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Feldname	Details
Dewey Class	512.3
Titel	Galois Theory Through Exercises ([EBook]) / by Juliusz Brzezinski.
Verfasser	Brzezinski, Juliusz
Other name(s)	SpringerLink (Online service)
Veröffentl	Cham : Springer International Publishing , 2018.
Physical Details	XVII, 293 p. 12 illus. : online resource.
Reihe	Springer undergraduate mathematics series 1615-2085
ISBN	9783319723266
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-72326-6
LINKS ZU 'VERWANDTEN WERKEN	Schlagwörter: . Algebra . Associative rings . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Galois theory . Group theory . Group Theory and Generalizations . Number Theory . Rings (Algebra) . Authors: Brzezinski, Juliusz . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 512.3 .

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Galois Theory Through Exercises

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