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Algebra Polynomials Galois Theory And Applications
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Book Synopsis Algebra: Polynomials, Galois Theory and Applications by : Frédéric Butin
Download or read book Algebra: Polynomials, Galois Theory and Applications written by Frédéric Butin and published by Courier Dover Publications. This book was released on 2017-01-09 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Precise, self-contained treatment advances from introductory material to extensions that contribute to a comprehensive understanding of the Galois group of a polynomial. Concludes with excellent discussions of several real-world applications. 2016 edition.
Book Synopsis Galois Theory by : Steven H. Weintraub
Download or read book Galois Theory written by Steven H. Weintraub and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.
Book Synopsis Galois Theory And Applications: Solved Exercises And Problems by : Mohamed Ayad
Download or read book Galois Theory And Applications: Solved Exercises And Problems written by Mohamed Ayad and published by World Scientific Publishing Company. This book was released on 2018-04-26 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Ayad’s aim was to create a collection of problems and exercises related to Galois Theory. In this Ayad was certainly successful. Galois Theory and Applications contains almost 450 pages of problems and their solutions. These problems range from the routine and concrete to the very abstract. Many are quite challenging. Some of the problems provide accessible presentations of material not normally seen in a first course on Galois Theory. For example, the chapter 'Galois extensions, Galois groups' begins with a wonderful problem on formally real fields that I plan on assigning to my students this fall.'MAA ReviewsThe book provides exercises and problems with solutions in Galois Theory and its applications, which include finite fields, permutation polynomials, derivations and algebraic number theory.It will be useful to the audience below:
Book Synopsis Galois Theory for Beginners: A Historical Perspective, Second Edition by : Jörg Bewersdorff
Download or read book Galois Theory for Beginners: A Historical Perspective, Second Edition written by Jörg Bewersdorff and published by American Mathematical Soc.. This book was released on 2021-07-15 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
Download or read book Galois Theory written by Ian Stewart and published by CRC Press. This book was released on 1990-05-15 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois theory is a fascinating mixture of classical and modern mathematics, and in fact provided much of the seed from which abstract algebra has grown. It is a showpiece of mathematical unification and of "technology transfer" to a range of modern applications. Galois Theory, Second Edition is a revision of a well-established and popular te
Download or read book Algebra written by Siegfried Bosch and published by Springer. This book was released on 2018-11-02 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date.
Download or read book Galois Theory written by Emil Artin and published by Courier Corporation. This book was released on 1998-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications. The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more. Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.
Download or read book Galois Theory written by David A. Cox and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to one of the most celebrated theories of mathematics Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox’s Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics. Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel’s theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. Anyone fascinated by abstract algebra will find careful discussions of such topics as: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois’s results about irreducible polynomials of prime or prime-squared degree Abel’s theorem about geometric constructions on the lemniscate With intriguing Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.
Download or read book Algebra written by Falko Lorenz and published by Springer Science & Business Media. This book was released on 2006-07-02 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.
Book Synopsis Galois Theory, Coverings, and Riemann Surfaces by : Askold Khovanskii
Download or read book Galois Theory, Coverings, and Riemann Surfaces written by Askold Khovanskii and published by Springer Science & Business Media. This book was released on 2013-09-11 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.
Book Synopsis Fields and Galois Theory by : John M. Howie
Download or read book Fields and Galois Theory written by John M. Howie and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews
Download or read book Galois Theory written by David A. Cox and published by John Wiley & Sons. This book was released on 2012-03-27 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . .will certainly fascinate anyone interested in abstractalgebra: a remarkable book!" —Monatshefte fur Mathematik Galois theory is one of the most established topics inmathematics, with historical roots that led to the development ofmany central concepts in modern algebra, including groups andfields. Covering classic applications of the theory, such assolvability by radicals, geometric constructions, and finitefields, Galois Theory, Second Edition delves into noveltopics like Abel’s theory of Abelian equations, casusirreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of severaltopics not covered in standard texts on Galois theory,including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois's results about irreducible polynomials of primeor prime-squared degree Abel's theorem about geometric constructions on thelemniscates Galois groups of quartic polynomials in allcharacteristics Throughout the book, intriguing Mathematical Notes andHistorical Notes sections clarify the discussed ideas andthe historical context; numerous exercises and examples use Mapleand Mathematica to showcase the computations related to Galoistheory; and extensive references have been added to provide readerswith additional resources for further study. Galois Theory, Second Edition is an excellent book forcourses on abstract algebra at the upper-undergraduate and graduatelevels. The book also serves as an interesting reference for anyonewith a general interest in Galois theory and its contributions tothe field of mathematics.
Book Synopsis Topological Galois Theory by : Askold Khovanskii
Download or read book Topological Galois Theory written by Askold Khovanskii and published by Springer. This book was released on 2014-10-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers. In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.
Download or read book Polynomials written by Cheon Seoung Ryoo and published by BoD – Books on Demand. This book was released on 2019-05-02 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.
Book Synopsis A Course in Galois Theory by : D. J. H. Garling
Download or read book A Course in Galois Theory written by D. J. H. Garling and published by Cambridge University Press. This book was released on 1986 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.
Download or read book Galois Theory written by Emil Artin and published by . This book was released on 2020-02 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
Book Synopsis Galois Theory and Its Algebraic Background by : D. J. H. Garling
Download or read book Galois Theory and Its Algebraic Background written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2021-07-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.
