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Can mathematics be a tool for personal growth and fulfillment for inmates in a high security federal prison, students, and people in general? The experiences of Christopher Jackson, who is an inmat...

Math courses graded on homework, tests, and a final examination can result in students putting together enough partial credit to pass the class without gaining a reasonable mastery of the course co...

Every mathematician I know is frustrated with the experience of having a new acquaintance proudly tell us that they are no good at math usually followed by a description of when they started to dis...

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students...

To understand the mechanisms leading to coexistence and exclusion, it is essential to establish information on the nutritional needs of species. We focused on the frequently coexisting Pseudo-nitzschia species, P. delicatissima and P. galaxiae, capable of forming blooms and producing domoic acid. We employed monoculture experiments to determine growth kinetic parameters important for understanding resource use (i.e. maximum specific growth rate, half-saturation coefficients for growth and cell quotas), and we coupled mixed-culture experiments and numerical modelling to explore the role of resource competition relative to unknown factors, such as allelopathy. Experimental results showed that both species had a high requirement for nitrogen (N) and low requirement for phosphorus (P), consistent with field observations of Pseudo-nitzschia blooms in N-rich conditions. The model accurately predicted the outcome of competition; P. galaxiae outcompeted P. delicatissima when considering only resource competition, but the population trajectories were better predicted when allelopathic effects were added. Since the competitive exclusion of P. delicatissima by P. galaxiae in our laboratory experiments is not consistent with observations of coexistence in the natural environment, the model was further modified to explore realistic ranges of population loss factors, such as sinking, demonstrating how coexistence is possible when these are considered.

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the type of writing assigned in my mathematical modeling course. Where the assignments are unusual, they are thoroughly described and I share my experiences on what worked well and what was not as successful. Where the assignments are more traditional, I offer an analysis of problems and pitfalls in teaching writing. Formal project reports for the class teach students how to write scientific articles. Unusual reflective assignments help students integrate their learning and apply it in new contexts.

Mata is Stata's matrix language. The Mata Matters column shows how Mata can be used interactively to solve problems and as a programming language to add new features to Stata. In this quarter's column, we investigate underflow and overflow and then delve into the details of how floating-point numbers are stored in the IEEE 754 floating-point standard. We show how to test for overflow and underflow. We demonstrate how to use the %21x format to see underflow and the %16H, %16L, %8H, and %8L formats for displaying the byte content of doubles and floats.

Stsatrisk is a wrapper for sts graph that adds a table to a survival plot with at-risk information, making it easy to create graphs that follow the list of recommendations given by Pocock et al. (2002) for Kaplan–Meier plots. We use stsatrisk to create plots in the desired format with the desired information.

stsatrisk is a wrapper for sts graph that adds a table to a survival plot with at-risk information, making it easy to create graphs that follow the list of recommendations given by Pocock et al. (2002) for KaplanÐMeier plots. We use stsatrisk to create plots in the desired format with the desired information. Copyright 2004 by StataCorp LP.

Local polynomial regression is a generalization of local mean smoothing as described by Nadaraya (1964)andWat s on (1964). Instead of fitting a local mean, one instead fits a local pth-order polynomial. Calculations for local polynomial regression are naturally more complex than those for local means, but local polynomial smooths have better statistical properties. The computational complexity may, however, be alleviated by using a Stata plugin. In this article, we describe the locpoly command for performing local polynomial regression. The calculations involved are implemented in both ado-code and with a plugin, allowing the user to assess the speed improvement obtained from using the plugin. Source code for the plugin is also provided as part of the package for this program. Copyright 2003 by StataCorp LP.

We study singularity formation in spherically symmetric solutions of the charge-one and charge-two sector of the (2+1)-dimensional S^2 sigma-model and the (4+1)-dimensional Yang-Mills model, near the adiabatic limit. These equations are non-integrable, and so studies are performed numerically on rotationally symmetric solutions using an iterative finite differencing scheme that is numerically stable. We evaluate the accuracy of predictions made with the geodesic approximation. We find that the geodesic approximation is extremely accurate for the charge-two sigma-model and the Yang-Mills model, both of which exhibit fast blowup. The charge-one sigma-model exhibits slow blowup. There the geodesic approximation must be modified by applying an infrared cutoff that depends on initial conditions.