There has been some recent discussion at Reddit of an attempt I made to turn some data from arXiv.0rg into a visualization of the relationships between research areas in mathematics. I was never completely pleased with the dataset.
Category Archives: Mathematics
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
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. Continue reading
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]
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.
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. Continue reading
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.
I somehow missed some great notes on recursion theory and incompleteness by Jeremy Avigad, written about on Ars Mathematica. As noted in the article, approaching incompleteness from the point of view of algorithms is a really accessible way of doing it. If you have some time, you should check it out. Continue reading
I have previously written about the Cauchy-Schwarz Inequality.
Here is another proof of this fun inequality. We start at a similar point to the previous proof Continue reading
I recently read The Cauchy-Schwarz Master Class by Michael Steele which, in addition to teaching the reader about inequalities, has a lot of fun and varied things to say about the Cauchy-Schwarz inequality.
First things, first, the Cauchy-Schwarz inequality in it’s simplest form says the following: