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Classroom Capsules and Notes

Note. We now return to our every-other-week schedule for featured articles, shown at the bottom of this page.

Capsules By Courses. We are organizing the capsules into courses, when possible using the same topics as are used in Course Communities. So far we have organized capsules for the following courses:

You may select topics within each course.


Featured Items

The author uses the Stolz-Cesàro theorem to compute the sums of the integer powers.

A solution to a probabilistic Putnam Exam Problem is presented.

The authors discuss the existence of functions from the nonnegative reals to the nonnegative reals that satisfy the functional equation underlying Candido`s identity.

Differentiate \(f(x)^{g(x)}\) first as if \(g\) was a constant, then as if \(f\) was a constant. Presto!

If \(r\) and \(s\) are algebraic numbers, then \(r + s\), \(rs\), and \(r/s\) are also algebraic. The proof provided in this capsule uses the ideas of characteristic polynomials, eigenvalues, and eigenvectors.

The "magic curve" is \(y=1/x\). Various calculus facts are shown by illustration using Riemann sums for the areas of portions of this curve.