Design, Implementation, and Assessment of an Undergraduate Interdisciplinary Watershed Research Laboratory

This article discusses the establishment of Shippensburg University's Burd Run Interdisciplinary Watershed Research Laboratory and the advantages of linking disciplinary perspectives across courses in geology, geography, biology, and teacher education. The laboratory provides an easily adaptable conceptual model for improving environmental science education at teaching-oriented institutions nationwide. Its success is largely attributable to three factors: the project is student-centered and goal specific; the selected watershed is accessible, diverse, and at a manageable scale; and the Laboratory Advisory Board provides for continuous revision, adaptation, and improvement. Educational levels: Graduate or professional

Strong coprimality and strong irreducibility of Alexander polynomials

A polynomial f(t) with rational coefficients is strongly irreducible if f(t^k) is irreducible for all positive integers k. Likewise, two polynomials f and g are strongly coprime if f(t^k) and g(t^l) are relatively prime for all positive integers k and l. We provide some sufficient conditions for strong irreducibility and prove that the Alexander polynomials of twist knots are pairwise strongly coprime and that most of them are strongly irreducible. We apply these results to describe the structure of the subgroup of the rational knot concordance group generated by the twist knots and to provide an explicit set of knots which represent linearly independent elements deep in the solvable filtration of the knot concordance group.Comment: 16 pages, 6 figure