Mathematics of Data

3 credits · Undergraduate credit

A basic introduction to data representation as vectors,matrices (graphs, networks), and tensors. Geometric methods for dimension reduction (manifold learning, diffusion maps, t-distributed stochastic neighbor embedding (t-SNE), etc.) and topological data reduction (introduction to computational homology groups, etc.). An application-based approach to spectral graph theory, address the ombinatorial meaning of eigenvalues and eigenvectors of matrices associated with graphs, and discuss extensions to tensors [1, 2]. An introduction to the application of dynamical systems theory to data [3, 4,5].