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Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 1214

This capsule discusses a way to show each non-zero element of certain rings have a multiplicative inverse. The approach is to set up a system of linear equations and the solution is the...

In how many ways can a pet photographer pose \(C\) cats, \(D\) dogs, and \(E\) emus? The problem, often called Smirnov`s problem,  has several practical applications and has been solved...

A visualization of the triple angle formulas for sines and cosines is presented.

The limit of the geometric mean of the first \(n\) integers raised to the real positive power \(s\), divided by their arithmetic mean is shown to be \((s+1)/e^s\). An elementary derivation of...

The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective...

The author gives a visual proof of the Pythagorean Theorem.

The author presents a geometric interpretation of Leibniz`s rule for differentiating under the integral sign, and gives an informal visual derivation of the rule.

Using basic linear algebra, the authors obtain a complete, easy to compute, winning strategy for the \(4 \times 4\) mini `Lights Out` game.

The Theorem “An infinite group is cyclic when each of its nonidentity subgroups have finite index” is proved and discussed, and a test to show groups are not cyclic is ...

The author gives a proof of the title as an application of Lagrange`s Theorem, allowing the theorem to be presented in the first semester of an undergraduate abstract algebra course.

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