This self-contained text presents state-of-the-art results on recurrent sequences and their
applications in algebra number theory geometry of the complex plane and discrete mathematics.
It is designed to appeal to a wide readership ranging from scholars and academics to
undergraduate students or advanced high school and college students training for competitions.
The content of the book is very recent and focuses on areas where significant research is
currently taking place. Among the new approaches promoted in this book the authors highlight
the visualization of some recurrences in the complex plane the concurrent use of algebraic
arithmetic and trigonometric perspectives on classical number sequences and links to many
applications. It contains techniques which are fundamental in other areas of math and
encourages further research on the topic. The introductory chapters only require good
understanding of college algebra complex numbers analysis and basic combinatorics. For
Chapters 3 4 and 6 the prerequisites include number theory linear algebra and complex
analysis.The first part of the book presents key theoretical elements required for a good
understanding of the topic. The exposition moves on to to fundamental results and key examples
of recurrences and their properties. The geometry of linear recurrences in the complex plane is
presented in detail through numerous diagrams which lead to often unexpected connections to
combinatorics number theory integer sequences and random number generation. The second part
of the book presents a collection of 123 problems with full solutions illustrating the wide
range of topics where recurrent sequences can be found. This material is ideal for
consolidating the theoretical knowledge and for preparing students for Olympiads.
