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Springer Undergraduate Mathematics Series

Galois Theory Through Exercises

Authors: Brzeziński, Juliusz

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  • 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
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eBook 18,18 €
28,88 € (listprice)
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valid through July 31, 2020
  • ISBN 978-3-319-72326-6
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Softcover 23,91 €
36,39 € (listprice)
price for Spain (gross)
valid through July 31, 2020
  • ISBN 978-3-319-72325-9
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About this Textbook

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.

About the authors

Juliusz Brzeziński 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.

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)

Table of contents (19 chapters)

Table of contents (19 chapters)
  • Solving Algebraic Equations

    Pages 1-8

    Brzeziński, Juliusz

  • Field Extensions

    Pages 9-11

    Brzeziński, Juliusz

  • Polynomials and Irreducibility

    Pages 13-17

    Brzeziński, Juliusz

  • Algebraic Extensions

    Pages 19-25

    Brzeziński, Juliusz

  • Splitting Fields

    Pages 27-33

    Brzeziński, Juliusz

Buy this book

eBook 18,18 €
28,88 € (listprice)
price for Spain (gross)
valid through July 31, 2020
  • ISBN 978-3-319-72326-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 23,91 €
36,39 € (listprice)
price for Spain (gross)
valid through July 31, 2020
  • ISBN 978-3-319-72325-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Galois Theory Through Exercises
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-72326-6
DOI
10.1007/978-3-319-72326-6
Softcover ISBN
978-3-319-72325-9
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XVII, 293
Number of Illustrations
12 b/w illustrations
Topics

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