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Book - Mathematical Expositions ( Volume One) Recursion Sequences, S. Muralidharan, Published by The Association of Mathematics, Teachers of India, April 2015
This book is an attempt to collect several interesting integer sequences that arise as recursion sequences. Here, the author has developed the theory of recursion sequences from ground up. All the important theorems are proved and several interesting applications such as Towers of Hanoi,
tiling problems are worked out in detail.
The book is organized as follows: In the first chapter, recursion sequences are introduced and several examples are discussed. The second chapter develops some techniques in Difference calculus that are used in solving recurrence relations. In Chapter 3, techniques for finding closed form solutions to linear homogeneous recurrence relations with constant coefficients are developed. This chapter contains several interesting counting problems that are solved using recurrence relations. In Chapter 4, methods for solving non homogeneous recurrence relations are discussed. Chapter 5 deals with systems of recurrence relations. Chapter 6 discusses the technique of using generating functions to solve recurrence relations. Some applications of generating functions to counting problems are also
discussed. Chapters 7 and 8 respectively deal with recurrence relations with variable coefficients and
non-linear recurrence relations respectively. Finally, in Chapter 9 some problems for practice are given.
This book can be used as supplementary reading material for a course in Discrete Mathematics for Engineering students.
It can also be referred by School students and teachers.