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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.

 

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Featured Items

Solving an expected value problem without using geometric series

An odd prime \(p\) has \((p-1)/2\) quadratic residues mod \(p\), and for relatively prime \(p\) and \(q\) there are \((p-1)(q-1)/2\) non-representable Frobenius numbers. The author discusses a relationship between quadratic residues and the Frobenius numbers that accounts for the presence of \((p-1)/2\) in both expressions.

A visual determination of the area of a right triangle is given using an inscribed circle.

The author gives two applications of a method for finding a function \(g\) such that \(f(g(x)) \geq f(x)\).

The authors discuss drawing Platonic solids.

The author uses Moebius inversion to prove Sylow's Third Theorem.