The famous Matrix-Tree Theorem describes the number of spanning trees in a graph, showing that it can be computed as the determinant of the associated graph Laplacian matrix. I will discuss some generalizations of this theorem and how they might be applied to the analysis of directed networks. This talk will be introductory and include complete, accessible, and elementary proofs of the theorems discussed.

The Abelian Sandpile model is a dynamical system on graphs that was one of the first examples of a system with self-organized criticality. It's also known for producing beautiful fractal patterns. In this talk, we'll learn about its history, some of its interesting properties, and about connections to other fields of mathematics. Finally, we'll mak some pictures! No previous knowledge is assumed, but if you came for the previous session on the matrix-tree theorem, you'll see some definite connections.

From Mary Boole's curve stitching to t-shirts bearing the Mandelbrot set, asthetically appealing mathematical visualizations have enchanted the senses and stimulated the mathematical mind throughout history. This talk will explore a system of graphical analysis on fractions in any base. As well as a tutorial on how to create these striking images, we will prove a few accessible number theoretical results explaining what they can tell us about the fractions they represent.

Created by Donald Knuth and released in 1978, the LaTex typesetting system has become the standard for creating beautifully formatted mathematical documents. It allows the user to create complex mathematical expressions in seconds that would take several minutes using other systems. Getting started with LaTex is fun and easy. In this meeting of Math Club, we invite you to come get set up and learn the basics of LaTex with our own Pieter Vandenberge. Afterwards, you will be able to write quicker than any of your friends..