The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns. The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
Michael A Radin earned his PhD 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 that portray periodic and eventually periodic cycles as part of his PhD thesis. He has several publications on the boundedness and periodic nature of solutions of rational difference equations, max$-$type difference equations and piecewise difference equations. During the last 20 years, Michael published several papers together with his undergraduate and graduate students at RIT and has publications with students and colleagues from Riga Technical University, University of Latvia, Pskov State University and Yaroslavl State University.
Michael also has publications in applied mathematics such as Neural Networking, Modelling Extinct Civilizations, Modelling Human Emotions and Economic Cycles. In addition, Michael organized numerous sessions on difference equations and applications at the annual American Mathematical Society meetings. Michael also regularly presents his research at international conferences such as the Conference on Mathematical Modelling and Analysis and the Volga Neuroscience Meeting. Recently Michael published four manuscripts on international pedagogy and has been invited as one of the keynote speakers at several international and multidisciplinary conferences: International Scientific Conference Society, Integration and Education held annually at the Rezekne Technical Academy in Latvia. Michael taught courses and conducted seminars on these related topics during his spring 2009 sabbatical at the Aegean University in Greece and during his spring 2016 sabbatical at Riga Technical University in Latvia. In addition, Michael taught a new course on "Introduction to Recognition of Patterns and Deciphering of Patterns" at the Rezekne Technical Academy in Rezekne, Latvia in May 2019. Michael's aim is to inspire students to learn.
Recently, Michael had the opportunity to implement his hands-on teaching and learning style in the courses that he regularly teaches at RIT and during his spring 2016 sabbatical in Latvia. This method confirmed to work very successfully for him and his students, kept the students stimulated and engaged and improved their course. Michael's aim is to make mathematics accessible to all students with different preparation levels.
