Galois Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Theories write by Francis Borceux. This book was released on 2001-02-22. Galois Theories available in PDF, EPUB and Kindle. Develops Galois theory in a more general context, emphasizing category theory.
Algebra and Galois Theories
Algebra and Galois Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebra and Galois Theories write by Régine Douady. This book was released on 2020-07-13. Algebra and Galois Theories available 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.
Galois Theory
Galois Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Theory write by Steven H. Weintraub. This book was released on 2008-10-20. Galois Theory available 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.
Differential Galois Theory through Riemann-Hilbert Correspondence
Differential Galois Theory through Riemann-Hilbert Correspondence - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Galois Theory through Riemann-Hilbert Correspondence write by Jacques Sauloy. This book was released on 2016-12-07. Differential Galois Theory through Riemann-Hilbert Correspondence available in PDF, EPUB and Kindle. 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.
Galois Theory Through Exercises
Galois Theory Through Exercises - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Theory Through Exercises write by Juliusz Brzeziński. This book was released on 2018-03-21. Galois Theory Through Exercises available in PDF, EPUB and Kindle. 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.
