(Ebook) Galois Theory by David A. Cox ISBN 9781118072059, 9781118218426, 1118072057, 1118218426, B00DWB6PMG

(Ebook) Galois Theory by David A. Cox ISBN 9781118072059, 9781118218426, 1118072057, 1118218426, B00DWB6PMG

Praise for the First Edition". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!"— Monatshefte fur MathematikGalois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galois theory of origami.In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including:The contributions of Lagrange, Galois, and KroneckerHow to compute Galois groupsGalois's results about irreducible polynomials of prime or prime-squared degreeAbel's theorem about geometric constructions on the lemniscatesGalois groups of quartic polynomials in all characteristicsThroughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study.Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics.ContentsPreface to the First Edition xviiPreface to the Second Edition xxiNotation xxiii1 Basic Notation xxiii2 Chapter-by-Chapter Notation xxvPART I POLYNOMIALS1 Cubic Equations 31.1 Cardan's Formulas 41.2 Permutations of the Roots 101.3 Cubic Equations over the Real Numbers 152 Symmetric Polynomials 252.1 Polynomials of Several Variables 25…