HSCI-302: Turing MacHines & Game Theory

This course will provide an introduction to the dynamical, computational side of mathematical logic. It contains two modules: Turing Machines and Game Theory. In the first module, we examine central theorems of George Cantor, Alan Turing, Alfred Tarski, Kurt Godel regarding Turing Machines and solvability. Then we quantify the computational power needed to solve a particular problem as well as the mathematical structure that can hold that computational power, which leads us to our second module. In the second module, we examine John Nash's Nobel-Prize-winning work in Game Theory. We will address questions such as: What does it mean to say the protein-folding problem is NP complete? What is a Perfect-Nash Equilibrium given Godel's Incompleteness Theorem ? We will focus on the automata, language theory, and numerical analytics of problem solving to investigate current large scale problems, from global warming, to protein folding in neural networks, to epidemiology.