Upon his discharge he re-entered Yale and graduated in 1949, then trained at the Juilliard School and the Mannes College of Music, studying with Roger Sessions and Felix Salzer, and later with Otto Luening, Emanuel Balaban and Izler Solomon.
John Rockwell of The New York Times has pointed out that Mayer was "especially known for his operas and songs ... his work sings out with real beauty, both in the vocal writing and the instrumental settings."
Distinguished artists have introduced his scores: Robert De Cormier led the New York Choral Society in its Lincoln Center premiere of "Spring Came on Forever"; sopranos Heidi Grant Murphy, Eleanor Steber and Christine Brewer have all premiered vocal-chamber works; and Leopold Stokowski (at eighty-eight) conducted Mayer's piano concerto Octagon at Carnegie Hall with William Masselos as soloist.
Mayer taught composition and orchestration at Boston University; was a guest lecturer at Yale, Columbia, the Pratt Institute and the Juilliard School; fulfilled writing and cultural assignments from the US Information Agency, one of which involved preparing lectures on American chamber opera to be delivered abroad; served on judging panels for the MacDowell Colony, the American Composers Orchestra, Composers Recordings, Inc., the National Opera Association and the National Federation of Music Clubs; and was Composer-in-Residence at the Conductors' Institute and Adirondack New Music Festival.
Among Mayer's works for young people are Hello, World!,[9] which was recorded with Eleanor Roosevelt as narrator,[10] the ballet The Snow Queen and the opera One Christmas Long Ago.