03610nam a22005655i 4500 978-3-031-66182-2 DE-He213 20251030113249.0 cr nn 008mamaa 241029s2024 sz | s |||| 0|eng d 9783031661822 978-3-031-66182-2 10.1007/978-3-031-66182-2 doi QA247-247.45 QA161.P59 PBF bicssc MAT002010 bisacsh PBF thema Hernandez, David. author. aut http://id.loc.gov/vocabulary/relators/aut 86769 Introduction to Galois Theory [electronic resource] / by David Hernandez, Yves Laszlo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVII, 193 p. 47 illus., 11 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Undergraduate Mathematics Series, 2197-4144 1 Invitation to Galois Theory -- 2 Basic Concepts of Group Theory -- 3 Basic Concepts of Ring Theory -- 4 Basic Concepts of Algebras Over a Field -- 5 Finite Fields, Perfect Fields -- 6 The Galois Correspondence -- 7 Addendum: Infinite Galois Correspondence -- 8 Cyclotomy and Constructibility -- 9 Solvability by Radicals -- 10 Reduction Modulo p -- 11 Complements -- 12 Review Exercises -- 13 Solutions to Exercises. This textbook provides an undergraduate introduction to Galois theory and its most notable applications. Galois theory was born in the 19th century to study polynomial equations. Both powerful and elegant, this theory was at the origin of a substantial part of modern algebra and has since undergone considerable development. It remains an extremely active research subject and has found numerous applications beyond pure mathematics. In this book, the authors introduce Galois theory from a contemporary point of view. In particular, modern methods such as reduction modulo prime numbers and finite fields are introduced and put to use. Beyond the usual applications of ruler and compass constructions and solvability by radicals, the book also includes topics such as the transcendence of e and π, the inverse Galois problem, and infinite Galois theory. Based on courses of the authors at the École Polytechnique, the book is aimed at students with a standard undergraduate background in (mostly linear) algebra. It includes a collection of exam questions in the form of review exercises, with detailed solutions. Algebraic fields. 70148 Polynomials. 64269 Group theory. 70149 Number theory. Field Theory and Polynomials. 70153 Group Theory and Generalizations. 70154 Number Theory. Laszlo, Yves. author. aut http://id.loc.gov/vocabulary/relators/aut 86770 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031661815 Printed edition: 9783031661839 Springer Undergraduate Mathematics Series, 2197-4144 75368 https://doi.org/10.1007/978-3-031-66182-2 ZDB-2-SMA ZDB-2-SXMS 64570 64570