Going beyond the basics: creating and inspiring problem solvers

This paper offers a general discussion of a complex student project used in a first-semester, first-year mathematics course that goes beyond the basics taught in the class and inspires creative problem solving. The project requires the student to model the transition of vehicles among regions of a vehicle rental company. A penalty cost is introduced when the regional inventory drops below an established threshold. The project allows the company to move vehicles by rail among regions to reduce or alleviate the penalty cost. In this phase of the project, student teams attempt to minimize the total cost to the company (penalty cost plus transportation costs), thus searching for an ‘optimal’ solution. The project allows the students to use technology to numerically develop an approximate solution to a problem that is easily understood, but whose analytical solution goes well beyond the scope of the course.     

Spaces Universal under Closed Embeddings for Finite-Dimensional Complete Metric Spaces

We shall prove that for every natural number n and every cardinalnumber there exists an n-dimensional complete metric spaceX_n, of weight such that every n-dimensional complete metricspace of weight is embeddable in X_n, as a closed subset.