Galois Theory Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Arithmetic Algebraic Geometry in Memory of Jan Nekovář

Explore cutting-edge advances in arithmetic algebraic geometry through expert lectures honoring mathematician Jan Nekovář's contributions to the field.

• YouTube
• 22 hours 11 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Franco-Asian Summer School on Arithmetic Geometry

Delve into advanced arithmetic geometry through expert lectures on p-adic cohomology, Galois representations, and Simpson correspondence from leading mathematicians.

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

Centre International de Rencontres Mathématiques

Number Theory and its Applications to Cryptography

Explore advanced number theory applications to cryptography through elliptic curves, Frobenius distributions, and pseudorandom generators in this comprehensive mathematical semester.

• YouTube
• 20 hours 5 minutes
• On-Demand
• Free Video

Fields Institute

Fields Number Theory Seminar

Explore advanced number theory through expert seminars covering Galois theory, elliptic curves, L-functions, Shimura varieties, and arithmetic geometry from leading researchers.

• YouTube
• 3 days 11 hours 48 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Junior Trimester Program - Topology

Explore advanced topology through expert lectures on operads, motivic Galois groups, L2-invariants, K-theory, and fusion systems from leading mathematicians.

• YouTube
• 2 days 16 hours 18 minutes
• On-Demand
• Free Video

ICTP Mathematics

Abstract Algebra

Master fundamental algebraic structures including groups, rings, and fields through comprehensive lectures by Lothar Göttsche at ICTP Mathematics.

• YouTube
• 1 day 6 hours 15 minutes
• On-Demand
• Free Video

Polynomial Equations - ax² + bx + c = 0

Explore polynomial equations from ancient Mesopotamian quadratics to 19th-century Abel-Galois theory in this historical mathematical journey by Oxford's Robin Wilson.

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

International Centre for Theoretical Sciences

The Tau of Ramanujan by Eknath Ghate

Explore Ramanujan's tau-function, its significance in Number Theory, and recent developments. Discover intriguing patterns and open problems in this fascinating mathematical sequence.

• YouTube
• 1 hour 50 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Prime, Knots and the Adele Class Space

Explore geometric connections between primes and knots through scaling site theory, adele class space, and finite abelian extensions of Q, revealing insights into number theory and topology.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Motives and Super-Representation Theory: Principles and Case Studies

Découvrez les principes et études de cas des motifs et de la (super-)théorie des représentations, explorant la théorie de Galois motivique abstraite.

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

Insights into Mathematics

Logical Difficulties with Cyclotomic Fields - Famous Math Problems 20

Explores logical issues in cyclotomic fields, focusing on the challenges of embedding roots of unity into complex numbers and the limitations of purely algebraic approaches.

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

Centre International de Rencontres Mathématiques

Class Field Theory - Lecture 1

Explore fundamental concepts of class field theory in this advanced mathematics lecture, delving into algebraic number theory and Galois theory.

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

NPTEL-NOC IITM

Separable Extensions: Multiple Roots, Derivatives, and Inseparable Polynomials - Part 1

Explore separable extensions, multiple roots, derivatives, and inseparable polynomials in field theory, enhancing understanding of algebraic structures.

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