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Springer Undergraduate Mathematics Ser.: Galois Theory Through Exercises by Juliusz Brzeziński (2018, Trade Paperback)

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About this product

Product Identifiers

PublisherSpringer International Publishing A&G

ISBN-103319723251

ISBN-139783319723259

eBay Product ID (ePID)240415296

Product Key Features

Number of PagesXvii, 293 Pages

Publication NameGalois Theory Through Exercises

LanguageEnglish

Publication Year2018

SubjectAlgebra / Abstract, Number Theory, Algebra / General, Geometry / Algebraic

TypeTextbook

Subject AreaMathematics

AuthorJuliusz BrzezińSki

SeriesSpringer Undergraduate Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Weight167.4 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Reviews"This book contains a collection of exercises in Galois theory. ... The book provides the readers with a solid exercise-based introduction to classical Galois theory; it will be useful for self-study or for supporting a lecture course." (Franz Lemmermeyer, zbMATH 1396.12001, 2018)

Number of Volumes1 vol.

IllustratedYes

Table Of Content1 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.

SynopsisThis 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.

LC Classification NumberQA247-247.45