10/01/2006-Topological spaces: [1]; [2]; [3]; [4]
12/01/2006-Examples of Topological spaces; Continuum functions; Open functions; Homeomorphism; Trajectory; [1]; [2]
17/01/2006-Manifolds; Chart; Coordinate system; Transition function; Example, stereographic projection; Compatible charts; Atlas; Differentiable manifold; Smooth functions; Full-back; Tangent vector and vector space; [1]; [2]
19/01/2006-Vector field; differential of a function; 1-form; Bracket product; Example: S^2; cotangent space: [1]; [2]
24/01/2006- Lie Bracket; pull back; Tensors and p-forms; Tensorial product; Examples: [1]; [2]
26/01/2006-p-forms; wedge product; p-form differential; Levi-civita tensor; Hodge operator; codifferential; laplacian; examples and exercises: [1]; [2]
31/01/2006-p-form classification; Hodge theorem; stokes theorem; examples; electromagnetic field; maxwell's equations on S^2: [1]; [2]
02/02/2006-Uniparametric group of transformations; Integral curve; Lie Derivative; Conection; Parallel transport; Killing equation; Killing vectors [1]; [2]

To follow the path:
look to the master,
follow the master,
walk with the master,
see through the master,
become the master.

Zen Poem