03396nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001700172050001400189072001600203072002300219072001500242100008600257245009300343250001800436264006900454300006600523336002600589337002600615338003600641347002400677490005800701505042300759520112301182650002902305650002402334650002502358650001902383650004102402650004502443650001902488700008202507710003402589773002602623776003602649776003602685830006502721856004602786912001402832912001502846999001702861978-3-031-66182-2DE-He21320251030113249.0cr nn 008mamaa241029s2024    sz |    s    |||| 0|eng d  a97830316618229978-3-031-66182-27 a10.1007/978-3-031-66182-22doi 4aQA247-247.45 4aQA161.P59 7aPBF2bicssc 7aMAT0020102bisacsh 7aPBF2thema1 aHernandez, David.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98676910aIntroduction to Galois Theoryh[electronic resource] /cby David Hernandez, Yves Laszlo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVII, 193 p. 47 illus., 11 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Undergraduate Mathematics Series,x2197-41440 a1 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.  aThis 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. 0aAlgebraic fields.970148 0aPolynomials.964269 0aGroup theory.970149 0aNumber theory.14aField Theory and Polynomials.97015324aGroup Theory and Generalizations.97015424aNumber Theory.1 aLaszlo, Yves.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9867702 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303166181508iPrinted edition:z9783031661839 0aSpringer Undergraduate Mathematics Series,x2197-414497536840uhttps://doi.org/10.1007/978-3-031-66182-2  aZDB-2-SMA  aZDB-2-SXMS  c64570d64570