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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

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The number 1089 has the curious property that when one reverses its digits, an integer multiple of itself is obtained. The author gives a structure theorem for certain sets of reversible numbers.

The author derives formulas for the coefficients of the characteristic polynomial of a square matrix in terms of the partial derivatives of its determinant, which is viewed as a function of the entries of the matrix.

Given symmetric unit vectors \(u_i\), conditions on real numbers \(x_i\) are considered to be able to conclude that \(\sum x_i u_i \Rightarrow x_i = 0\) for all \(i\). Different kinds of “symmetry” lead to different conclusions.

This article presents an algebraic proof of the primitive root theorem.

This article models the life of a chain letter as a branching process.