## Spring 2008

[2/1] [2/6] [2/7] [2/26] [3/4] [3/18] [3/25] [4/1] [4/8] [4/14] [4/15] [4/16] [4/24] [4/29] [5/1] [5/2]

**2/1: Dots, Arrows, and Representation Theory
**Jennifer Froelich

Department of Mathematics

University of Iowa

Quivers and their respective path algebras appear in many branches of abstract algebra including representation theory, and they can be useful tools when determining certain algebraic objects. We will explore path algebras, their sometimes nice structures, and the relationship between quivers and representation theory.

Date: 2/1

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**2/6: Finding Order in the Unknown: The Erdos-Szekeres Theorem
**Karen Lange

Mathematics Department

University of Chicago

One goal of mathematics to find regularity in the midst of chaos. It is a fact from analysis that any infinite sequence of distinct real numbers has an infinite increasing or decreasing subsequence. But what if we are only given a finite sequence of distinct real numbers? Does a reasonably long increasing or decreasing subsequence still exist? We will prove the beautiful Erdos-Szekeres Theorem that exactly answers these questions.

Date: 2/6

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**2/7: Exploring Partitions of Numbers
**Stephanie Treneer

Department of Mathematics

Dartmouth College

A partition of a positive integer n is a sequence of positive integers that sum to n. The partition function p(n) counts the partitions of n without regard to order. This deceptively simple function has led to a rich theory. We'll look at two elementary methods for analyzing partitions: Ferrers graphs and generating functions. We'll then briefly discuss the connection between partitions and modular forms, which has led to some recent surprising results about p(n).

Date: 2/7

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**2/26: Technology Service Continuity for Dickinson College
**Terry Mollett

Director, User Services

Dickinson College

The widespread adoption of systems, applications, and information technologies by Dickinson College has proven to be extremely beneficial. Although beneficial, the dependence upon these technology resources has exposed various Dickinson College departments to a significant level of vulnerability to potential disruption.

A major project initiative for the Library and Information Services Division is the creation of an effective and executable service continuity plan for all administrative areas within Dickinson College. In this presentation we will discuss the Service Continuity Impact Analysis process. This process is used to identify critical information technology resources utilized by each administrative department on the Dickinson College campus. Once identified, the goal is determine the required and expected recovery point objective (RPO) and the recovery time objective (RTO) for the various technology services.

Date: 2/26

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**3/4: Creating a Proof of Concept Knowledge Base Application for Statistical Analysis of PennDOT Highway Safety Data
**Jerry Cichocki

Project Manager

GeoDecisions

Albert Sarvis

Project Manager

GeoDecisions

This presentation will provide a summary of a recent research project to develop a proof of concept (POC) knowledge base for crash data analysis for PennDOT. An overview of the PennDOT motivation for this project and a theoretical description of what a Knowledge Base application can do will be presented. We will show how the knowledge base POC has provided PennDOT a model for an innovative tool to analyze crash data and use statistical algorithms to identify new patterns and relationships. We will further explain how the tool can use spatial and non spatial criteria to create relationships between crashes, causative factors and corrective actions while a user interface component provides the ability to visually traverse these relationships and display the spatial records on a digital map. Details of the statistical analysis and the project outcome will also be discussed.

Date: 3/4

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**3/18: Math and Art: The Good, the Bad, and the Pretty**

Annalisa Crannell

Department of Mathematics and Computer Science

Franklin & Marshall College

Dust off those old similar triangles, and get ready to put them to new use in looking at art! We're going to explore the mathematics behind perspective paintings---a mathematics that starts off with simple rules, and yet leads into really lovely, really tricky mathematical puzzles. Why do artists use vanishing points? What's the difference between 1-point and 3-point perspective? What's the difference between a perspective artist and a camera? We'll look at all of these questions, and more.

Date: 3/18

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**3/25: Iterated Maps and Intrinsic Localized Modes
**Lars English

Department of Physics and Astronomy

Dickinson College

Solid-state physics is all about lattices. Many properties of crystalline solids are explained in terms of collective modes of the associated lattice. These modes are generally plane waves that extend throughout the physical space of the crystal, although impurities in the lattice lead to spatially localized modes. However, only recently has it been recognized that spatial localization can also occur in perfectly pure lattices when the lattice dynamics is nonlinear. The subject of this talk is to show how these intrinsic localized modes arise from a dynamical-systems perspective. We will find that they are a consequence of a homoclinic orbit of an iterated map.

Date: 3/25

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/1: Predictive Modeling using Binary Logistics Regression - Shaping the Class of 2011
**Mike Johnson, PhD

Director, Institutional Research

Dickinson College

Christian Millichap ('08)

Mathematics major

Dickinson College

We discuss the challenges and the lessons learned while developing a new enrollment management predictive model. Simply put, "who should we admit?" They developed a binary logistics regression model using historical data and a relatively new software package called "Rapid Insight Analytics". The model provides information regarding things like yield, net tuition revenue, and the quality of the incoming class. Cleaning the data, establishing a modeling approach, interpreting the results, and validation were real challenges motivated by the quick turnaround time required and the critically important decisions resulting from the model output.

Date: 4/1

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/8: Bloodless Victory on the Battlefield After Next
**COL (Retired) Kevin J. Cogan

U.S. Army

Thirty years military active duty, Colonel, U.S. Army Signal Corps; former Chair of Management, U.S. Army War College; Bachelor of Science, West Point; Master of Science, Columbia University; currently senior analyst, command and control group, U.S. Army War College, Carlisle, Pennsylvania, USA

The convergence of robotics, weapons lethality, and a highly networked environment on the battlefields of the future give rise to time-compressed response times, which in the limit, will call for the removal of human real-time decision making in order to maximize effects-based operations. Will guarantees of precision strikes from autonomous systems negate the need for commanders at the tactical and operational levels? Can rules of engagement be embedded in the sensor-shooter link with a high degree of ethics and assurance? Can an automated battlefield become so lethal that no one dares to venture on it? These questions and their hypothetical answers raise the possibility of realizing Sun Tzu's quote: "To subdue the enemy without fighting is the supreme excellence." To produce such a battlefield will require advanced technologies, vision, and shared international intelligence.

Date: 4/8

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/14: Infinitesimals and the Hyperreal Numbers
**Brian Wynne

Colgate University

Infinitesimals played an important role in the early development of Calculus but were abandoned by later mathematicians for lack of a satisfactory theoretical foundation. In 1960, using methods from mathematical logic, Abraham Robinson provided such a foundation by constructing the hyperreal numbers. I will discuss the basic features of the hyperreal numbers and show how they may be used to prove some classical theorems from Calculus.

Date: 4/14

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/15: Software Design and Engineering
**Nate Mitchell ('09) and Colin Angevine ('09)

Dickinson College

You thought skydiving was extreme? Try eXtreme Programming.

In this week's Math/CS Chat, Nate Mitchell '09 and Colin Angevine '09 will share their experiences from their Spring 2007 independent study Software Design and Engineering. They will discuss the principles of eXtreme Programming (XP), and how this methodology leads to an improved programming experience and stronger code. They will describe the XP workflow with concrete examples and from there discuss what it is about the mindset of XP that makes the approach so valuable. In particular, the talk will focus on test-driven development and how this initially counter-intuitive practice can be a powerful tool for developing software.

Date: 4/15

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/16: Integer Partitions
**Thotsaporn (Aek) Thanatipanonda

Rutgers University

An integer partition is a way of splitting a number into integer parts. Let p(n) be the number of integer partitions of n. For example, p(4)=5 since 4=3+1=2+2=2+1+1=1+1+1+1. We will talk about partition identities, such as the number of integer partitions into odd parts equals the number of integer partitions into distinct parts. We will also give a bijective proof of these partition identities.

Date: 4/16

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/24: From the Pigeon Hole Principle to Ramsey Theory
**Christian Avart

Emory University

If 9 pigeons are sitting in 8 pigeon holes, there must be one hole with more than one pigeon inside. This obvious statement, often referred to by mathematicians as the Pigeon Hole Principle, turns out to have surprisingly clever applications. For example, this principle implies that right now, there are two people living in the state of Pennsylvania who have the exact same number of hairs on their scalp. In this talk, we will prove this statement and explore several other simple, intriguing, and even beautiful mathematical facts that were derived from this principle. This will lead us to the proof of an elegant and fundamental theorem of mathematics called Ramsey Theorem. The talk will be self-contained and accessible to anyone curious about the subject.

Date: 4/24

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**4/29: The Topology of Robots Moving on Graphs
**Christian Millichap ('08)

Dickinson College

Suppose a number of robots are transporting items across a factory floor and we do not want these robots to collide. This problem has a topological solution - construct the space of all possible arrangements of the robots on the factory floor and remove all the arrangements that could potentially result in collisions. If the robots are programmed to function only on this space then they will never collide. These spaces are cell-structures that when glued together form interesting topological spaces.

Date: 4/29

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**5/1: A New Approach for Evolving Robotic Controllers
**Ryan Zeigler ('08)

Dickinson College

In some cases, it is easier to evolve control strategies for robots than to code reactive strategies by hand. However, genetic algorithms require evaluation of large numbers of potential solutions. In most cases, this requires to the use of simulations to actually perform the evolution. It has previously been shown that control strategies evolved in simulation often fail when used on a physical robot. This project evaluates new approaches to solving this problem in comparison with traditional methods.

Date: 5/1

Location: Tome 115

Time: 12:00-12:50

Lunch provided

**5/2: Applying a Genetic Algorithm to the Localization Problem using an Extremely Sensing Limited Robot
**Mark Veronda ('08)

Dickinson College

This project explores implementing a Genetic Algorithm to have a robot find out where it is on a given map. Although this could be accomplished with GPS receivers and laser range-finding devices, they are expensive and fragile. This project investigates what is the possibility of using a single sonar sensor device to localize a robot. Results have shown that this is a feasible approach and that a robot using this method is able to determine its location on a map.

Date: 5/2

Location: Tome 115

Time: 12:00-12:50

Lunch provided