Basics of Topology; complexes on data; homology; topological Persistence; computing Betti numbers; reconstruction from data; topology inference from data; computing optimized homology cycles; reeb graphs from data; topology of Laplace operators, spectra approximation.

Same as Reference

1. Edelsbrunner, H. and Harer, J. L., Computational Topology, American Mathematical Society(2010).

2. Dey, T. K., Curve and Surface Reconstruction: Algorithms with Mathematical Analysis, Cambridge Univ. Press (2011).

3. Hatcher, A., Algebraic Topology, Cambridge Univ. Press (2001).