Review the item:
As her teachers had recommended,
Madison tried to study in the library but discovered that the good
music, unlimited soda, and big tables at the campus café made a great
place to do homework during fall semester, Madison must have eaten 150 pizza
slices while she slogged through Fundamentals of Biology.
The comma between recommended and Madison is completely correct. As her teachers had recommended is a subordinate clause, so it cannot stand alone. Madison tried to study in the library ... begins a main clause.
When a subordinate clause introduces a main clause, you need a comma between them.