first principles vs rudiments

first principles and rudiments both are nouns.

Word	Noun	Adjective	Verb	Adverb
first principles	Yes	No	No	No
rudiments	Yes	No	No	No

As nouns, first principles and rudiments are synonyms defined as:

first principles and rudiments: the elementary stages of any subject (usually plural)

Other synonyms of first principles include alphabet.

first principles (noun)	rudiments (noun)
the elementary stages of any subject (usually plural)	the elementary stages of any subject (usually plural)
	a statement of fundamental facts or principles