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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 describes explicitly the projective plane as a surface formed from a square by joining each pair of opposite edges in a definite way.

The authors provide a proof, accessible to beginning number theory students, of Chebychev`s upper bound on the number of primes no greater than n.

The author gives a visual proof of the fact that the sum of (2k-1)(-1)n-k from k = 1 to n is n.

A theorem justifying iteration of improper integrals for which Fubini`s Theorem does not apply is presented.

If two elements in a group are positioned symmetrically about the main diagonal line in the multiplication table, then the two elements are conjugate.

Once students master the Integral Test, it is useful to show that there cannot be a series on the boundary between convergence and divergence.