Galois Theory Courses and Certifications

Galois Theory

This course is an attempt to present the theory in such alight, and in a manner suitable for undergraduate and graduate students as well as researchers.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Mathemaniac

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

See why quintic equations lack a general formula through an intuitive tour of Galois groups, field extensions, and solvability.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Bill Buchanan OBE

Addition, Multiplication and Division in Galois Fields GF(2^m)

An introduction to arithmetic in GF(2^m), using polynomial representations and primitive polynomials for addition, multiplication, division, and cryptographic computations.

• YouTube
• 22 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

NPTEL-NOC IITM

Existence Theorem for Finite Fields

Explore the existence theorem for finite fields, proving their existence for every prime power order.

• YouTube
• 15 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Subfields of a Finite Field

Explore the concept of subfields within finite fields, understanding their properties and significance in abstract algebra and number theory.

• YouTube
• 12 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Wolfram

Finite Fields and Their Applications

Explore new Mathematica 13.3 features for finite field computations, including arithmetic, mappings, and polynomials. Learn about upcoming linear algebra and equation solving capabilities.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Math at Andrews

Constructibility

Explore which figures can be constructed with compass and straightedge, and why angle trisection, cube doubling, and circle squaring are impossible.

• YouTube
• 6 hours
• Self-Paced
• Free Video

École normale supérieure

Introduction à la théorie de Galois

67 ratings at Coursera

La théorie de Galois relie les extensions de corps et les groupes de permutations pour calculer les symétries des racines, notamment après réduction modulo p.

• Coursera
• 11 weeks, 1 hour a week
• Self-Paced
• Free Online Course

Insights into Mathematics

Wild Trig - An Introduction to Rational Trigonometry

Discover a revolutionary algebraic approach to trigonometry using quadrance and spread instead of angles and irrational numbers for more efficient geometric calculations.

• YouTube
• 19 hours 47 minutes
• Self-Paced
• Free Video