Overview
- 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
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (19 chapters)
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Front Matter
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
About this book
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.
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Authors and Affiliations
About the author
Bibliographic Information
Book Title: Galois Theory Through Exercises
Authors: Juliusz Brzeziński
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-72326-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-72325-9Published: 03 April 2018
eBook ISBN: 978-3-319-72326-6Published: 21 March 2018
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XVII, 293
Number of Illustrations: 12 b/w illustrations
Topics: Field Theory and Polynomials, Number Theory, Algebraic Geometry, Associative Rings and Algebras, Commutative Rings and Algebras, Group Theory and Generalizations