Supplementary Problems

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


In this chapter, we present 100 problems without solutions (but occasionally with some hints, comments or references). These are original, interesting or challenging problems covering various aspects of Galois theory. Several of these problems can be used as a starting point for student projects, such as problems related to the normal core of groups, Galois index, the notion of elements of field extensions essentially defined over a subfield. Some of the problems are suitably structured in order to introduce some interesting topics that are typically not covered in standard texts on the subject, incl. Dedekind’s duality, Tschirnhausen’s transformations and the lunes of Hippocrates.


  1. [B]
    G.M. Bergman, Exercises supplementing those in Ian Stewart’s “Galois Theory”, 3rd Edition,
  2. [Ca]
    J.S. Calcut, Rationality and the Tangent Function,
  3. [E]
    H.M. Edwards, Essays in constructive mathematics, Springer, 2005.Google Scholar
  4. [G]
    K. Girstmair, Hippocrates’ Lunes and Transcendence, Expo. Math., 21 (2003), 179–183.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [MP]
  6. [Tsch]
    N.G. Tschebotaröw, Grundzüge der Galois’schen Theorie, H. Schwerdtfeger (ed.), P. Noordhoff, 1950.Google Scholar
  7. [V]
    J.K. Verma, Exercises in field theory and Galois theory,

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Juliusz Brzeziński
    • 1
    • 2
  1. 1.Department of Mathematical SciencesUniversity of GothenburgGöteborgSweden
  2. 2.Chalmers University of TechnologyGöteborgSweden

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