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We generalize parts of the Müntz-Szász theorem by considering the denseness of sets span{x 1 , x 2 , . . .}, where the i 's grow polynomially. We develop a new interpolation technique to illustrate more precisely what is missing from the closure of the Müntz sets. This is a robust technique which allows for perturbations.

Textbooks and websites today abound with real data. One neglected issue is that statistical investigations often require a good deal of "cleaning" to ready data for analysis. The purpose of this dataset and exercise is to teach students to use exploratory tools to identify erroneous observations. This article discusses the merits of such an exercise and provides a team project, problem data, cleaned data for instructors, and reflections on past experiences. The main goal is to give instructors a prepared project for their students to perform realistic data preparation and subsequent analysis. The data for this project involve categorical and continuous variables for subjects age 65 and over testing calcium, inorganic phosphorus, and alkaline phosphatase levels in the blood. The project described in this article involves summary analysis, but the cleaned data could also be used for projects on independent samples t-tests, analysis of variance, or regression.

These notes provide a brief introduction to topological groups with a special emphasis on Pontryaginvan Kampen's duality theorem for locally compact abelian groups. We give a completely self-contained elementary proof of the theorem following the line from [36]. According to the classical tradition, the structure theory of the locally compact abelian groups is built parallelly.

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