Galois Theory [Stewart]

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Galois Theory 
BY Ian Stewart

Summary

Galois Theory, Fourth Edition by mathematician and popular science author Ian Stewart is a comprehensive textbook tailored to educate undergraduate mathematics students on classical Galois theory and Galois groups. First published in 1973, this updated edition continues its long-standing tradition of offering a rigorous yet engaging approach to abstract algebra while aligning with modern university curricula.

 A major highlight of this fourth edition is the replacement of the traditional topological proof of the fundamental theorem of algebra with a simpler, more accessible argument based on point-set topology and standard analysis estimates. The book also features a thoroughly revised chapter on ruler-and-compass constructions, offering a more elegant framework alongside streamlined mathematical proofs. Expanding on these concepts, a new section covers angle-trisector constructions, presenting a direct and fascinating application of the core theoretical methods. 

To provide deeper context, Stewart incorporates a new retrospective chapter that examines Évariste Galois's original work and separates historical reality from common assumptions. Every core concept is thoroughly grounded with clear formulas, detailed theorems, and intuitive explanations throughout the text. The educational material is supported by over 200 exercises designed to reinforce student comprehension across various difficulty levels. 

Furthermore, the volume includes fully updated academic references and rich historical commentary to provide a complete learning experience. Ultimately, this textbook remains a staple resource that effectively bridges classical algebraic history with contemporary undergraduate mathematics education.


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