# Arc Length and the Frenet-Serret Apparatus, Lecture Notes - Mathematics

Arc length and frenet serret apparatus, reparameterization, create a unit speed curves, tangent vector, curvature, frenet serret basis vectors, example halix

# Differential Geometry, Lecture Notes - Mathematics

Differential geometry, introduction, curvature, possible definition, curves in space, parameterization, geometric interpretation, surface in space, intrinsic verses extrinsic properties

# Consequences of Gauss-Bonnet Formula, Lecture Notes - Mathematics

Consequences of gauss bonnet formula, triangles on a sphere, gauss bonnet theorem, definition examples and proofs

# Differential Geometry, Lecture Notes - Mathematics

Differential geometry, introduction, curvature, possible definition, curves in space, parameterization, geometric interpretation, surface in space, intrinsic verses extrinsic properties

# Arc Length and the Frenet-Serret Apparatus, Lecture Notes - Mathematics

Arc length and frenet serret apparatus, reparameterization, create a unit speed curves, tangent vector, curvature, frenet serret basis vectors, example halix

# Consequences of Gauss-Bonnet Formula, Lecture Notes - Mathematics

Consequences of gauss bonnet formula, triangles on a sphere, gauss bonnet theorem, definition examples and proofs

# Proof of Gauss-Bonnet Formula, Lecture Notes - Mathematics

Proof of gauss bonnet formula, preliminaries, geodesic coordinate patches, angular variation, topology, null homotopy, boundary, rotation index theorem

# Parallel Transport, Lecture Notes - Mathematics

Parallel transport, introduction, definition and theory, equator of unit sphere, tangent vector, small circle, differential equation for parallel vectors, along geodesic, angles between vectors, geodesics on a sphere, foucault pendulum

# Manifolds, Lecture Notes - Mathematics

Manifolds, introduction, klein bottle, tangent space, vector fields, lie brackets, differential curves, parallel vectors, metric coefficients, riemann metric, christoffel symbols, riemann curvature tensor

# Parallel Transport, Lecture Notes - Mathematics

Parallel transport, introduction, definition and theory, equator of unit sphere, tangent vector, small circle, differential equation for parallel vectors, along geodesic, angles between vectors, geodesics on a sphere, foucault pendulum

# Proof of Gauss-Bonnet Formula, Lecture Notes - Mathematics

Proof of gauss bonnet formula, preliminaries, geodesic coordinate patches, angular variation, topology, null homotopy, boundary, rotation index theorem

# Arc Length and the Frenet-Serret Apparatus, Lecture Notes - Mathematics

Arc length and frenet serret apparatus, reparameterization, create a unit speed curves, tangent vector, curvature, frenet serret basis vectors, example halix

# Consequences of Gauss-Bonnet Formula, Lecture Notes - Mathematics

Consequences of gauss bonnet formula, triangles on a sphere, gauss bonnet theorem, definition examples and proofs