**The John H. Barrett Memorial Lectures
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**John H. Barrett (1922-1969)**

John H. Barrett was born in Randall, Kansas on December 20, 1922. He received his M.S. and PhD from the University of Texas in 1946 and 1951, respectively. His PhD thesis was on differential equations of non-integer order directed by Hyman Joseph Ettlinger. He held faculty positions at the University of Delaware (1951-1956), Yale University (1955-1956), and the University of Utah (1956-1961) before coming to the University of Tennessee (1961-1969). In January 1969, John Barrett died from complications following a kidney transplant, in the prime of his mathematical and administrative career.

J. Barrett was an expert on oscillation and disconjugacy theory of linear differential equations, a subject that bears his permanent mark. One of his widely known contributions was the extension of the classical Prüfer transformation for 2nd order scalar differential equations to systems of differential equations [1]. According to [1], there is a transformation analogous to the well-known Prϋfer [2] polar-coordinate transformation for a real self-adjoint linear homogeneous differential equation of the second order.

John Barrett came to the University of Tennessee in the fall of 1961 as a Professor of Mathematics. Upon his arrival, he immediately initiated a seminar in ordinary differential equations which attracted a number of graduate students. Through this seminar, his classes, and his personal contact, he was a major force in the Graduate Program in the Department of Mathematics in the early 1960s.

Professor Barrett became Head of the Mathematics Department in 1964. Through his efforts and influence, several active research groups were established at the University of Tennessee and by 1967, the number of faculty in the department had more than doubled. The Barrett Lecture series is a fitting reminder of his many contributions to the University and research community.

**References**

1. J.H. Barrett, A Prüfer transformation for matrix differential equations*, **Proc. Amer. Math. Soc.*, 8 (1957), 510-518.

2. H. Prϋfer, Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Funktionen*, **Math. Ann*. 95 (1926), 499-518.

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