# Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 1211

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 Smirnovs 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 Lagranges Theorem, allowing the theorem to be presented in the first semester of an undergraduate abstract algebra course.