Introductory Mathematics for Quantum Chemistry

An elementary discussion of some of the mathematics employed in studying Quantum Chemistry in a style appropriate for persons who have not taken advanced mathematical instruction.

Student Performance in Traditional vs. Online Format: Evidence from an MBA Level Introductory Economics Class

All previous studies comparing online and face-to-face format for instruction of economics compared courses that were either online or face-to-face format and regressed exam scores on selected student characteristics. This approach is subject to the econometric problems of self-selection omitted unobserved variables. Our study uses two methods to deal with these problems. First we eliminate self-selection bias by using students from a course that uses both instruction formats. Second, we use the exam questions as the unit of observation, and eliminate omitted variable bias by using an indicator variable for each student to capture the effect of differences in unobserved student characteristics on learning outcomes. We report the finding that students had a significantly greater chance of answering a question correctly if it came from a chapter covered online.

The Devil’s Calculus: Mathematical Models of Civil War

In spite of the movement to turn political science into a real science, various mathematical methods that are now the staples of physics, biology, and even economics are thoroughly uncommon in political science, especially the study of civil war. This study seeks to apply such methods - specifically, ordinary differential equations (ODEs) - to model civil war based on what one might dub the capabilities school of thought, which roughly states that civil wars end only when one side’s ability to make war falls far enough to make peace truly attractive. I construct several different ODE-based models and then test them all to see which best predicts the instantaneous capabilities of both sides of the Sri Lankan civil war in the period from 1990 to 1994 given parameters and initial conditions. The model that the tests declare most accurate gives very accurate predictions of state military capabilities and reasonable short term predictions of cumulative deaths. Analysis of the model reveals the scale of the importance of rebel finances to the sustainability of insurgency, most notably that the number of troops required to put down the Tamil Tigers is reduced by nearly a full order of magnitude when Tiger foreign funding is stopped. The study thus demonstrates that accurate foresight may come of relatively simple dynamical models, and implies the great potential of advanced and currently unconventional non-statistical mathematical methods in political science.