Galois Theory Through Exercises
Bok, 2018

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.

Field extension, Galois group, Normal extension, Separable extension, Galois extension, Solvable equation

Författare

Juliusz Brzezinski

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Ämneskategorier

Algebra och logik

DOI

10.1007/978-3-319-72326-6

ISBN

978-3-319-72325-9

Utgivare

Springer

Mer information

Senast uppdaterat

2019-01-12