To set up a many to many relationship in MongoDB you should set up a relationship table:
Courses: [{name: algebra, id: 3}, {name: bio, id: 4}, {name: PE, id: 5}]
Students: [{name: billy, id 1}, {name: shelly: id2}]
Student_Courses: [{courseId: 3, studentId: 1}, {courseId: 4, studentId: 1}, {courseId: 4, studentId: 2} ]