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The Center for Applied Mathematics at Cornell University sponsored a Special Year on Resource Management and Environmental Problem Solving in 1987-88 culminating in a Symposium on Mathematical Approaches to Resource Management and Epidemiology (October 28-30, 1987), aimed at identifying critical problems and new directions demanding mathematical attention, in these areas. The contributions of the invited speakers, recorded in this volume, describe and analyze models in areas such as cell population growth, plant population dynamics, and the spread of AIDS. They also address methodological aspects, and theoretical and interdisciplinary issues including the interplay between population biology, management, and economics, and the relationship between models and data. Throughout authors review past contributions and point to new directions.