Research and Publications
| Dr. Adrian Gentle: |
Gravity is the weakest of the four fundamental physical interactions, and yet is almost solely responsible for the large-scale structure and evolution of the Universe. General relativity (GR) is Einstein's geometric theory of gravity, which both supersedes Newtonian gravity and also encompasses it in the appropriate limit, predicts the existence of black holes and gravitational waves, ripples in the fabric of space and time.
With the advent of a world-wide network of gravitational wave detectors we stand on the threshold of a revolutionary new branch of astronomy, a new "window on the universe". The complexity of the Einstein equations, which govern general relativity, necessitate the use of computer simulations to interpret the observations of these gravitational wave detectors.
Dr. Gentle studies the formulation of the Einstein equations used in these simulations, as well as an alternative approach, known as Regge calculus, which uses a discrete lattice to model the structure of spacetime.
| Dr. Sangwoo Heo : |
Forecasting Accuracy of American Stock Option Prices via Approximation Models
Forecasting accuracy of option pricing models has always been a topic of interest because of increasing volatility in domestic and international security markets. The primary objective of this study is to examine the accuracy of approximating formulas for pricing American Options.
| Dr. Doris Mohr: |
An Analysis of NAEP Data
Dr. Mohr is examining data from the mathematics portion of the National Assessment of Educational Progress (NAEP), which is administered every other year on a nation-wide basis. In particular, she is looking at the items on the assessment to see how they align with the Indiana Academic Standards. She will then compare the performance of Indiana students in grades 4 and 8 to the nation as a whole.
| Dr. Kathy Rodgers: |
Studying College Mathematics Placement Testing for High School Students
The goal of this research project is to reduce the percentage of incoming freshmen from the targeted high schools that place into a remedial math class and to increase the percentage of students who place into the appropriate college-level math course by administering a college-level mathematics placement test to high school juniors.
| Dr. Yalcin Sarol: |
Dr. Sarol's research interests lie in the fields of Stochastic Analysis and Financial Mathematics. He is particularly interested in the financial models and stochastic partial differential equations where the random noise is driven by fractional Brownian motion or more irregular Gaussian processes.
<a href="http://en.wikipedia.org/wiki/Fractional_Brownian_motion" target="_blank"> Fractional Brownian motion</a> was initially used in the modelling of hydrological phenomena. Later, it was used in various fields such as network traffic, computer graphics, and financial mathematics. Various developments of stochastic calculus with respect to fractional Brownian motion has been presented in the recent years which led researchers to many interesting problems.
| Dr. Ruben Schweiger: |
Dr. Schwieger is continuing to work on his Solar Pump project and will do so some during the summer. Though funding from the FRCWA has concluded, he has materials to continue work. He has developed a new design for the solar collectors and will be creating and testing those.
Dr. Schwieger also continues work on Problem Solving and Mathematics Concept teaching and learning, and he scheduled to present two or three papers on these during the 2006-2007 school year. He has just concluded presentation of three papers for the TTT conference sponsored by SWICTM in Evansville.
| Dr. William Wilding: |
Dr. Wilding’s current research interests include topics related to optimal strategies in tournament poker. Two such topics are equity modeling and analysis of push/fold poker. Equity modeling approximates the value of different chip stack positions in a tournament and is fundamental in quantifying and comparing the value of possible future actions. Push/fold poker is a simplified poker game which is particularly useful in approximating optimal strategies in no-limit poker when the blinds and antes are large compared to the chip stacks of the players.
Other research interests include fitting distributions to stock index and wealth data as well as modeling entry-level placement into mathematics courses.
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