- 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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- About this Textbook
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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
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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
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“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)
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Solving Algebraic Equations
Pages 1-8
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Field Extensions
Pages 9-11
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Polynomials and Irreducibility
Pages 13-17
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Algebraic Extensions
Pages 19-25
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Splitting Fields
Pages 27-33
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Table of contents (19 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Galois Theory Through Exercises
- Authors
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- Juliusz Brzeziński
- 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
