Riemannian Geometry Courses and Certifications

NPTEL-NOC IITM

Mathematical Preliminaries II - Riemannian Geometry

Discover Riemannian geometry fundamentals including geodesic equations, affine connections, and covariant differentiation in this mathematical exploration.

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

NPTEL-NOC IITM

Mathematical Preliminaries II - Riemannian Geometry - Local Inertial Frames and Geodesic Coordinates

Explore geodesic coordinates and local inertial frames in Riemannian geometry through fundamental mathematical concepts and applications.

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

NPTEL-NOC IITM

Mathematical Preliminaries II - Riemannian Geometry

Explore point particle motion on Riemannian manifolds, geodesic equations, metric symmetries, Killing vectors, and integrals of motion in this mathematical physics foundation.

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

NPTEL-NOC IITM

Mathematical Preliminaries II - Riemannian Geometry

Discover parallel transport, auto-parallel equations, torsion tensors, metricity, and Levi-Civita connections in this essential Riemannian geometry foundation.

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

NPTEL-NOC IITM

Mathematical Preliminaries II - Riemannian Manifolds

Explore Riemannian manifolds, metric tensors, coordinate transformations, and tensor operations essential for advanced differential geometry and physics applications.

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

Introduction to optimization on smooth manifolds: first order methods

Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).

• edX
• 6 weeks, 5-6 hours a week
• Self-Paced
• Free Online Course (Audit)

The Royal Institution

The Extraordinary Theorems of John Nash

Explore John Nash's revolutionary contributions to game theory and geometric analysis with Fields Medal winner Cédric Villani, delving into the world of mathematical genius and groundbreaking theorems.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Mathemaniac

Exponentiating Vectors, Derivatives, and Vector Fields - Mathematical Concepts Explained

Explore the concept of exponentiation applied to vectors, derivatives, and vector fields, uncovering connections between seemingly different mathematical ideas and their practical applications.

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

Riemannian Geometry

Rigorous study of Riemannian metrics, curvature, geodesics, completeness, variation formulas, Jacobi fields, and comparison geometry.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course

Mathemaniac

The Gauss-Bonnet Theorem in Differential Geometry - From Intuition to Generalization

Delve into the fundamental Gauss-Bonnet theorem through visual explanations, exploring Gaussian curvature, parallel transport, and geodesics while uncovering its deep connections to differential geometry.

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

Introduction into General Theory of Relativity

1 rating

Solve standard problems of relativistic gravitation: derive Einstein equations from the Einstein-Hilbert action, analyze Schwarzschild and Kerr black holes, gravitational waves, and Friedmann-Robertson-Walker cosmology.

• Coursera
• 12 weeks
• No Longer Offered
• Paid Course