More often than not, the term Alma Mater is applied to one's place of undergraduate studies.
Would it be reasonable of me to apply this term to a university where I received my doctoral degree?
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There is literally nothing in the term specifying an undergraduate program. From Wikipedia: Alma mater (Latin: alma mater, lit. 'nourishing mother'; pl: almae matres) is an allegorical Latin phrase used to proclaim a school that a person has attended or, more usually, from which one has graduated.
Sure, you can use it for your doctoral institution. I doubt anyone will notice.