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Author: Jörg Bewersdorff
Publisher: American Mathematical Soc.
ISBN: 0821838172
Category : Mathematics
Languages : en
Pages : 202
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Book Description
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: Jörg Bewersdorff
Publisher: American Mathematical Soc.
ISBN: 0821838172
Category : Mathematics
Languages : en
Pages : 202
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Book Description
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: Emil Artin
Publisher:
ISBN:
Category : Galois theory
Languages : en
Pages : 82
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Book Description
Author: Tamás Szamuely
Publisher: Cambridge University Press
ISBN: 1139481142
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.
Author: Patrick Morandi
Publisher: Springer Science & Business Media
ISBN: 1461240409
Category : Mathematics
Languages : en
Pages : 294
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Book Description
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: D. J. H. Garling
Publisher: Cambridge University Press
ISBN: 9780521312493
Category : Mathematics
Languages : en
Pages : 180
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Book Description
This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.
Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1475768982
Category : Mathematics
Languages : en
Pages : 380
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Book Description
The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
Author: Marius van der Put
Publisher: Springer Science & Business Media
ISBN: 3642557503
Category : Mathematics
Languages : en
Pages : 446
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Book Description
From 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: Jacques Sauloy
Publisher: American Mathematical Soc.
ISBN: 1470430959
Category : Mathematics
Languages : en
Pages : 303
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Book Description
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.
Author: Juliusz Brzeziński
Publisher: Springer
ISBN: 331972326X
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This 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.
Author: M. M. Postnikov
Publisher: Courier Corporation
ISBN: 9780486435183
Category : Mathematics
Languages : en
Pages : 132
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Book Description
Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. The source of modern abstract algebra and one of abstract algebra's most concrete applications, Galois theory serves as an excellent introduction to group theory and provides a strong, historically relevant motivation for the introduction of the basics of abstract algebra. This two-part treatment begins with the elements of Galois theory, focusing on related concepts from field theory, including the structure of important types of extensions and the field of algebraic numbers. A consideration of relevant facts from group theory leads to a survey of Galois theory, with discussions of normal extensions, the order and correspondence of the Galois group, and Galois groups of a normal subfield and of two fields. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n ≥ 5.
