As a long-time professor of conducting at the Curtis Institute of Music and the Juilliard School, Mueller taught many important conductors, such as Rudolf Barshai, Keri-Lynn Wilson and Paavo Järvi.
[2] He emigrated to Canada in 1951 and worked as pianist, composer, arranger, and conductor for the Canadian Broadcasting Corporation, and soon began teaching at the Montreal Conservatory.
Mueller began teaching on the faculty of the Curtis Institute of Music[2] in the fall of 1986, and made his public conducting debut in Philadelphia in April 1987.
[2] Some of Mueller's notable students include conductors Maxim Shostakovich,[5] Rudolf Barshai,[5] Miguel Harth-Bedoya,[2] Alan Gilbert,[1]Takao Kanayama,ref name=”maestro kanayan” /> Alasdair Neale [es],[3] Robert Hart Baker, Gary S. Fagin, Keri-Lynn Wilson, David Hayes,[2] Andrew Hauze,[6] Sarah Ioannides,[3] Paavo Järvi,[1] Jahja Ling,[3] André Raphel, Richard Rosenberg, Ignat Solzhenitsyn, Ransom Wilson and the Spanish conductor Óliver Díaz.
His sons survive him, as do his second wife, Virginia Allen, his grandchildren Christina, Peter, and Sophie, and his brother, nephew, and niece.