This class will look at how various classical mathematical concepts and results have recently been applied in unexpected ways. At their inception, these ideas typically had a home in abstract mathematics and were (likely) developed without any applications in mind. However, recent years have seen a proliferation of applications of such “old” mathematics to stunning effect. The class will cover several of these applications by first introducing the mathematics behind each of them from the classical point of view and then examining how a novel application has infused it with new purpose. Some specific applications – arising from classical number theory, linear algebra, graph theory, topology, geometry, and probability – will be machine learning, cryptography, quantum computing, signal processing, robotics, data analysis, and gerrymandering. Here are some more specific relationships:

• Euler's Theorem  →  cryptography adn cryptocurrency

• Steiner Isoperimetric Inequality  →  gerrymandering

• Perron-Frobenius Theorem  →  Google PageRank algorithm

• singular value decomposition →  machine learning

• Fourier transform  →  quantum computing

• topology →  topological quantum computing

• homology  →  topological data analysis

• configuration spaces  →  robotics

• knot theory  →  DNA and molecular knotting

• simplicial complexes  →  signal processing

• graph theory  →  social media networks 

• numerical analysis →  GPS and LIDAR

• differential equations →  modeling desease spread