Algebra And Galois Theories PDF Download
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Author | : Régine Douady |
Publisher | : Springer Nature |
Total Pages | : 462 |
Release | : 2020-07-13 |
Genre | : Mathematics |
ISBN | : 3030327965 |
Download Algebra and Galois Theories Book in PDF, ePub and Kindle
Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Author | : Francis Borceux |
Publisher | : Cambridge University Press |
Total Pages | : 360 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780521803090 |
Download Galois Theories Book in PDF, ePub and Kindle
Develops Galois theory in a more general context, emphasizing category theory.
Author | : Steven H. Weintraub |
Publisher | : Springer Science & Business Media |
Total Pages | : 220 |
Release | : 2008-10-20 |
Genre | : Mathematics |
ISBN | : 0387875751 |
Download Galois Theory Book in PDF, ePub and Kindle
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.
Author | : Emil Artin |
Publisher | : American Mathematical Soc. |
Total Pages | : 137 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821841297 |
Download Algebra with Galois Theory Book in PDF, ePub and Kindle
'Algebra with Galois Theory' is based on lectures by Emil Artin. The book is an ideal textbook for instructors and a supplementary or primary textbook for students.
Author | : M.M. Postnikov |
Publisher | : Elsevier |
Total Pages | : 123 |
Release | : 2014-07-10 |
Genre | : Mathematics |
ISBN | : 1483156478 |
Download Foundations of Galois Theory Book in PDF, ePub and Kindle
Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.
Author | : Siegfried Bosch |
Publisher | : Springer |
Total Pages | : 352 |
Release | : 2018-11-02 |
Genre | : Mathematics |
ISBN | : 3319951777 |
Download Algebra Book in PDF, ePub and Kindle
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.
Author | : Rajnikant Sinha |
Publisher | : Springer Nature |
Total Pages | : 351 |
Release | : 2019-12-28 |
Genre | : Mathematics |
ISBN | : 9811398496 |
Download Galois Theory and Advanced Linear Algebra Book in PDF, ePub and Kindle
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
Author | : Jörg Bewersdorff |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821838172 |
Download Galois Theory for Beginners Book in PDF, ePub and Kindle
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.
Author | : Patrick Morandi |
Publisher | : Springer Science & Business Media |
Total Pages | : 294 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461240409 |
Download Field and Galois Theory Book in PDF, ePub and Kindle
In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.
Author | : Edgar Dehn |
Publisher | : Courier Corporation |
Total Pages | : 225 |
Release | : 2012-09-05 |
Genre | : Mathematics |
ISBN | : 0486155102 |
Download Algebraic Equations Book in PDF, ePub and Kindle
Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.