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Browse Classroom Capsules and Notes

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The paper presents a guided collection of problems investigating when groups are isomorphic to proper subgroups.

The author explores integration of radially symmetric functions of several variables.

This is a discusion of the importance of the existence of limits in L'Hôpital's Rule.

An analytic proof of the fact that for any triangle \(ABC\), \(G=\frac{1}{3}(A+B+C)\) is the centroid of the triangle.

A simple characterization of the condition that, for an integer-sided triangle, one angle is twice another.

An alternative to partial fractions for certain integral calculations

Using substitutions to derive equations for the ellipse and hyperbola

A polar coordinate proof of the fact that the focal radii of an elipse (hyperbola) make equal angles with the tangent.

An extension of the fact that \(1/n!\) is the content (volume) of a particular \(n\)-dimensional simplex

Simple proofs of the formulas for the derivatives of \(\sin x\) and \(\cos x\) when \(x\) is acute