Salzman was born September 8, 1933 in New York City and attended Forest Hills High School (1946–1950). After studying composition with Marris Mawner at the New York High School of Music and Art (1949–51), he continued his studies (majoring in music and minoring in literature) at Columbia University (BA 1954), where his teachers included Jack Beeson, Lionel Trilling, Otto Luening and Vladimir Ussachevsky. He pursued postgraduate work at Princeton University (MFA 1956) with Milton Babbitt, Roger Sessions, Earl Kim, Edward T. Cone, Arthur Mendel, Oliver Strunk and Nino Pirrotta. A Fulbright Fellowship (1956–58) enabled him to study at the Accademia di Santa Cecilia in Rome with Goffredo Petrassi, and at the Darmstädter Ferienkurse with Karlheinz Stockhausen, Bruno Maderna and Luigi Nono.