# Topological Data Analysis

In this research stream, we will learn about the tools and theory of Topological Data Analysis (TDA). Topological Data Analysis is an area of applied mathematics which uses the tools of topology and geometry to study the shape and structure of data. A fundamental hypothesis of TDA is that data come as samples from an underlying space with shape properties, and understanding that shape is important to understanding the studied phenomena. Applications of TDA include a diverse range of fields, such as cancer biology, neuroscience, image analysis, dimensionality reduction for high dimensional data, signal analysis, and feature selection, to name a few.

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In this stream, our goal is to do novel research in both the theory and applications of Topological Data analysis. Students will learn about Topology and Data analysis, and develop math literacy skills, such as reading, writing, and discussing quantitative topics. There will be opportunities to do research in the theory of TDA, such as developing and proving mathematical theorems and generating examples in the area of computational topology, which provides the mathematical tools for the application of TDA. There will also be opportunities to create and implement algorithms in Python for the computation of mathematical invariants and quantitative summaries given by TDA. Finally, there will be opportunities for collaboration with other areas of science, to pose and investigate quantitative questions in different disciplines, using TDA software