He received his Bachelor of Science in Engineering from Princeton University in 1957 as a member of Phi Beta Kappa and Sigma Xi.
In summer 1957 he was research associate at Sperry Gyroscope Company in Great Neck, New York.
From 1961 to 1965 Uman was associate professor of electrical engineering at the University of Arizona in Tucson.
At Arizona Uman taught and conducted research in electromagnetics and gaseous electronics and became interested in the physics of lightning.
In 1971 Uman became a professor in the Department of Electrical and Computer Engineering at the University of Florida in Gainesville.
LLP is now a division of Vaisala and is the world leader in the sale of lightning locating equipment.