Welcome, one and all, to the 41st Carnival of Mathematics! Step right up and marvel at the amazing, the astounding, the *prime* number 41! It is, of course, the 41st natural number, and is equal to the product of itself and 1!

Perhaps more interesting is the fact that 41 is a twin, supersingular, Germain, Eisenstein, Proth, and Newman-Shanks-Williams prime (which has to be some kind of record). It is also a centered square number.

We begin with a very accessible discussion of infinite sets, and the difference between countable and uncountable, by Carnival XL host Barry Leiba, in Countable and uncountable sets, part 1, at Starting at Empty Pages. (There’s also a part 2.)

How cool would it be to have a Mathematician for President? Denise tells us all about James Garfield and his proof of the Pythagorean Theorem over at Let’s Play Math.

The Central Limit Theorem is a well-known result in statistics, but in order to use it, one must assume a sufficiently large number of samples. John Cook, from The Endeavor, wants to know about quantifying the error in the central limit theorem, and how close an approximation we can really get. He also compares three methods of computing standard deviation – turns out they’re not all equally good.

Motivated by a confusing chapter in a book on game theory, Rod Carvalho decided to analyze the “Tragedy of the Commons” in Bandwidth-Sharing Games, over at Reasonable Deviations. In his words:

Suppose that *n* players would like to have part of a shared resource: each player wants to send information along a shared channel of known maximum capacity. I analyze this problem using a game-theoretic approach.

Barry Wright III, at 3 Style Life, goes in depth on elections in Facts about the Copeland Score (with PDF continuation), a way to generalize the Condorcet winner to elections that don’t have a Condorcet winner.

Music and math often go hand in hand, and David Stutz gives us a lot to think about in more musical Turing machines, at the synthesist. Inspired by Neal Stephenson’s new book *Anathem*, Stutz led a choral performance of a 3-state, 2-symbol Turing machine that performed binary addition. From there, things really take off!

Mike Croucher, 2-time Carnival host and owner of Walking Randomly, and a Mathematica power user, shows us how to Simulate Harmonographs. (A harmonograph is the result of letting a pendulum with a pencil attached to it swing over a piece of paper, like a Spirograph, but cooler.) Then he asks the question: NAG – The Ultimate MATLAB Toolbox? Read to find out if the Numerical Algorithm Group has hit a home run.

Looking for help with your math homework? Visit VideoJug’s math repository for a collection of advice videos on math.

Technology can be a great tool in teaching, and Maria, from Teaching College Math Technology Blog, demonstrates How Tablets Enhance the Math. Derivatives have never looked better.

Last, but certainly not least, how would you get a computer to use ordinal numbers? Mark Dominus tackles the question in Representing ordinal numbers in the computer and elsewhere, over at The Universe of Discourse.

An accidentally missed submission (sorry Jason!) comes from Jason Dyer. His entry, Visual Clarity in the Naming of Variables, examines how using similar letters for different variables can be confusing to students, and he offers several alternatives.

That’s it for #41, but tune in on October 24 for the next edition, hosted by The Endeavor.