Ayres earned his Bachelor of Science degree from Washington College, Maryland and his master's and doctoral degrees from the University of Chicago. He taught during 1921–4 at Ogden College and another four years at Texas A&M before coming to Dickinson College in 1928. He was promoted to associate professor in June, 1935. In 1943 he was named the Susan Powers Hoffman Professor of Mathematics. From 1938 until his retirement in June, 1958, he served as chairman of the mathematics department. Ayres was also an instructor in the Army Air Corps program at the college, 1943–44, and authored Basic Mathematics of Aviation, which was adopted across the Air Corps training system. In all, he wrote seven textbooks. Along with his teaching, he also served as assistant registrar and registrar between 1941 and 1945.

• Basic Mathematics for Aviation (1943)
• Schaum's Outline Series:
  • Abstract Algebra, with Deborah Arangno, Lloyd R. Jaisingh
  • Calculus, with Elliott Mendelson
  • College Mathematics, with Philip Schmidt
  • Theory and Problems of Differential Equations
  • Theory and Problems of Differential and Integral Calculus; in Si Metric Units, J.C. Ault (Adapter)
  • Theory And Problems of Mathematics of Finance
  • Theory And Problems of Matrices
  • Theory and Problems of Modern Algebra
  • Theory and Problems of Plane and Spherical Trigonometry
  • Theory and Problems of Projective Geometry
  • Theory and Problems of Trigonometry, with Robert E. Moyer

• Frank J. Ayres, Jr. (1901–1994), archives.dickinson.edu
• Frank Ayres, Jr. at the Mathematics Genealogy Project