"...took that course at the University of Chicago."

Chicago University is a great school. I am familiar with it. 

"Notre Dame is the 18th ...but it is not among the highest ranking ones...."

Not bad -- out of 4,300  degree granting US universities -- to be 18th after Princeton (#1), only a little over 175 years old, Catholic in values/standards, and one of the top 10 universities in the country with the largest endowment$ (ahead of Duke, Chicago, Vanderbilt, etc., in that regard). It takes great pride in those achievements. Only two other Catholic universities -- Louvain University [ranked #1 university of Belgium] and Catholic University of Chile [ ranked #2 university of Chile] -- have higher rankings in their respective countries.