The Cooper Union for the Advancement of Science and Art, founded back in 1859, is a small college in New York City's artsy East Village that focuses on art, architecture and engineering. It is among the nation's most selective schools, with a 12% acceptance rate and just under 900 undergraduate students enrolled.

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But getting in pays off: While the cost of tuition is $44,550, every student receives at least a half-tuition scholarship, currently worth $22,275 a year. Cooper Union alumni also tend to thrive in the competitive art and architecture worlds. Famous former students include Thomas Edison, sculptor Augustus Saint-Gaudens, and director and screenwriter Patty Jenkins.

One reason for Cooper Union's past popularity, and its high placement on many "value college" lists, was its free tuition policy. But in 2014, the school started charging tuition, a decision that many alumni, faculty and students questioned and criticized. The school is working toward returning to the earlier model in 2029.