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Galois Theory Through Exercises

Galois Theory Through Exercises

Paperback

Series: Springer Undergraduate Mathematics

AlgebraGeneral MathematicsGeometry

ISBN10: 3319723251
ISBN13: 9783319723259
Publisher: Springer Nature
Published: Apr 3 2018
Pages: 293
Weight: 0.97
Height: 0.65 Width: 6.14 Depth: 9.21
Language: English
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.

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Algebra