TL;DR
This paper presents an accessible introduction to Galois theory, connecting abstract algebraic concepts with historical problems of solving polynomials by radicals, suitable for undergraduates and graduates.
Contribution
It offers a concise, minimally prerequisite-based textbook that links modern algebraic structures to their historical origins in polynomial solvability.
Findings
Clarifies the connection between Galois groups and polynomial solvability
Provides a pedagogical approach to teaching Galois theory
Bridges abstract algebra with historical mathematical problems
Abstract
Born from years of teaching undergraduate and graduate algebra courses at Chongqing University, this text is designed to introduce Galois theory while minimizing prerequisites. It seeks to reconnect the abstract machinery of modern algeba: groups, rings, and fields with the historical problem that inspired its creation: determining when a polynomial can be solved by radicals. By anchoring abstract concepts in concrete motivation, we hope to illuminate both the ``how" and the ``why" of algebraic structures.
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Taxonomy
TopicsPolynomial and algebraic computation · History and Theory of Mathematics · Algebraic Geometry and Number Theory