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Author: Helmut Völklein
Publisher: Cambridge University Press
Published: 1999-07-29
Total Pages: 294
ISBN-13: 9780521637473
DOWNLOAD EBOOKCollection of articles by leading experts in Galois theory, focusing on the Inverse Galois Problem.
Author: Francis Borceux
Publisher: Cambridge University Press
Published: 2001-02-22
Total Pages: 360
ISBN-13: 9780521803090
DOWNLOAD EBOOKStarting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.
Author: Julio R. Bastida
Publisher: Cambridge University Press
Published: 1984-12-28
Total Pages: 354
ISBN-13: 9780521302425
DOWNLOAD EBOOKThis 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.
Author: Marius van der Put
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 446
ISBN-13: 3642557503
DOWNLOAD EBOOKFrom the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author: Jörg Bewersdorff
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 202
ISBN-13: 0821838172
DOWNLOAD EBOOKGalois 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: M.M. Postnikov
Publisher: Elsevier
Published: 2014-07-10
Total Pages: 123
ISBN-13: 1483156478
DOWNLOAD EBOOKFoundations 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: D. J. H. Garling
Publisher: Cambridge University Press
Published: 1986
Total Pages: 180
ISBN-13: 9780521312493
DOWNLOAD EBOOKThis textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.
Author: John Swallow
Publisher: Cambridge University Press
Published: 2004-10-11
Total Pages: 224
ISBN-13: 9780521544993
DOWNLOAD EBOOKCombining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.
Author: John M. Howie
Publisher: Springer Science & Business Media
Published: 2007-10-11
Total Pages: 230
ISBN-13: 1852339861
DOWNLOAD EBOOKA 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
Author: Juliusz Brzeziński
Publisher: Springer
Published: 2018-03-21
Total Pages: 296
ISBN-13: 331972326X
DOWNLOAD EBOOKThis textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
