國立虎尾科技大學 |

Galois theory through exercises

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Galois theory through exercises/ by Juliusz Brzezinski.
作者:	Brzezinski, Juliusz.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xvii, 293 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Galois theory - Congresses. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-72326-6
ISBN:	9783319723266

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

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

1077347
Galois theory
--Congresses.

LC Class. No.: QA214 / .B794 2018

Dewey Class. No.: 512.32

Galois theory through exercises
LDR:02651nam a2200325 a 4500 001 925216
003 DE-He213
005 20181011141230.0
006 m d
007 cr nn 008maaau
008 190625s2018 gw s 0 eng d
020 $a 9783319723266 $q (electronic bk.)
020 $a 9783319723259 $q (paper)
024 7 $a 10.1007/978-3-319-72326-6 $2 doi
035 $a 978-3-319-72326-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA214 $b .B794 2018
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512.32 $2 23
090 $a QA214 $b .B916 2018
100 1 $a Brzezinski, Juliusz. $3 1202765
245 1 0 $a Galois theory through exercises $h [electronic resource] / $c by Juliusz Brzezinski.
260 $a Cham : $c 2018. $b Springer International Publishing : $b Imprint: Springer,
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.
650 0 $a Galois theory $v Congresses. $3 1077347
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Field Theory and Polynomials. $3 672025
650 2 4 $a Number Theory. $3 672023
650 2 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Group Theory and Generalizations. $3 672112
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Springer undergraduate mathematics series. $3 839247
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-72326-6
950 $a Mathematics and Statistics (Springer-11649)