College of Science & Engineering: Mathematics Department

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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:

What Mathematics Do Students Know? Implications from NAEP for Curriculum and Policy

The National Assessment of Educational Progress (NAEP) is the nation’s best source of data on the mathematics performance of pre-college students. The National Center for Education Statistics (NCES) provides overall results each time an assessment is completed but the analyses NCES provides are too general to have direct impact on teaching and curriculum development. This project builds on descriptions of the strengths and weaknesses of mathematics curricula completed in recent years by the Indiana University School Mathematics Assessment Project (IU-SMAP). Specific objectives for this project include determination of (a) change over time in students’ mathematics skills, particularly algebra skills and skills necessary for reasoning and sense making, (b) the relationship between performance and mathematics curricula, (c) the relationship between high school course taking and specific mathematics skills, and (d) variation in the above relationships based on race/ethnicity, SES, and other demographic variables.

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 Probability Theory and Stochastic Processes with applications in Financial Mathematics. For details, please visit his webpage at http://www.usi.edu/science/math/ysarol/research.html

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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