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Friday, 3:00  3:20 p.m., G219 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., G221 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., G219 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., G221 Crapo Hall



Brandon Borkholder, RoseHulman Institute of Technology



Title:

Breaking the MD5



Abstract:

The MD5 hash function and its family are security algorithms that have been used worldwide 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., G219 Crapo Hall



J.D. McKeel, University of Evansville



Title:

IdealDivisor Graphs of Commutative Rings



Abstract:

Recall that a zerodivisor 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 zerodivisor graph of R whose vertices are nonzero zerodivisors. We recognize {0} simply as an ideal of R and begin to construct idealdivisor graphs of R with respect to an arbitrary ideal I. We find and compare the diameters of zerodivisor and idealdivisor graphs of direct products of commutative rings.

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Friday, 4:10  4:30 p.m., G221 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., G219 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 pseudoranges 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 leastsquares 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., G221 Crapo Hall



Lee McDaniel, RoseHulman Institute of Technology



Title:

Benford and Winning Streaks



Abstract:

Benford’s 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 Benford’s law has been used to detect fake coin toss data, and more seriously, tax fraud. What exactly is Benford’s law? What data sets conform to this law and what are their common characteristics? Can Benford’s law be applied to other data sets (naturally and manmade) occurring in the world around us everyday?

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Saturday, 10:10  10:30 a.m., G219 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 twomirror system and a closed twomirror 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., G219 Crapo Hall



Eric Reyes, RoseHulman 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 simplelooking 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., G219 Crapo Hall



Donald Brown, University of Cincinnati



Title:

Thermal Imaging of Circular Inclusions



Abstract:

This talk will describe some results from the 2005 RoseHulman REU Inverse Problems group. We consider the inverse problem of recovering a circular defect (inclusion) from some arbitrary 2dimensional Domain knowing only thermal data on the boundary. By applying the Laplace Transform to the timedependent 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., G219 Crapo Hall



Hari Ravindran, RoseHulman 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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