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Exploratory Galois Theory - John Swallow

Exploratory Galois Theory

Hardcover Published: 3rd May 2016
ISBN: 9780521836500
Number Of Pages: 208

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Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. The author organizes the theory around natural questions about algebraic numbers, and exercises with hints and proof sketches encourage students' participation in the development. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. Exploratory Galois Theory includes classical applications, from ruler-and-compass constructions to solvability by radicals, and also outlines the generalization from subfields of the complex numbers to arbitrary fields. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.

'The exploration-based approach to the subject is very down-to-earth, entertaining, motivating, encouraging and enlightening, making the text highly suitable for undergraduate courses, for seminars, or for self-paced independent study by interested beginners.' Zentralblatt MATH
"...a beautiful and comprehensive expostition of the abstract theory is greatly enhanced by the computational aspects with the help of software." MAA Reviews, Alvaro Lozano-Robledo, Cornell University

Preliminaries
Algebraic numbers, field extensions, and minimal polynomials
Working with algebraic numbers, field extensions, and minimal polynomials
Multiply-generated fields
The Galois correspondence
Some classical topics
Historical note
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521836500
ISBN-10: 0521836506
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 208
Published: 3rd May 2016
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 24.18 x 19.91  x 2.18
Weight (kg): 0.62

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