I'm not posting as much as I did last year, when I was on sabbatical (gasp, shock, surprise), so making Forbes-blog links dump posts a monthly thing is probably just about sustainable.
-- What Math Do You Need For Physics? It Depends: Some thoughts about, well, the math you need to learn to be a physicist. Which may not be all that much, depending on your choice of subfield. Prompted a nice response from Peter Woit, too.
-- Physics And The Science Of Finding Missing Pieces: One of several recent-ish posts prompted by my last term teaching from Matter and Interactions.
-- How To Make A White Dwarf With Lasers And Cold Atoms: An explanation of ultracold plasma physics, prompted by a visit and a very nice colloquium talk by Tom Killian from Rice.
-- Here's The Physics That Got Left Out Of 'Arrival': As noted previously, the movie adaptation of Ted Chiang's "Story of Your Life" is very god but would've been better if they'd kept more of the physics from the original story. This is an explanation of that physics.
- Three Candidates For The 'Hamilton' Of Physics: Because I needed something frivolous and morale-boosting, some suggestions for splashy Broadway biographies of some notable physicists.
So, that's the month of November for you. The math and Arrival posts did really well, traffic-wise, but I'm probably happiest with the cold plasma one. But, you know, such is science blogging.
The text "nice response from Peter Woit" links to your Forbes article, not to Woit's response. That's a shame, since Woit's reply was a very good and thoughtful.
Dammit, I hate when that happens. I've been using this laptop for ages, and still get tripped up by the "Fn" key that's right where "Ctrl" is on my desktop.
Your math article was interesting, as was the Woit response. I loved your ending. Perhaps you should reply to your students with "You need to know enough mathematics to be able to solder a diode onto a circuit board."
My take is that physics requires total fluency in some very narrow subsets of intermediate-level undergrad mathematics. You may or may not need to take an entire course to pick those up. (At the beginning you need a class; later you just need a book.) You might consider making up a list of what your physics majors need to LEARN from their math classes so they won't throw the baby out with the bathwater when they forget most of it in the weeks after a math final exam.
I'd be a little stronger on the harmonic oscillator. Its importance is that it is one of the relatively few systems that can be solved in closed form within quantum mechanics and classical mechanics. Students in calculus begin to believe that every problem can be solved, but that is because they only see the ones that can be done with a year or two of calculus. As just one example, I don't recall the Airy function being treated in my DE class. And if a triangular potential is such a rude problem, no wonder we use oscillators and square wells when we need to approximate something more complicated as a check on numerical solutions.
Along that same line, most of what students need to know about complex analysis is how to use Cauchy's residue theorem, followed closely by knowing how to read a book.
Some might include Euler's formula, but I consider that basic mathematics that should be learned in an intro physics or DE class. Woit's point about Fourier analysis is well taken. It is also basic mathematical physics because shows why those oscillators are so useful.
And I'd also add that the LANGUAGE of linear algebra (just terminology and definitions) is most of what people actually use. Find a way to teach that separate from the math department or the pre-req chain in your own classes.
The only topics clearly missing from your wide-ranging list of what specialists might need to know would be group theory and the numerical solution of various types of mathematical problems. (The latter was one plus of your use of Matter and Interactions.)