According to the UW’s Almanac, the tuition for a semester when you started in fall 1959 was $300. (Had you been an in-state student, it would have been $110.) It continued at that rate through the 1959–60 and 1960–61 academic years. But then came a big boost, to $362.50 per semester in 1961–62, and then to $375 per semester in 1962–63. If you took a more-or-less standard eight semesters to graduate (spring and fall through those four years), you spent a total of $2,675 on tuition.
You graduated at the right time, by the way, as tuition has continued to rise. In 1963–64, it jumped to $500 per semester. By the fall of 1988, a single semester cost $2,819.50, more than your entire college education. In the 2011–12 year, tuition and fees run $12,707.38 per semester for a full-time, out-of-state undergrad. That’s enough to pay for four and three-quarters of your degrees.