*Here is a technique for proving the fundamental theorems of analysis that provides a unified way to pass from local properties to global properties on the real line, just as ordinary induction...*

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A typical first course on linear algebra is usually restricted to vector spaces over the real numbers and the usual positive-definite inner product. Hence, the proof that \(\dim(\mathcal{S...

*Hölder’s inequality is here applied to the Cobb-Douglas production function to provide simple estimates to total production.*

*Mathematical elegance is illustrated by rewriting the product and quotient rules of basic calculus in strikingly parallel forms. Applications are given for which these forms suggest meaning....*

*The author provides a somewhat recreational application of limit interchange and L'Hopital's rule. The goal is to hint at the importance of limit/sum interchange in Analysis without,...*

Using a simple trigonometric limit, the author provides an intuitive geometric proof of the Singular Value Decomposition of an arbitrary matrix.

*Motivated by the observation that the derivatives of \(e^x\) are all positive and the derivatives of \(e^{-x}\) alternate sign, the author asks what kinds of ``sign patterns" are possible...*

*The author provides a simple context and some history in which actuarial computations take place.*

*In a classic pouring problem, given two jugs with capacities \(m\) and \(n\) pints, where \(m\) and \(n\) are relatively prime integers, and an...*

*Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to...*