ON A HILL OVERLOOKING the shores of Lake Champlain, at the foot of the Green Mountains, the University of Vermont combines faculty-student relationships most commonly found in a small liberal arts college with the resources of a major research university. Located in Burlington, a thriving urban center, the university is home to over 9,040 undergraduates, 1,351 graduate students, 406 medical students and more than 1,292 full- and part-time faculty.