Moja prijateljica je studentica matematike na velikom fakultetu.

In Croatian, possessive adjectives agree in gender, number, and case with the noun they describe.

• prijateljica is a feminine noun (friend – female friend).
• The basic forms of “my” are:
  • moj – masculine (e.g. moj prijatelj – my [male] friend)
  • moja – feminine (e.g. moja prijateljica – my [female] friend)
  • moje – neuter (e.g. moje dijete – my child)

Since prijateljica is feminine singular in the nominative case, you must use moja.

Both mean friend, but they differ in grammatical and natural gender:

• prijatelj – masculine noun, usually a male friend
• prijateljica – feminine noun, usually a female friend

So:

• Moj prijatelj je student. – My (male) friend is a student.
• Moja prijateljica je studentica. – My (female) friend is a student.

je is the 3rd person singular form of the verb biti (to be) in the present tense: on/ona/ono je = he/she/it is.

In Moja prijateljica je studentica..., it functions just like “is” in English:

• Moja prijateljica – my friend (subject)
• je – is (verb)
• studentica – (a) student (predicate)

Unlike English, Croatian does not use “is” as a continuous auxiliary (e.g. is doing), but here it’s the same basic idea: linking subject and complement.

Croatian often has separate masculine and feminine forms for professions and roles:

• student – masculine (male student)
• studentica – feminine (female student)

Since prijateljica is female, the noun that describes her is also feminine, so we say:

• Moja prijateljica je studentica. – My (female) friend is a (female) student.

The word matematike is in the genitive singular case.

In Croatian, after words like student / studentica, when you say what someone is a student of, you use the genitive:

• studentica + genitive of the subject field
  
  • studentica medicine – a medical student
  • student fizike – a physics student
  • studentica matematike – a mathematics student

So:

• matematika – nominative (basic form, “mathematics”)
• matematike – genitive (“of mathematics”)

Literally, na velikom fakultetu is “on/at a big faculty/college”.

In Croatian, both na and u can mean “at” depending on the noun and the typical expression:

• na fakultetu – at college / at the faculty
• na sveučilištu – at the university
• u školi – at school
• u uredu – in/at the office

For institutions like fakultet, the idiomatic preposition is na, not u. So na fakultetu simply means at college/at the faculty, not “on the faculty” in the literal English sense.

Because they are both in the locative singular masculine:

• fakultet is a masculine noun.
• After na in the sense of “at (a place)”, Croatian uses the locative case.
• In the masculine singular locative,
  • the noun fakultet becomes fakultetu
  • the describing adjective velik becomes velikom

Adjective and noun must agree in:

• gender: masculine
• number: singular
• case: locative

Hence na velikom fakultetu (at a big faculty/college).

Not really; the meaning is different:

• In Croatian, fakultet ≈ college / (single) university faculty – a higher education institution where you study for a degree (e.g. Faculty of Science, Law School, etc.).
• In English, faculty more often means:
  • the staff of a university, or
  • a division within a university (Faculty of Arts).

When translating Moja prijateljica je studentica matematike na velikom fakultetu, fakultet is best rendered as:

• “at a large university” or
• “at a big college”, depending on context.

Croatian has no articles like a/an or the, so:

• na velikom fakultetu can mean both:
  • at a big university/college
  • at the big university/college

Context tells you whether we’re talking about a specific one or just any big one.

If you want to emphasize indefinite (“some big university”), you can add a word like:

• na nekom velikom fakultetu – at some big university

If it’s already clear from context which university, you just say na velikom fakultetu, and it works like “at the big university”.

You can change the word order, but:

• Moja prijateljica je studentica matematike na velikom fakultetu.
  – neutral, most natural order; first we say what she is, then where.

• Moja prijateljica je na velikom fakultetu studentica matematike.
  – grammatically correct, but it sounds slightly marked, with more focus on where she is a student.

Croatian word order is flexible because of cases; meaning doesn’t change, but emphasis can. For a straightforward statement, the original order is preferred.

You could, but the meaning changes slightly.

• Moja prijateljica je... – clearly my (female) friend.
• Prijateljica je... by itself sounds like:
  • “(The) friend is…” – referring to some known friend in context, or
  • in many contexts, it would feel incomplete or unclear.

In everyday speech, possessive pronouns like moja / tvoja / njegova are usually kept, unless context makes the possessor completely obvious.

Because matematika is the subject/field, not the profession/role.

In Croatian:

• studentica matematike – a student of mathematics
• matematičarka – a (female) mathematician

So:

• Moja prijateljica je studentica matematike.
  – My (female) friend is a mathematics student.
• Moja prijateljica je matematičarka.
  – My (female) friend is a mathematician.

Saying moja prijateljica je matematika would sound like “my friend is mathematics (itself)”, which is not correct.