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Professor Meyer was born in Denver on March 24, 1921, the son of Chandler Meyer and Adda Burnett Meyer. He attended South High School in Denver before earning a bachelor's degree from Pomona College in 1943, a master's degree from Brown University in 1945 and a Ph.D. degree from Stanford University in 1949. His doctoral thesis advisor was George Polya. Dr. Meyer's first academic appointment was as assistant professor at the University of Arizona, Tucson in 1949. He was promoted to associate professor in 1955. In 1957 he accepted a position as assistant professor of mathematics at the University of Colorado, Boulder. He was promoted to associate professor in 1960 and to full professor in 1968. Upon his retirement in 1990 he received the title of Professor Emeritus.

Professor Meyer had strong interests in the history of mathematics and in classical analysis (real and complex) and he frequently taught courses in those areas. He was an active member of a research seminar for faculty and graduate students on the analytic theory of continued fractions and related topics for nearly 40 years with Professors W. J. Thron, Arne Magnus and William B. Jones and frequent visitors from the University of Trondheim, Norway, Professors Haakon Waadeland, Olav Njastad and Lisa Lorentzen. He published research articles on continued fractions, capacity, asymptotic series and approximation theory. His textbook, An Introduction to Axiomatic Systems, appeared in 1974. He was fluent in French and wrote scholarly articles for French publications.

In the Mathematics Department Professor Meyer served as an undergraduate advisor and for many years was a member of the Undergraduate Program Committee which he chaired for two years. For the College of Arts and Sciences he directed the department's honors program, was a member of the Honors Council and served on the committee for transfer evaluation from junior colleges in Colorado. He was active in Sigma Xi, serving as secretary and treasurer for the CU Chapter. He was the president of the Alpha Chapter of Phi Beta Kappa of Colorado for the years 1970-73. Burnie enjoyed traveling, especially in France; he held season tickets for the Colorado Rockies baseball games; and he had a deep appreciation for classical music and reading, in French as well as in English. He spent a great deal of time after retirement tutoring immigrants in English as a second language.