDF Download
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Author | : Zhe-Xian Wan |
Publisher | : World Scientific |
Total Pages | : 360 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9789812385703 |
Download Lectures on Finite Fields and Galois Rings Book in PDF, ePub and Kindle
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Author | : Zhe-xian Wan |
Publisher | : World Scientific Publishing Company |
Total Pages | : 354 |
Release | : 2003-08-12 |
Genre | : Mathematics |
ISBN | : 9813102268 |
Download Lectures On Finite Fields And Galois Rings Book in PDF, ePub and Kindle
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
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 | : Zhexian Wan |
Publisher | : |
Total Pages | : |
Release | : 2003 |
Genre | : |
ISBN | : 9789812795076 |
Download Lectures on Finite Fields and Galois Rings Book in PDF, ePub and Kindle
Author | : N. Jacobson |
Publisher | : Springer |
Total Pages | : 304 |
Release | : 1975 |
Genre | : Mathematics |
ISBN | : |
Download Lectures in Abstract Algebra Book in PDF, ePub and Kindle
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.
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 | : W. M. Schmidt |
Publisher | : |
Total Pages | : 284 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9783662206843 |
Download Equations Over Finite Fields Book in PDF, ePub and Kindle
Author | : Wolfgang M. Schmidt |
Publisher | : |
Total Pages | : 338 |
Release | : 1975 |
Genre | : Diophantine analysis |
ISBN | : |
Download Lectures on equations over finite fields Book in PDF, ePub and Kindle
Author | : Zhe-xian Wan |
Publisher | : World Scientific Publishing Company |
Total Pages | : 387 |
Release | : 2011-09-13 |
Genre | : Mathematics |
ISBN | : 9813108223 |
Download Finite Fields And Galois Rings Book in PDF, ePub and Kindle
A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.
Author | : Adriano M. Garsia |
Publisher | : Springer |
Total Pages | : 232 |
Release | : 2020-10-07 |
Genre | : Mathematics |
ISBN | : 9783030583729 |
Download Lectures in Algebraic Combinatorics Book in PDF, ePub and Kindle
Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.