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Dorin Andrica,Ovidiu Bagdasar

Recurrent Sequences: Key Results, Applications, and Problems

Recurrent Sequences: Key Results, Applications, and Problems

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  • More about Recurrent Sequences: Key Results, Applications, and Problems


This book provides a comprehensive introduction to recurrent sequences and their applications in various fields of mathematics, including algebra, number theory, geometry, and discrete mathematics. It covers recent research areas and promotes visualizations, concurrent perspectives, and connections to other areas of mathematics. The first part of the book covers key theoretical elements, while the second part includes a collection of problems with full solutions. It is suitable for scholars, academics, undergraduate students, and advanced high school and college students preparing for competitions.

Format: Paperback / softback
Length: 402 pages
Publication date: 25 September 2021
Publisher: Springer Nature Switzerland AG


This comprehensive text delves into the realm of recurrent sequences, exploring their applications in various fields such as algebra, number theory, geometry of the complex plane, and discrete mathematics. With a readership spanning from scholars and academics to undergraduate students and advanced high school and college students preparing for competitions, the book aims to provide a thorough understanding of this topic. The content is highly current, focusing on areas where significant research is currently underway. Among the novel approaches showcased in this book, the authors emphasize the visualization of certain recurrences in the complex plane, the concurrent utilization of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and the establishment of connections to numerous applications. The book incorporates techniques that hold significance in other branches of mathematics, fostering further exploration of the subject. The introductory chapters assume a solid foundation in college algebra, complex numbers, analysis, and basic combinatorics. For Chapters 3, 4, and 6, prerequisites include number theory, linear algebra, and complex analysis.

The first part of the book establishes the foundational theoretical elements necessary for a deep comprehension of the topic. It proceeds to present fundamental results and notable examples of recurrences, showcasing their properties. The geometry of linear recurrences in the complex plane is intricately explained through numerous diagrams, leading to surprising connections to combinatorics, number theory, integer sequences, and random number generation.

The second part of the book comprises a collection of 123 problems with comprehensive solutions, illustrating the diverse applications of recurrent sequences. This material serves as an excellent resource for consolidating theoretical knowledge and preparing students for further exploration of this captivating field.

Weight: 635g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030515041
Edition number: 1st ed. 2020

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