Links for the proposed History of Mathematics course.

Here's a history of math course taught by Schechter, Fall 1999 at Vanderbilt.
The text is David M. Burton, "THE HISTORY OF MATHEMATICS, Fourth Edition"
This course emphasizes the history of numbers, calculus, geometry and set theory and logic. JB, you are the Vanderbilt expert, is a 252 course upper or lower division?
His "Common errors in undergraduate mathematics" should be required reading for secondary education majors.
It starts out: "I am tired of seeing these same old errors over and over again. (I would rather see new, original errors!) ". More than just fun reading, this guy really has does hit exactly the most common errors I see year after year. Yes, it includes the linearity of radicals.

The MAA had an "Institute for the History of Mathematics and Its Uses in Teaching, 1999. Here's the uninformative link:

Here's a $30 30 minute MAA video which can't cover all that much. Journey through Genius:

Here's a well-organized math history page from CalState Northridge
It includes the history overview link:

I didn't know there was such a thing as Hawaiian Geometry. I'm still not convinced
but here's the link to "Geometry in Hawaiian History".

This seems to be the biggest and most-linked math history site
but I haven't found much here or in any other site dealing with actual courses.

Here are other typical math history links, again, not much dealing with courses:

Here is a list of texts on the history of mathematics, no comments on the good vs. the bad:

Here's a UCLA math history course but just the course description, no text is listed

Find out what the pneumonic "Oh heck another hour of algebra" stands for:

Few universities offer history of math. Here's the course description for Berkeley's:
History of Mathematics -- Mathematics (MATH) 160 [4 units] Course Format: Three hours of lecture per week. Prerequisites: 53, 54, and 113. Description: History of algebra, geometry, analytic geometry, and calculus from ancient times through the seventeenth century and selected topics from more recent mathematical history. (SP) (from the 1999-2001 General Catalog updated as of 9/21/2000)
The text used is Katz, History of Mathematics, Pearson-Longman.
The calculus and precalculus texts Berkeley uses are similar to ours. It appears they are switching
from Hallet-Hughes to Stewart. They also use Cohen for precalculus:

Here's a web page from Swarthmore. It doesn't look like a course but it's listed under the WebCT banner.
Famous Problems in the History of Mathematics.