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Friday, 3:00 - 3:20 p.m., G-219 Crapo Hall
Tim Blaharski, Sienna Heights
Title: Mathematics, it's almost like cheating
Abstract: This presentation will analyze impartial gaming theory using a game called Nim. Moreover, any impartial game can be related to a Nim game. Two additional games, Kayles and Chomp, will be analyzed using the Nim strategies.

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Friday, 3:00 - 3:20 p.m., G-221 Crapo Hall
Matthew Spensor, Evansville
Title: A Markov Analysis of the Pathfinder Game
Abstract: We construct a mathematical model of the Pathfinder game on The Price is Right. Specifically, we use the theory of absorbing Markov chains to approximate the probability of winning a game of Pathfinder. We conclude by comparing the theoretical value obtained with values computed using statistics compiled from recent games. Furthermore, we discuss likely causes of discrepancies between these values.

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Friday, 3:30 - 3:50 p.m., G-219 Crapo Hall
Jasmine Spady, Hillsdale College
Title: Knots in Chemistry
Abstract: Although the average human being does not understand the meaning of the word chiral, almost every human being is born with a pair of chiral objects, their hands. Even their DNA is chiral. In fact, many biomolecular structures are chiral. In todays world of bioengineered drugs, determining chirality is extremely important. In the human body, one form of a chiral drug can cure while the other can kill. My talk will discuss some of the elementary aspects of knot theory and how they apply to chemistry and determining the chirality of different structures.

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Friday, 3:30 - 3:50 p.m., G-221 Crapo Hall
Brandon Borkholder, Rose-Hulman Institute of Technology
Title: Breaking the MD5
Abstract: The MD5 hash function and its family are security algorithms that have been used world-wide for nearly a decade. Just a few years after creation there were hints of weakness and now there are algorithms to crack it efficiently. How do these algorithms work? Is the MD5 completely broken? How can a potential hacker exploit this weakness to undermine the trust of those who use it?

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Friday, 4:10 - 4:30 p.m., G-219 Crapo Hall
J.D. McKeel, University of Evansville
Title: Ideal-Divisor Graphs of Commutative Rings
Abstract: Recall that a zero-divisor of a ring R is an element such that there exists an element b giving ab=0. For a commutative ring R we can form the zero-divisor graph of R whose vertices are nonzero zero-divisors. We recognize {0} simply as an ideal of R and begin to construct ideal-divisor graphs of R with respect to an arbitrary ideal I. We find and compare the diameters of zero-divisor and ideal-divisor graphs of direct products of commutative rings.

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Friday, 4:10 - 4:30 p.m., G-221 Crapo Hall
Candice Ohm, Siena Heights University
Title: Using Mathematical Modeling to Develop an Optimal Inventory Strategy for Perishable Products
Abstract: This presentation will address the creation of an optimal inventory strategy for the ordering and storing of perishable products. Inventory records were tracked at a local restaurant for several perishable products. The data was used in two different types of models and the results were compared. The first model is analytical and discrete. It is a network flow model that results in a dynamic programming algorithm which solves for the minimum inventory cost. The other is theoretical and continuous. Calculus was used to determine an optimal replenishment cycle number to minimize inventory cost.

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Friday, 4:40 - 5:00 p.m., G-219 Crapo Hall
Mathew Cosgrove, Miami University
Title: GPS Navigation Solution- An Alternative Way to Solve for User Position Using GPS
Abstract: This talk will deal with the various new methods of solving for pseudo-ranges by using closed form solutions, iterative techniques based on linearization and Taylor series expansion in three variables followed by a brief discussion of Kalman filtering. Most of the talk will focus on the iterative techniques and the use of matrices to solve sets of linear equations as well as the use of a basic least-squares solution. The applications of this new technique allow for compensation of various forms of error in positioning such as Ionospheric error, and clock bias.

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Friday, 4:40 - 5:00 p.m., G-221 Crapo Hall
Lee McDaniel, Rose-Hulman Institute of Technology
Title: Benford and Winning Streaks
Abstract: Benfordís law describes the distribution of the first significant digit of a surprisingly large number of naturally occurring (e.g., river lengths, mountain heights, populations) data sets. The law was first discovered during a seemingly unrelated scientific study by American astronomer Simon Newcomb while skimming the pages of a logarithm book. Today Benfordís law has been used to detect fake coin toss data, and more seriously, tax fraud. What exactly is Benfordís law? What data sets conform to this law and what are their common characteristics? Can Benfordís law be applied to other data sets (naturally and man-made) occurring in the world around us everyday?

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Saturday, 10:10 - 10:30 a.m., G-219 Crapo Hall
Leonie VanderHoff, Siena Heights University
Title: A Mathematical Look into Kaleidoscopes
Abstract: Using mirrors and mirror systems to produce attractive images has led to the study of this topic. This presentation will address an open two-mirror system and a closed two-mirror system (the traditional toy kaleidoscope). Along with the geometry of the placement of the mirrors, the mathematics of kaleidoscopes involves linear algebra, group theory and a bit of graph theory. The study of these systems will reveal a relationship to dihedral groups and wallpaper groups.

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Saturday, 10:40 - 11:00 a.m., G-219 Crapo Hall
Eric Reyes, Rose-Hulman Institute of Technology
Title: Do Dogs Really Know Calculus?
Abstract: Least squares is a regression technique frequently used by engineers and scientists to gain insight into data generating processes. In 2003, Timothy Pennings of Hope College asked the question: "Do Dogs Know Calculus?" In an effort to determine if his dog minimized the retrieval time during a game of fetch, Pennings collected data. We take a second look at the data he acquired and the statistical analyses. We show how a simple-looking problem can require an intricate analysis. We use modern methods to detect and compensate for violations in the standard least squares assumptions. And, we seek to answer the question: Do Dogs Really Know Calculus?

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Saturday, 11:10 - 11:30 a.m., G-219 Crapo Hall
Donald Brown, University of Cincinnati
Title: Thermal Imaging of Circular Inclusions
Abstract: This talk will describe some results from the 2005 Rose-Hulman REU Inverse Problems group. We consider the inverse problem of recovering a circular defect (inclusion) from some arbitrary 2-dimensional Domain knowing only thermal data on the boundary. By applying the Laplace Transform to the time-dependent Heat Equations we may obtain information about the position and size of such a defect knowing only this thermal boundary data of D and approximations to the solution. The main mathematical tool utilized to carry out these calculations is known as the Reciprocity Gap Functional (closely related to Green's Theorem).

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Saturday, 11:40 - 12:00 p.m., G-219 Crapo Hall
Hari Ravindran, Rose-Hulman Institute of Technology
Title: Investigating the Shape of a Cookie
Abstract: This is a continuation of the previous two talks on the Shape of a Cookie. The goal of the investigation is the establishment of an asymptotic expansion for the shape of a cookie with an elliptical base domain. The talk summarizes the work towards this goal over the past summer and during this academic year. This research was funded in part by a Joseph B. and Reba A. Weaver Undergraduate Research Award.

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