Americans abbreviate anything they can, Col. When I worked with the U.S. Navy, the abbreviations and acronyms took me a couple of years to figure out. And when they start pronouncing the acronyms... horrendous. And then... the LAYERED acronyms are enough to make you cry. I.e. an acronym that is formed from a longer phrase that itself contains an acronym.
I'm as guilty as the rest, though in the specific case you names, we see a nuance of difference. For us, "mathematics" is the name of the subject you study in school. However, "math" is more specific or perhaps you would prefer, "narrower in scope." For example, this phrase is absolutely correct in USA usage: "If the observation disagrees with the theory, the math is always wrong." Here, we do not say that all of mathematics is wrong, but that subset that relates to the given theory - the math inherent in the theory - is erroneous.
But then again, blame old computers with limited memory. When considering a course catalog many moons ago when I was a college lad, you didn't have Terabyte memories or even Gigabyte memories. You considered yourself DAMNED lucky to be able to talk about Megabyte memories. So course catalogs became MATH 101 or FREN 200 or ENGL or SPAN or ENGR or PHYS or PSYC or HIST or etc.etc.etc. because old computers didn't have that much memory. Abbreviations became commonplace.
So when college kids started talking about their schedule for the semester, it was "Oh, I've got MATH 102 with Dr. Schmidlap on ..." And somewhere in there, we gained the habit.