He attended Austin College in Sherman, Texas, where he was awarded both a Bachelor's and master's degrees in History.
After earning his master's degree, he served in the United States Navy, stationed at Charleston, South Carolina.
Monroe's first teaching position was at Schreiner College in Kerrville, Texas, for the 1959 summer term.
[2] As secretary of the Aspirations Committee, he drafted the report which recommended some key changes at Texas A&M in the early 1960s – including co-education, non-compulsory Corps membership, racial integration, and high admission standards; and as Dean of Faculties was part of the 1970s administrative team which laid the basic foundations for today's Texas A&M University.
[4] In 1980, Monroe was appointed as the President of the University of Texas at El Paso, a position he held until 1987.