We conducted a quantitative analysis to determine how the prerequisite path of students taking calculus I impacts their grade performance. We began by investigating the performance of students that took college algebra and trigonometry versus those that took pre-calculus ahead of their credit-bearing calculus I attempt. We concluded that there was a significant difference between the two prerequisite routes. We then performed regression analysis to view the number of credit prerequisite credit hours, including multiple attempts, as a predictor of calculus I GPA and A-proportion. We found a strong negative correlation between these variables. We hope this study can be replicated at other institutions and in other fields to help university policymakers with decision-making regarding course listings.

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Abstract. Associated to a Coxeter system (W, S) there is a contractible simplicial complex Σ called the Davis complex on which W acts properly and cocompactly by reflections. Given a positive real multiparameter q, one can define the weighted L 2 -(co)homology groups of Σ and associate to them a nonnegative real number called the weighted L 2 -Betti number. Not much is known about the behavior of these groups when q lies outside a certain restricted range, and weighted L 2 -Betti numbers have proven difficult to compute. In this article we propose a program to compute the weighted L 2 -(co)homology of Σ by considering a thickened version of this complex. The program proves especially successful provided that the weighted L 2 -(co)homology of certain infinite special subgroups of W vanishes in low dimensions. We then use our complex to perform computations for many examples of Coxeter groups, in most cases providing explicit formulas for the weighted L 2 -Betti numbers.

In this paper, we show that if we decompose a polygon into two smaller polygons, then by comparing the number of extremal vertices in the original polygon versus the sum of the two smaller polygons, we can gain at most two globally extremal vertices in the smaller polygons, as well as at most two locally extremal vertices. We then will derive two discrete Four-Vertex Theorems from our results.Definition 2.1. We say that a polygonal curve is generic if the maximal number of vertices that lie on a circle is three and no three vertices are collinear.Observe that all regular polygons are not generic.

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