This document provides an introduction to Galois groups, which characterize the symmetries of the roots of polynomial equations. It discusses how Galois groups describe the relationships between roots and the transformations that map one root to another. Specifically, it examines the cubic equation x3 - 3x + 1 = 0 in detail, finding its three real roots and demonstrating that their relationships form a cyclic group C3, which is the Galois group of this equation. Finally, it introduces the more general concept of an algebraic field and the Galois procedure for solving polynomial equations.
This document provides an introduction to Galois groups, which characterize the symmetries of the roots of polynomial equations. It discusses how Galois groups describe the relationships between roots and the transformations that map one root to another. Specifically, it examines the cubic equation x3 - 3x + 1 = 0 in detail, finding its three real roots and demonstrating that their relationships form a cyclic group C3, which is the Galois group of this equation. Finally, it introduces the more general concept of an algebraic field and the Galois procedure for solving polynomial equations.
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El documento lista y describe recursos didácticos de la Web 2.0 como Wikis, videos, redes sociales, mapas, blogs, agregadores de contenido, comunicación, fotos, gráficos y presentaciones. Incluye Wikispaces, Youtube, Facebook, Google Maps, Blogger, Google, Skype, Panoramio, Gliffy y SlideShare como ejemplos de estos recursos, junto con enlaces ejemplificando su uso.