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Classroom Capsules and Notes





Classroom Capsules and Notes brings together the best of 112 years of the short classroom materials from the MAA print publications.

Table of Featured Items

Using Tangent Lines to Define Means

The authors define and discuss a wide variety of means. One of the authors was an undergraduate student.
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A Dynamical Systems Proof of Fermat's Little Theorem

An interesting unusual visual and rigorous proof of Fermat`s Little Theorem, with unusual generalizations
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Power Distribution in Four-Player Weighted Voting Systems

Interesting example of 5 possible power distributions in a 4-player veto-proof voting system.
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A Graph of Primes

The graph obtained by constructing an edge between each pair of primes with difference a power of 2 is not connected.
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The Square Roots of 2x2 Matrices

The Cayley-Hamilton theorem may be used to determine explicit formulae for all the square roots of 2 X 2 matrices.
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A Surprising Application of the Integral of 1 - F(x) to Revenue Projection

The author describes an integral that represents the proportion of wages covered by Social Security and exposed to taxation.
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