applied math vs mathematics

applied math and mathematics both are nouns.

Word	Noun	Adjective	Verb	Adverb
applied math	Yes	No	No	No
mathematics	Yes	No	No	No

As nouns, mathematics is a hypernym of applied math; that is, mathematics is a word with a broader meaning than applied math:

applied math: the branches of mathematics that are involved in the study of the physical or biological or sociological world
mathematics: a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

Other hypernyms of applied math include math, maths.

applied math (noun)	mathematics (noun)
the branches of mathematics that are involved in the study of the physical or biological or sociological world	a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement