I’ll admit it: before grad school I wasn’t fully clear on the
distinction between statistics and applied mathematics. In fact
— gasp! — I may have thought statistics was a branch of
mathematics, rather than its own discipline. (On the contrary:
see Cobb & Moore (1997) on “Mathematics, Statistics, and
Teaching”; William Briggs’s blog; and many others.) Of course
the two fields overlap considerably; but clearly a degree in one
area will not emphasize exactly the same concepts as a degree in
the other. One such difference I’ve seen is that statisticians
have a greater focus on variability. That includes not just
quantifying the usual uncertainty in your estimates, but also
modeling the variability in the underlying population. In many
introductory applied-math courses and textbooks I’ve seen, the
goal of modeling is usually to get the equivalent of a point
estimate: the system’s behavior after converging to a steady
state, the maximum or minimum necessary amount of something,
etc. You may eventually get around t