Enroll Course: https://www.coursera.org/learn/theorie-de-galois
If you have ever been intrigued by the world of polynomials and the underlying structures that govern their roots, then the Coursera course ‘Introduction à la théorie de Galois’ is a must-take. This course delves into the fascinating realm of Galois theory, a cornerstone of modern algebra that connects polynomial equations with group theory.
### Course Overview
The course begins with a solid introduction to the problems surrounding polynomial equations, gradually leading students through the classical criteria for solvability. It covers essential concepts such as field extensions, algebraically closed fields, and the primitive element lemma, providing a robust foundation for understanding the more complex aspects of Galois theory.
### Syllabus Breakdown
The syllabus is thoughtfully structured, starting with basic polynomial results and moving into advanced topics. Here’s a brief overview of what you can expect:
1. **Introduction**: An overview of polynomial equations and preliminary results.
2. **Extensions de corps**: Understanding algebraic closures and the primitive element lemma.
3. **Polynôme minimal**: Exploring conjugate elements.
4. **Corps fini**: Delving into finite fields and their automorphisms.
5. **Théorie des groupes I & II**: Covering basic group theory and the non-solvability of symmetric groups.
6. **Correspondance de Galois**: The Galois correspondence and its implications.
7. **Cyclotomie**: General cyclotomic extensions and Kummer theory.
8. **Théorèmes de résolubilité de Galois**: Criteria for solvability and Galois theory in degree p.
9. **Réduction mod p**: Investigating Galois groups of polynomials through reduction modulo p.
10. **Compléments**: Applications of cyclotomic fields and more.
### Why You Should Enroll
This course is not just for mathematicians; it is suitable for anyone with a keen interest in algebra and its applications. The teaching style is engaging, and the course materials are well-organized, making complex topics accessible. The hands-on exercises and quizzes reinforce learning, ensuring that you can apply the concepts effectively.
### Conclusion
In summary, ‘Introduction à la théorie de Galois’ is an excellent course that provides a deep understanding of Galois theory. Whether you are a student, a professional, or simply a math enthusiast, this course will enrich your knowledge and appreciation of algebra. I highly recommend enrolling and embarking on this mathematical journey!
### Tags
– Galois Theory
– Coursera
– Mathematics
– Algebra
– Polynomial Equations
– Group Theory
– Online Learning
– Education
– Field Extensions
– Mathematical Concepts
Enroll Course: https://www.coursera.org/learn/theorie-de-galois