### Remember the New Math? Blame it on Sputnik!

Remember when "The New Math" had us all learning set theory in elementary school?  I hated set theory, and had no idea why we were learning it.  This week, years, (ahem, many), year later, I found out what it was all about: Sputnik!  While researching a book in the--as it turns out--aptly named New Mathematical Library, I found the historical link.

The NML was a series of books commissioned by the School Math Study Group (SMSG).  A quick dive into Wikipedia turned up the interesting fact that the SMSG was formed after Sputnik flew over.  The US decided we were going to need far more scientists and engineers than we had available.  The solution to the problem back then made logical sense: increase the number of math literate students available.  Hence, the SMSG gave us the NML, a series of excellent books that: "make available to high school students short expository books on various topics not usually covered in the high school curriculum", and the New Math.  If only they'd told us what the New Math was for!

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

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 rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### 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 concept very simpl…