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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.

Notes: Sequences and Series is part of One-Variable Calculus. We felt that since this topic had so many capsules associated with it, we wanted to introduce sub-topics. Also, the Number Theory collection of capsules does not correspond to a course in Course Communities, but has topics selected by the Editorial Board for Classroom Capsules and Notes.



Featured Items

The author discusses several conditions that guarantee the correlation of the union of two bivariate data sets is greater than common correlation of the two data sets.

The derivative of arctangent is derived directly from the definition of derivative by using some clever inequalities.

The author investigates the graph of a quartic polynomial with inflection points and finds many regularities, some involving the Golden Ratio.

The tangent of the sum formula is proved by using an inscribed quadrilateral whose longest side is the diameter of the circle, and the diagonals are perpendicular to the pair of oposite sides, respectively.

The author gives a synthetic geometric proof answering the question in the title of the paper.

Following his senior seminars, the author discusses Fermat's last theorem for rational and irrational exponents, in which the rational solutions are characterized.