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. 

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 which we shall use as a stand-in for an unknown value .  The unknown variable is known to have the property that

For the Love of Inequalities

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

The Cauchy–Schwarz Inequality IV

The Cauchy-Schwarz inequality,

holds for any pair of lists of numbers, and , for . 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.

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.

The Cauchy–Schwarz Inequality III

I have previously written about the Cauchy-Schwarz Inequality here and here.  To recap, the Cauchy-Schwarz inequality,

holds for any pair of lists of numbers, and , for .    Now, I have given two proofs so far, and here is a  third.  We will proceed by induction on the number of variables.  

LaTeX2WP, a LaTeX to WordPress converter

If you write a lot of mathematics on WordPress, then you might find it useful to look at Luca Trevisan’s LaTeX2WP. As you might have guessed, it converts LaTeX to something you can paste into a WordPress blog editing environment. It seems to use python which should be easy to use on a Linux-based system and would probably require something like Cygwin on a Windows machine.

Goolge Wave Invitations

If you have been late to the party with Google Wave, Lifehacker has a donation thread where kindhearted souls with an excess of Google Wave invitations offer them to all who are interested.  You are going to need an active account on Lifehacker to request an invitation from most people, which is not as easy as it might seem.  However, a few people just paste their email in their comment, so you can just email them directly without needing to comment on Lifehacker.  I was able to get an invitation for a friend using Lifehacker’s donation thread so it seems to work.

[Hat tip: Lifehacker]