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Galois Theory Through Exercises

  • Juliusz Brzeziński

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Juliusz Brzeziński
    Pages 1-8
  3. Juliusz Brzeziński
    Pages 9-11
  4. Juliusz Brzeziński
    Pages 13-17
  5. Juliusz Brzeziński
    Pages 19-25
  6. Juliusz Brzeziński
    Pages 27-33
  7. Juliusz Brzeziński
    Pages 35-41
  8. Juliusz Brzeziński
    Pages 43-45
  9. Juliusz Brzeziński
    Pages 47-50
  10. Juliusz Brzeziński
    Pages 51-58
  11. Juliusz Brzeziński
    Pages 59-63
  12. Juliusz Brzeziński
    Pages 65-71
  13. Juliusz Brzeziński
    Pages 73-75
  14. Juliusz Brzeziński
    Pages 77-80
  15. Juliusz Brzeziński
    Pages 81-83
  16. Juliusz Brzeziński
    Pages 85-91
  17. Juliusz Brzeziński
    Pages 93-107
  18. Juliusz Brzeziński
    Pages 109-150
  19. Juliusz Brzeziński
    Pages 151-175
  20. Juliusz Brzeziński
    Pages 177-234
  21. Back Matter
    Pages 235-293

About this book

Introduction

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.

Keywords

Galois theory Galois theory exercises Galois theory computer-assisted examples cubic and quartic equations finite fields cyclotomic fields Galois resolvents lunes of Hippocrates inverse Galois problem solving algebraic equations of low degrees field extensions zeros of polynomials algebraic field extensions automorphism groups of fields Galois groups of finite field extensions Galois extensions Galois modules Solvability of equations

Authors and affiliations

  • Juliusz Brzeziński
    • 1
  1. 1.Department of Mathematical SciencesUniversity of GothenburgSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-72326-6
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-72325-9
  • Online ISBN 978-3-319-72326-6
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site