Topological Data Analysis (TDA) is a framework for data analysis and machine learning and represents a breakthrough in how to effectively use geometric and topological information to solve Big Data problems. TDA provides meaningful summaries (in a technical sense to be described) and insights into complex data problems.

In this class, we will start with an overview of TDA and describe the core algorithm, "Mapper." We will do this concretely through a carefully worked out example that we will return to as the material gets more complex so that the technique is transparent and concrete. The class will include both the theory and real-world problems that have been solved using TDA. After taking this class, you will understand:

- How the Mapper algorithm works and how it improves on existing 'classical' data analysis techniques.
- How Mapper forms a framework for many machine learning algorithms and tasks.

- How to interpret the algorithmic output (called an extended Reeb graph or ERG) and have concrete examples how it has been applied in real-world applications.

Note: You will need knowledge of Calculus and basic statistics. A Machine Learning background is also preferred to give context to the examples.