Experiencing the Norm
Jasper G. Burch

ABSTRACT: A Norm is defined by || * || p = ( |e 1| p |e 2| p |e 3| p ... |e n| p ) 1/p . In this presentation, the norm will be examined as a function of p. It will be shown to be a monotone decreasing function and || * || â ? will be found. Cases when 0 < p < 1 will then be examined. Properties of the norm as p approaches 0 will be explored.

The Optimal Assignment Problem
Jeff Cluckey

ABSTRACT: The optimal assignment problem discusses how to assign workers to jobs in the most effective way, given a measure of how effective each worker is at each job. We discuss a solution to this problem and some applications.

Understanding First-Order Logic through Automation in Java
Ashish Dixit

ABSTRACT: My research involves development of an “Automated Theorem Proving Assistant” using Java and exploration of the fundamental concepts of first-order logic through the automation process. The goal is an enhanced understanding of the techniques of first-order logic through analysis of the process of development. The talk will focus on the software development process in this project and the problems encountered. It will also include a report on the results of the project.

Minimizing Risks, Maximizing Rewards: Modeling Financial Time Series Data
with ARCH and GARCH
Raluca Dragusanu

ABSTRACT: Traditional time-series models such as Autoregressive (AR) and Moving Average (MA) models are based on the homoskedasticity assumption, which translates into a constant variance for the errors of a model. This assumption has been shown to be inappropriate when dealing with some economic and financial market data. A new class of models - conditional heteroskedastic models – was developed to deal with data that does not exhibit constant variance of the errors. The most well- known models in this class are the Autoregressive Conditional Heteroskedastic model (ARCH) and its generalized version (GARCH). Stock market volatility, the square root of the variance of stock returns presents a very good application of this type of model. In finance, volatility is the expression of risk. Since we must take risks to achieve rewards, finding appropriate methods to forecast volatility is necessary in order to optimize our behavior and, in particular, our portfolio. I will present the general properties of the ARCH and GARCH models and use both Monte Carlo simulations and known financial time series data to test their performance.

Applications of a Graphical Information System to Ice Hockey
Travis Gingras

ABSTRACT: Statistics and sports have been related for many years, and recently the art of using statistics to observe players tendencies has become more and more common among coaches. This project looks to investigate patterns of shots taken by the St. Lawrence Men’s hockey team using a geographic information system. ArcGIS is a mapping program generally designed for geographical data, but in this project we have defined a database to store information about individual shots in multiple hockey games while placing them on a map of the offensive zone of a hockey rink. We can then study patterns and look for the trends that might benefit individual players or the team as a whole.

Investigating the Effectiveness of the Bootstrap
James D. Hall

ABSTRACT: The statistical procedure known as “bootstrapping” is used to approximate a sampling distribution for any statistic by resampling from an original sample with replacement in order to draw conclusions about the shape, center and variability of the sample statistic. These methods avoid traditional assumptions such as assuming a certain population is normally distributed. We give a brief description of bootstrapping techniques and demonstrate via computer simulation (using the statistical software packages R and Fathom) the effectiveness, in terms of coverage and average width, of bookstrap confidence intervals compared to traditional confidence intervals in standard situations and in cases where standard assumptions fail.

The Gossip Number and the Email Gossip Number
Kristen MacMurray

ABSTRACT: Assume every person in a group of people has a unique tidbit of gossip to share. How many conversations must occur before everyone in the group knows all the gossip? It depends on what we assume about the conversations. The gossip number assumes that conversations occur between two people who tell each other everything they know. The email gossip number assumes that one person shares all the gossip that he or she knows with all his or her friends in a mass mailing. We discuss some interesting results about the gossip number and the email gossip number of a graph.

ROC Confidence Regions Using Radial Sweep Methods
Yordan D. Minev

ABSTRACT: One methodology for evaluating the matching performance of biometric authentication systems is the receiver operating characteristics (ROC) curve. A biometric authentication system matches physiological characteristics to a database of such characteristics. The ROC curve graphically illustrates the relationship between type I and type II statistical errors when varying a threshold across a genuine and an imposter match distributions. In biometric authentication, genuine users are generally those that the system should accept and imposters are those that the system should reject. In this project ROC confidence regions are created using radial sweep methods. Radial sweep is based on converting the type I and type II errors to polar coordinates. The goal of the project is to estimate the performance of each biometric system via a confidence region and to identify the most effective method for computing such a confidence region for a ROC curve of that system’s performance.

Sudoku: Annoying Time-Waster or Mathematical Ingenuity? (Or Both?)
Catherine Sheard, Hugh C. Williams High School, Canton, N.Y.

ABSTRACT: Sudoku, a highly addictive game that has swept the nation, involves numbers – but is it math? Placing the numbers 1 through 9 in little boxes so that each digit appears only once per row, column, and sub-square isn’t math, is it? Yes, it is! This talk will explore the mathematics behind generating and solving Sudokus, and will also present the history behind these puzzles. From its humble beginnings as Euler’s Latin Square to its recent explosion throughout Europe and America , Sudoku has sent puzzle enthusiasts scrambling for erasers and computer programmers scratching their heads over the complexity of these seemingly simple grids.

Sequential Analysis for the Beta-Binomial
Emily Sheldon

ABSTRACT: In this talk we attempt to derive an equation from the Beta-binomial distribution that can be used to apply sequential probability ratio testing to biometric devices. We first examine sequential analysis testing methods and then apply them to examples of multiple independent bernoulli trials. We use these examples to illustrate the decision of when to stop testing. Lastly we examine the Beta-binomial distribution and derive an equation that can be used in sequential analysis methodology.