[bkcooper]

The bullet points this article (and the one by Chad Orzel it links to) mentions are the common most used things day-to-day by basically anybody doing physics. However, I think stopping at that level of mathematical background would make reading a lot of the existing literature hard. Woit mentions complex analysis, but at least that usually comes up in mathematical methods classes, at least at the level needed to understand the arguments where it is used. Some math that I often found myself wanting more of includes differential geometry (I find physics introductions to tensor manipulation to be very heavy on mechanics and terrible on intuition for what you're actually doing) and functional analysis.

Both articles leave out numerical analysis or scientific computing, which I think is a huge gap. I certainly felt like my education left the impression that these things were way more straightforward than they actually are.