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Periodic Character and Patterns of Recursive Sequences

  • Developing intuition about pattern recognition

  • Developing graphical intuition and analysis about periodic trait

  • Enhance efficiency in fast speed computing


Table of contents

About this book


This textbook on periodic character and patterns of recursive sequences focuses on discrete periodic patterns of first order, second order and higher order difference equations. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in Calculus I and Discrete Mathematics, this book serves as a core text for a course in Difference Equations and Discrete Dynamical Systems. The text contains over 200 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a first-hand introduction to patterns of periodic cycles and patterns of transient terms with exercises for most sections of the text, preparing them for significant research work in the area.


periodic cycles eventually periodic cycles even ordered cycles odd ordered cycles unique periodic cycles linear difference equations non-autonomous difference equations piece-wise difference equations max-type difference equations rational difference equations

Authors and affiliations

  1. 1.School of Mathematical SciencesRochester Institute of TechnologyRochesterUSA

About the authors

Michael A. Radin earned his Ph.D. at the University of Rhode Island in 2001 and is currently an associate professor of mathematics at the Rochester Institute of Technology. Michael started his journey analyzing difference equations with periodic and eventually periodic solutions as part of his Ph.D. thesis and published many papers on boundedness and periodic nature of solutions of rational difference equations, max-type difference equations and piece-wise difference equations. Michael published several papers together with his Master’s students and undergraduate students at RIT and has publications with students and colleagues from Riga Technical University and University of Latvia.

Bibliographic information


“The book is well written and it provides a good introductory reference in the field of difference equations and discrete mathematics.” (Ioannis P. Stavroulakis, zbMATH 1429.39001, 2020)