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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

This capsule discusses an alternative way of examining the Fibonacci sequence. As a result, a class of generalized  Fibonacci sequences of numbers can be defined.

Starting with a homework problem on combinations, the capsule applies the "checkerboard" logic to derive identities involving summing squares and cubes.

Mathematical elegance is illustrated by rewriting the product and quotient rules of basic calculus in strikingly parallel forms. Applications are given for which these forms suggest meaning. Corresponding rules for second derivatives are given; the product rule is familiar, but the quotient rule is less so.

This paper offers a visual illustration of the fact that every octagonal number is the difference of two squares.

Finding multiples of a prime in Pascal's triangle visually

This note describes how to generate exercises allowing students to study nonstandard operations on familiar objects.