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Browse Classroom Capsules and Notes

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A real matrix is called square-palindromic if, for every base \(b\), the sum of the squares of its rows, columns, and four sets of diagonals (as described in the article) are unchanged when...

The author clarifies the wording of Cramer's rule, sidestepping a common misconception.  The Kronecker-Capelli theorem is introduced to help see Cramer's rule in a more complete...

Like Pascal’s triangle, Faulhaber’s triangle is easy to draw: all you need is a little recursion.  The author demonstrates that the rows are the coefficients of polynomials...

The author considers the effects of inflation and interest rates on computing the present value of $100 three years from now.

It is well known that maximal ideals in the ring of continuous functions on the closed interval \([0, 1]\) are not finitely generated. Less well known is the fact that these ideals are not...

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...

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...

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