Cookie Monster Numbers, Journal Reading, and Mini-Blogging

I just spent the last several minute taking it easy at the end of my day reading a little bit about set theory. It wasn't the dry and/or indecipherable stuff some of you might remember from first grade thanks to the 'new math'. Nope, this article on set theory was on something called the Cookie Monster Number, the least number of moves that Cookie Monster can take to empty a set of jars of cookies if he can only take the same amount of cookies from every jar on each move. Since I'm headed off to bed for the night, rather than rehash the subject here, I'll spend competitora little bit of time telling you about where you can read more on the subject.

For a brief intro to the Cookie Monster Number, check out +Richard Green's mini-blog on G+. Specifically, you'll want the post on Cookie Monster[1]. For those reading this on my blog as opposed to G+, the Facebook competitor from Google has actually become quite the mini-blogging site for scientists of all flavors. For a quick sampling of what's available you can check out the circle of folks that follow Richard Greens math posts[6]. While it's becoming more diverse all the time, the circle still contains a large number of very interesting science writers and readers for that matter.

If you'd like to delve even further into the Cookie Monster Number, you can check out the article I was reading[2] tonight in the College Mathematics Journal from the +Mathematical Association of America.

The journals from the MAA are all my current favorites. When I entered physics as an undergraduate, I was immediately advised to read journals in my field even if I didn't understand them at first. No offense to the +American Physical Society, but try as I might, I got nothing from Physical Review A-D and Letters until I was a grad. student. Now that I have the background, I'm of course loving these journals, but I digress... What I should have been reading and what I would heartily advise any undergrad in science to read are the MAA journals:

College Mathematics Journal[3]

Mathematics Magazine[4]

and American Mathematics Monthly[5]

I've listed them from what I perceive to be the simplest to the most complex. They're well written and generally fun. There's always at least one great article that I can comprehend, month after month, and no matter what your field, these journals can help you build the mathematical foundations you'll need.

References
1. Richard Green on Cookie Monster
https://plus.google.com/101584889282878921052/posts/8qWvSaLJVGD

2. Cookie Monster and Fibonacci Sequences
http://www.jstor.org/discover/10.4169/college.math.j.45.2.129?uid=3739920&uid=2&uid=4&uid=3739256&sid=21103590207767

and the open access version on Arxiv
http://arxiv.org/abs/1305.4305

3. http://www.jstor.org/action/showPublication?journalCode=collmathj

4. http://www.jstor.org/action/showPublication?journalCode=mathmaga

5. http://www.jstor.org/action/showPublication?journalCode=amermathmont

6. Richard Green's Engager Showcase Circle
https://plus.google.com/101584889282878921052/posts/KjVfRTXA5Go

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain ...

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1. While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero. This is typically explained in the following way. While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare. That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2]. Cabrera was utilizing a loop type of magnetic monopole detector. Its operation is in...

The Alcubierre Warp Drive Tophat Function and Open Science with Sage

I transferred yesterday's Mathematica file with the Alcubierre warp drive[2] line element and space curvature calculations to the +Sage Mathematical Software System today, (the files been added to the public repository [3]). If you haven't used Sage before, it's a Python based software package that's similar in functionality to Mathematica. Oh, and it' free. I also worked a little more on understanding the theory, but frankly, I made far more progress with the software than the theory. What follows will be a little more of the Alcubierre theory, plus, a cool Sage interactive demo of one of the Alcubierre functions[1], as well as a bit about my first experience with using Sage. Theory The theory is fun, but it's moving slowly. Here's the chalk board from this morning's discussion Alcubierre setup the derivation using something called the 3+1 formalism which means we consider space to be flat, (in this case), slices that are labelled ...

Copasetic Flow

Search This Blog