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Galois theory through exercises

Brzezinski, Juliusz.

Galois theory through exercises

Record Type:	Electronic resources : Monograph/item
Title/Author:	Galois theory through exercisesby Juliusz Brzezinski.
Author:	Brzezinski, Juliusz.
Published:	Cham :Springer International Publishing :2018.
Description:	xvii, 293 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Galois theoryTextbooks.
Online resource:	http://dx.doi.org/10.1007/978-3-319-72326-6
ISBN:	9783319723266$q(electronic bk.)

Galois theory through exercises
Brzezinski, Juliusz.

Galois theory through exercises[electronic resource] /by Juliusz Brzezinski. - Cham :Springer International Publishing :2018. - xvii, 293 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

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.

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.

ISBN: 9783319723266$q(electronic bk.)

Standard No.: 10.1007/978-3-319-72326-6doiSubjects--Topical Terms:

444563
Galois theory
--Textbooks.

LC Class. No.: QA214 / .B794 2018

Dewey Class. No.: 512.32

Galois theory through exercises
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100 1 $a Brzezinski, Juliusz. $3 809973
245 1 0 $a Galois theory through exercises $h [electronic resource] / $c by Juliusz Brzezinski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xvii, 293 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer undergraduate mathematics series, $x 1615-2085
505 0 $a 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.
520 $a 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.
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650 2 4 $a Field Theory and Polynomials. $3 274058
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Group Theory and Generalizations. $3 274819
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830 0 $a Springer undergraduate mathematics series. $3 544774
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