Galois Theory Through Exercises | Taschenbuch

Cover: 9783319723259 | Galois Theory Through Exercises | Juliusz Brzezi¿ski | Taschenbuch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Juliusz Brzezi¿ski is Professor Emeritus at the Department of Mathematical Sciences, which is a part of the University of Gothenburg and the Chalmers University of Technology, Sweden. His research concentrates on interactions between number theory, algebra and geometry of orders in algebras over global fields, in particular, in quaternion algebras. He is also interested in experimental number theory.

Zusammenfassung

Provides a hands-on approach to learning Galois theory, focusing on problem-solving exercises

Features almost 500 exercises with hints, answers or solutions

Includes Maple tutorials and exercises

Inhaltsverzeichnis

1 Solving algebraic equations.- 2 Field extensions.- 3 Polynomials and irreducibility.- 4 Algebraic extensions.- 5 Splitting fields.- 6 Automorphism groups of fields.- 7 Normal extensions.- 8 Separable extensions.- 9 Galois extensions.- 10 Cyclotomic extensions.- 11 Galois modules.- 12 Solvable groups.- 13 Solvability of equations.- 14 Geometric constructions.- 15 Computing Galois groups.- 16 Supplementary problems.- 17 Proofs of the theorems.- 18 Hints and answers.- 19 Examples and selected solutions.- Appendix: Groups, rings and fields.- References.- List of notations.- Index.

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xvii 293 S. 12 s/w Illustr. 293 p. 12 illus.
ISBN-13:	9783319723259
ISBN-10:	3319723251
Sprache:	Englisch
Herstellernummer:	978-3-319-72325-9
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Brzezi¿ski, Juliusz
Auflage:	1st ed. 2018
Hersteller:	Springer International Publishing Springer International Publishing AG Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 17 mm
Von/Mit:	Juliusz Brzezi¿ski
Erscheinungsdatum:	03.04.2018
Gewicht:	0,476 kg

Artikel-ID: 111054960