Enroll Course: https://www.coursera.org/learn/theorie-de-galois
Are you fascinated by the symmetries of polynomial roots and the underlying structures that govern their behavior? The Coursera course “Introduction à la théorie de Galois” offers an in-depth exploration of Galois theory, a fundamental area of abstract algebra that has shaped modern mathematics. This course provides a comprehensive overview, starting from classical concepts like the non-solvability of certain polynomial equations, to advanced techniques involving Galois groups and reduction modulo prime numbers.
The syllabus is thoughtfully structured, beginning with an introduction to polynomial roots and extending into complex topics such as field extensions, minimal polynomials, and Galois correspondence. It covers essential algebraic structures, including finite fields, and delves into the properties of groups, with a special focus on resolvable and non-resolvable groups. Notably, the course explores cyclotomic extensions, Kummer theory, and the resolvability criteria established by Galois.
What makes this course stand out is its balance between theory and practical applications. It demonstrates how reduction modulo p can be used to analyze Galois groups of integer-coefficient polynomials, ultimately leading to insights into cyclotomy and other number-theoretic phenomena.
Whether you’re a student, researcher, or math enthusiast, this course will deepen your understanding of one of the most beautiful and profound theories in mathematics. The lectures are accessible yet rigorous, making complex topics manageable with step-by-step explanations and illustrative examples.
I highly recommend “Introduction à la théorie de Galois” to anyone interested in algebra, number theory, or mathematical symmetries. Enroll today and start unraveling the elegant structures that underpin polynomial equations and their solutions.
Enroll Course: https://www.coursera.org/learn/theorie-de-galois