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Lectures On Finite Fields
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Book Synopsis Lectures on Finite Fields and Galois Rings by : Zhe-Xian Wan
Download or read book Lectures on Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Finite Fields by : Xiang-dong Hou
Download or read book Lectures on Finite Fields written by Xiang-dong Hou and published by American Mathematical Soc.. This book was released on 2018-06-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Finite Fields and Galois Rings by : Zhexian Wan
Download or read book Lectures on Finite Fields and Galois Rings written by Zhexian Wan and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures in Abstract Algebra by : N. Jacobson
Download or read book Lectures in Abstract Algebra written by N. Jacobson and published by Springer. This book was released on 1975 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Equations Over Finite Fields by : W.M. Schmidt
Download or read book Equations Over Finite Fields written by W.M. Schmidt and published by Lecture Notes in Mathematics. This book was released on 1976-08 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Finite Fields by : Gary L. Mullen
Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Lectures in Algebraic Combinatorics by : Adriano M. Garsia
Download or read book Lectures in Algebraic Combinatorics written by Adriano M. Garsia and published by Springer. This book was released on 2020-10-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Fields and Galois Rings by : Zhe-Xian Wan
Download or read book Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific Publishing Company. This book was released on 2011-09-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Errata(s) Errata
Book Synopsis Lectures in Algebraic Combinatorics by : Adriano M. Garsia
Download or read book Lectures in Algebraic Combinatorics written by Adriano M. Garsia and published by Springer Nature. This book was released on 2020-10-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Visual Group Theory by : Nathan Carter
Download or read book Visual Group Theory written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Book Synopsis Finite-Dimensional Division Algebras over Fields by : Nathan Jacobson
Download or read book Finite-Dimensional Division Algebras over Fields written by Nathan Jacobson and published by Springer Science & Business Media. This book was released on 2009-12-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
Book Synopsis Class Field Theory by : Jürgen Neukirch
Download or read book Class Field Theory written by Jürgen Neukirch and published by Springer Science & Business Media. This book was released on 2013-04-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields.
Book Synopsis Introduction to Finite Fields and Their Applications by : Rudolf Lidl
Download or read book Introduction to Finite Fields and Their Applications written by Rudolf Lidl and published by . This book was released on 1986 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book presents an introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications. The second part is devoted to a discussion of the most important applications of finite fields especially information theory, algebraic coding theory and cryptology (including some very recent material that has never before appeared in book form). There is also a chapter on applications within mathematics, such as finite geometries. combinatorics. and pseudorandom sequences. Worked-out examples and list of exercises found throughout the book make it useful as a textbook.
Book Synopsis Lecture Notes on Motivic Cohomology by : Carlo Mazza
Download or read book Lecture Notes on Motivic Cohomology written by Carlo Mazza and published by American Mathematical Soc.. This book was released on 2006 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis Fields and Rings by : Irving Kaplansky
Download or read book Fields and Rings written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1972 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Book Synopsis Finite Fields, with Applications to Combinatorics by : Kannan Soundararajan
Download or read book Finite Fields, with Applications to Combinatorics written by Kannan Soundararajan and published by American Mathematical Society. This book was released on 2022-11-09 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
