This project allows students to better understand the scope and pace of climate change by conducting their own analyses. Using data readily available from NASA and NOAA, students can apply their knowledge of regression models (or of the modeling of rates of change). The results lend themselves to a writing assignment in which students demonstrate…

Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

The project models the conductive heat loss through the ceiling of a home. Students are led through a sequence of tasks from measuring the area and insulation status of a home to developing several functions leading to a net savings function where the depth of insulation is the input. At this point students use calculus or a graphing utility to…

This project classifies groups of small order using a group's center as the key feature. Groups of a given order "n" are typed based on the order of each group's center. Students are led through a sequence of exercises that combine proof-writing, independent research, and an analysis of specific classes of finite groups…

Designing an optimal Norman window is a standard calculus exercise. How much more difficult (or interesting) is its generalization to deploying multiple semicircles along the head (or along head and sill, or head and jambs)? What if we use shapes beside semi-circles? As the number of copies of the shape increases and the optimal Norman windows…

We introduce playing games on the shadows of knots and demonstrate two novel games, namely, "To Knot or Not to Knot" and "Much Ado about Knotting." We discuss winning strategies for these games on certain families of knot shadows and go on to suggest variations of these games for further study.

A number triangle, discovered using a recurrence formula similar to that of Pascal's triangle, yields sequence A077028 from the Online Encyclopedia of Integer Sequences.

Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three non-collinear points from S, the center of the circle through those three points is also an element of S. A problem appearing on the Macalester College Problem of the Week website stated that a finite set of points in the plane,…

The five Platonic solids are constructed (as graphs) from their rotational symmetry groups. The constructions are based on an idea of Bertram Kostant and are quite simple; conjugacy classes in the group are the vertices of the graphs and products determine adjacency.