ABSTRACT: Hoping to beat the stock market? That may seem optimistic and trying may seem too risky in these times. The Capital Asset Pricing Model (CAPM), developed in 1964, was a breakthrough in mathematical finance. Although the CAPM cannot tell you how to beat the market, it can help give a fair  assessment of potential returns. One goal of the CAPM is to help organize a portfolio that maximizes the return for a given level of risk or minimizes risk for a specific return. The second use is to estimate expected returns on specific investments, both existing securities and new issues that have not yet been  traded. This presentation will outline how the CAPM works, its applications and some mathematical ideas on which it is based.

Dennis Leahy

"Properties of Random Graphs"

ABSTRACT: A random graph is simply a collection of vertices and edges where the edges occur by some  random process. Because of the aspect of randomness in these graphs, can theory be helpful in determining the likelihood of certain graphical properties? For example, what is the probability that a random graph will be connected or planar or ? This talk will discuss how such probabilities can be calculated and how they might depend on the graph size (n) and probability for each edge (p).

ABSTRACT: Chemical Graph Theory, a branch of mathematical chemistry that is concerned with the analysis of all consequences of connectivity in a chemical graph, will be the focus of my discussion. I will talk briefly about general graph theory in order to give an understanding of how the two subjects are connected. Topics discussed within chemical graph theory will include Huckel theory and topological  indices. The accuracy of conclusions that can be drawn within this subject will be examined. Examples pertaining to actual compounds and their natural chemical characteristics will be used.