*The author relates a personal story of a post-WWII assignment in the U.S. Navy. His analysis of data from a test of a harbor mine-detecting algorithm leads to a novel construction of the...*

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*When is the average of sums of powers of integers itself a sum of the ﬁrst \(n\) integers raised to a power? We provide all solutions when averaging two sums, and provide some conditions...*

The Cantor subset of the unit interval \([0,1)\) is large in cardinality and also large algebraically, that is, the smallest subgroup of \([0,1)\) generated by the Cantor set (using addition mod...

*The author presents a variety of double and triple integrals designed to exercise a student's ability to visualize the interplay between an integrand and the region over which it is...*

*Using two well known criteria for the diagonalizability of a square matrix plus an extended form of Sylvester's Rank Inequality, the author presents a new condition for the diagonalization...*

*Here is a technique for proving the fundamental theorems of analysis that provides a unified way to pass from local properties to global properties on the real line, just as ordinary induction...*

A typical first course on linear algebra is usually restricted to vector spaces over the real numbers and the usual positive-definite inner product. Hence, the proof that \(\dim(\mathcal{S...

*Hölder’s inequality is here applied to the Cobb-Douglas production function to provide simple estimates to total production.*

*Mathematical elegance is illustrated by rewriting the product and quotient rules of basic calculus in strikingly parallel forms. Applications are given for which these forms suggest meaning....*

*The author provides a somewhat recreational application of limit interchange and L'Hopital's rule. The goal is to hint at the importance of limit/sum interchange in Analysis without,...*