I read from the free dictionary that the three words "rudiment", "fundamental", and "foundation" are listed as synonyms in thesaurus, with their individual meanings in regard to the learning of a discipline being
rudiment: a fundamental element, principle, or skill, as of a field of learning; the first principles or elementary stages of a subject.
fundamental: a basic principle, rule, law, or the like that serves as the groundwork of a system; essential part.
foundation: the basis or groundwork of anything.
Despite the definition of each word, I am still not quite sure whether these words can be used interchangeably or have some shades of meaning when they refer to the learning of a discipline. For example, do:
"I have acquired the rudiments of quantum mechanics."
"I have acquired the fundamentals of quantum mechanics."
"I have acquired the foundations of quantum mechanics."
sound the same or slightly differently? Does "rudiments" suggest less comprehensive knowledge, which may be anecdotal, of quantum mechanics than "fundamentals" and "foundations"? I make this speculation on the basis that "rudiment" also has other meanings:
a mere beginning, first slight appearance, or undeveloped or imperfect form of something
an organ or part in its earliest recognizable form, esp one in an embryonic or vestigial state.
That being so, is there any difference between "fundamentals" and "foundations" in this context? It's like the both suggest essential knowledge for having an adequate understanding of quantum mechanics.