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Discrete dynamics is the study of change. In particular, it shows how to translate real world situations into the language of mathematics. With the increase in computational ability and the recent interest in chaos, discrete dynamics has emerged as an important area of mathematical study. This text is the first to provide an elementary introduction to the world of dynamical systems. The aim of the text is to explain both the wide variety of techniques used to study dynamical systems and their many applications in areas ranging from population growth to problems in genetics. This investigation leads to the fruitful concepts of stability, strange attractors, chaos, and fractals. Very little previous mathematical knowledge is assumed and students with an elementary exposure to calculus and linear algebra will be able to follow the text easily. A large number of worked examples and exercises are provided to assist instruction. Throughout, students are encouraged to experiment with models of dynamical systems on computers and explore this fascinating area of mathematics on their own.