Galois Theory Courses and Certifications

Insights into Mathematics

Galois Theory II - Historical Introduction to Polynomial Equations

Historical exploration of Galois' insights on polynomial equations, focusing on field extensions and symmetry groups. Explains the key to understanding equation solvability and the quintic's insolvability.

• YouTube
• 30 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Solvable Groups: Polynomial Solvability and Galois Theory - Part 1

Explore solvable groups, their connection to polynomial solvability, and their applications in Galois theory and field theory.

• YouTube
• 27 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

The Fundamental Theorem of Galois Theory - Lecture 1

Explore the fundamental theorem of Galois Theory, delving into its core principles and applications in algebraic structures.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Fields Institute

Splitting Differential Equations Using Galois Theory

Discover how Galois theory provides powerful techniques for splitting and analyzing differential equations in this advanced mathematical exploration.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Chennai Mathematical Institute;  NPTEL

Introduction to Galois Theory

Explore algebraic structures, field extensions, and Galois groups. Delve into fundamental theorems and applications like insolvability of quintics and cyclotomic extensions.

• Swayam
• 8 weeks
• On-Demand
• Free Online Course

NPTEL-NOC IITM

Solvability by Radicals - Lecture 37

Explore solvability by radicals, examining examples and radical extensions to deepen understanding of algebraic problem-solving techniques.

• YouTube
• 37 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Galois Extensions and Galois Groups - Lecture 14

Explore Galois extensions and groups, delving into fundamental concepts and initial examples in algebraic theory.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Insights into Mathematics

Galois Theory I - Introduction to Polynomial Equations and Symmetries

Explore Galois theory's insights into solving polynomial equations, from quadratic to quartic, and the historical development of algebraic problem-solving techniques.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Mathemaniac

Why You Can't Solve Quintic Equations - Galois Theory Approach

Explore the fascinating world of Galois theory and discover why quintic equations can't be solved using a formula, with insights accessible to math enthusiasts of all levels.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Locality Galois Group of Meromorphic Germs in Several Variables

Explore the structure of meromorphic germs in several variables through locality algebras, focusing on multiple zeta functions and Feynman integrals. Discover applications in analytic renormalisation.

• YouTube
• 45 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Massey Products in Galois Cohomology - Part 1

Delve into advanced Galois cohomology concepts, focusing on Massey products, the Norm-Residue Theorem, and their applications in understanding absolute Galois groups of fields through expert mathematical analysis.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Fields with the Absolute Galois Group of ℚ

Explore how fields with absolute Galois groups isomorphic to ℚ share arithmetic properties, impacting Birational Section Conjecture and Hilbert's Tenth Problem approaches.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Gresham College

How Does Mathematics Last? Heritage and Heritage-Making in Mathematics

Explore how mathematical knowledge survives across generations through libraries, examining 19th-century French mathematicians' collections and school systems to understand heritage-making in mathematics.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Fields Institute

Galois Groups of Lacunary Sparse Polynomial Systems

Explore Galois groups in lacunary sparse polynomial systems, examining their properties and applications in algebraic geometry and number theory.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Quintics, Braids and Billiards, After Abel

Explore the intricate connections between quintic equations, braid theory, and billiard dynamics in this advanced mathematical lecture by Curtis McMullen from Harvard University.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video