Galois theory (Q2883337)

The first edition of the author's comprehensive textbook on classical Galois theory appeared in 2004 and has become one of the great standard primers on the subject from that time on. The outstanding features of this excellent text have been described at length in the review in [Zbl 1057.12002] of the original edition, and therefore we may refer to that exhaustive account as for details and appraisals. NEWLINENEWLINEFor the present second edition of the book, the well-tried text of which has been left basically intact, a few changes have been made. Apart from the correction of numerous typographical errors and the addition of sixteen new references to the bibliography, the notation section was expanded to include all notation used in the text, and some exercises were replaced by others, with a gain of six exercises altogether. However, and more importantly, some new material has been added, too. More precisely, Section 13.3 (on computing Galois groups of polynomials) contains now a new subsection devoted to the Galois group of irreducible separable quartics in all characteristics of the ground field, based on ideas of the author's colleague Keith Conrad.NEWLINENEWLINE NEWLINEMoreover, the discussion of the use of Maple for computations with symmetric polynomials (Section 2.3) has been updated, and there is a new Appendix C on possible student projects for self-study. Most of the projects listed here are reasonably short and manageable, where many of them are based on optional sections of the text. Finally, the author has provided a new chart showing the relation between the (now as before) fifteen chapters and the four main parts of the book, which helps both students and instructors use the book more efficiently.NEWLINENEWLINE NEWLINEIn view of these improvements and enhancements, the current second edition of this unique introduction to classical (and practical) Galois theory has become even more useful and valuable for students and teachers. As already stated in the review of the first edition, this textbook reflects the beauty and significance of the mathematical jewel ``Galois theory'' just impressively as the author's passion, expertise, mathematical culture, and instructional mastery. There is barely a better introduction to the subject, in all its theoretical and practical aspects, than the book under review.