## Happy Holidays

For anybody that has been checking my blog, I am probably not going to have anything new to post until mid-January. Enjoy the holidays.

## The Elements of Statistical Learning

The second edition of The Elements of Statistical Learning: Data Mining, Inference, and Prediction is available free online.  It is a diverse introduction to many, many ways of using ample computational power to handle the sort of complicated data situations that are common in the modern information-rich environment.  Continue reading

## Best Proximate Value

My Oxford English Dictionary describes proximate as meaning,

Closely neighbouring, immediately adjacent, next, nearest (in space, serial order, quality, etc.); close, intimate

In this article, a proximate value will mean a value $p$ which we shall use as a stand-in for an unknown value $x$.  The unknown variable $x$ is known to have the property that

$a \leq x \leq b$

## For the Love of Inequalities

My divagations concerning the Cauchy-Schwarz inequality have not gone unnoticed. Continue reading

## The Cauchy–Schwarz Inequality IV

The Cauchy-Schwarz inequality,

$\displaystyle\sum_{i=1}^n{a_i^2}\sum_{i=1}^n{b_i^2} \geq \left(\sum_{i=1}^n{a_ib_i}\right)^2,$

holds for any pair of lists of $n$ numbers, ${a_i}$ and ${b_i}$, for $i=1,2,\ldots,n$. I am about to discuss a fourth proof of the Cauchy-Schwarz inequality. I have previously presented a first, second and third proof.  The fourth proof involves some algebraic pyrotechnics where we measure the difference between the expressions on each side of the Cauchy-Schwarz inequality. Continue reading

## Inside the Putnam

An article at the blog, The Accidental Mathematician, reflects on the experience of being on the committee that chooses the questions for the William Lowell Putnam Competition. Several rejected questions are discussed and the reasons for their rejection are also discussed.

[Hat tip: The Accidental Mathematician]

## Planarity

I recently discovered the game, Planarity. The goal of the game is to take a graph and put it in a form where none of the edges cross. That is to say, to prove that it is planar. If you don’t know what I’m saying; or you think it sounds boring; or you think it sounds complicated; go play it anyway. It’s lots of fun.