Georgia Institute of Technology College of Sciences

Mathematics can help all of us sort through some complicated scenarios, with changing inputs, and changing conclusions.  I will illustrate this with some examples.  Porker hands and Jury selection bias:  Expert testimony that I gave in a death penalty case.  Specificity of testing:  A random person tests positive for COVID.  Do they have the disease?  Designing pooled testing for the disease.  When is it effective?

I will present a proof of Gauss's Law of Quadratic Reciprocity based on permutations and the mathematics of dealing cards.

Did you know that a wheel or a ball bearing does not need to be round? Convex regions that can roll smoothly come in many remarkable shapes and have practical applications in engineering and science. Moreover, the mathematics used to describe them, known as convex geometry, is a subject that beautifully ties together analysis and geometry. I'll bring some of these objects along and tell the class how to describe them effectively and recount their interesting history.

The Probabilistic Method is a powerful tool for tackling many problems in discrete mathematics and related areas.
Roughly speaking, its basic idea can be described as follows. In order to prove existence of a combinatorial structure with certain properties, we construct an appropriate probability space, and show that a randomly chosen element of this space has the desired property with positive probability.
In this talk we shall give a gentle introduction to the Probabilistic Method, with an emphasis on examples.