Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 891 - 900 of 1211

Filter by subject

An Intuitive Proof of Brouwer's Fixed Point Theorem in \(\Re^2\)

The authors demonstrate that the intuitive graphical proof of the Brouwer Fixed Point Theorem for single variable functions can be generalized to functions of two variables.

An Application of the Dominated Convergence Theorem to Mathematical Statistics

The authors give a "simple, conceptual" proof of the fact that the t-distribution converges to the standard normal. The proof is accessible to undergraduates.

A Nonconverging Newton Sequence

The possible behavior of Newton`s method when there are no real solutions is discussed.

Proof without Words: Sum of Squares

The squares are summed visually.

Proof without Words: Completing the Square

There is a visual representation of the completion of the square.

Names of Functions: The Problems of Trying for Precision

Mathematics notation is discussed, focusing on the importance, inconsistencies, eccentricities and abbreviations.

A Hardy Old Problem

The authors discuss and generalize a problem Hardy posed.

An Alternative to the Integral Test

An alternative to the integral test for the convergence of an infinite series is proposed which yield inequalities useful in error analysis.