The Material Girl and her 17-year-old daughter caused a big stir on campus when they arrived for a tour. Lourdes is apparently interested in the university's musical theatre programme.
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Madonna attended the institution before she went to New York to launch her pop career, and she has said she would Lourdes to follow in her footsteps.
"I want my daughter to go to school there," Madonna said in an interview before her Super Bowl halftime performance in 2012. "I keep telling her, Ann Arbor is an awesome place," she continued – referring to the city where the university is located.
The pop star tried to keep the mother-daughter visit low key – wearing black and oversize sunglasses, but inevitably word got out about the famous visitor.
"There was a lot of excitement," Michigan University vocal performance student told US publication People.
"Someone announced to my choir class Madonna was in the building, and choir wasn't productive anymore after that."
As well as their tour, the VIP visitors ate lunch at one of the halls of residence, and visited the dean's office.