# Classroom Capsules and Notes

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

##### Equivalent Inequalities

The article demonstrates that four inequalities can be derived from each other.

##### Integration by Parts and Infinite Series

Infinite series representing several functions, and several series representing $\pi$ are derived using tabular integration by parts.

##### No Fooling! Newton's Method Can Be Fooled

Various examples of convergent Newton sequences which do not converge to a zero of the underlying function are given.

##### An Integral Domain Lacking Unique Factorization into Irreducibles

The author displays an example of a domain where factorization is not unique.

##### Butterflies in Quadrilaterals: A Comment on a Note by Sidney Kung

The Butterfly Theorem is generalized to include Sidney Kung`s Butterfly Theorem.

##### Sum-Difference Numbers

The author characterizes the positive integers that are the products of two pairs of factors such that the sum of one pair equals the difference of the other.