Topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important topological properties include connectedness and compactness.

Topology and business

Nothing as applicable as an abstract theory. Topology might seem abstract and foundational (like number theory) but has a wide range of applications in life. The combination of topology and data science, in particular, is called topological…

What is persistent homology?

About topological data analysis and persistent homology in particular.

Stochastic Neighbor Embedding on MNIST

Around t-Distributed stochastic neighbor embedding.

Topological Data Analysis

Topological Data Analysis (TDA) employs modern mathematical concepts such as functors, and posseses such desirable properties as success in coordinate-freeness and robustness to noise.

Discrete calculus on graphs

This is an overview of the discrete differential calculus on graphs with an emphasis on the usage of Mathematica to perform related calculations.