I didn't major in math, but it seems to me that introductory probability and statistics courses aren't the most demanding courses in the world of maths, nor are they "advanced" mathematics. I'll say the same for the requirement for "any" course that using computers or graphing calculators significantly. First semester calculus would satisfy that requirement. In all honesty, to make the claim that these courses are advanced kind of makes Austin's point for him.

Single and multivariable calculus is covered in introductory-level textbooks. Linear algebra is the real thing, but if only one course is required, it's the introductory-level course that they sell For Dummies books for. So, again, not advanced in my book. Real math, yes, but not very advanced.

I couldn't agree more with Austin about needing someone mathy by the time GT students get into geometry. For one reason why, see this thread.