The exhaustive list of topics in Computational Topology in which we provide Help with Homework Assignment and Help with Project is as follows:
- Open and Closed Sets.
- Neighborhoods.
- Definition of Topology.
- Basis for Topology.
- Continuous maps.
- Connectedness.
- Pathconnectedness Compactness.
- Separation.
- Quotient Topology.
- Manifolds: with and without boundary.
- Surfaces: orientable and non-orientable, their topology.
- Classification of closed surfaces.
- Simplicial complexes and simplicial maps.
- Triangulations.
- Euler characteristics.
- Maps on surfaces.
- Groups and concept of Homotopy.
- Fundamental group and its calculations.
- Homology.
- Computation of homology of closed surfaces.
- Delaunay triangulations.
- Voronoi diagrams.
- Filtration and Persistence.
- Critical points.
- Applications