Overview
- Appropriate for math olympiad competitors; Contains challenging problems and solutions
- Teaches techniques and facts that are central to mathematics
- Presents a diverse range of state-of-the-art topics and developments
- Illustrates unexpected connections between various mathematical topics
- Results are supported by numerous illustrations
Part of the book series: Problem Books in Mathematics (PBM)
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About this book
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.
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Keywords
Table of contents (8 chapters)
Reviews
“What a delightful, current, compactly written book. This book could serve as a stand-alone text i) for an advanced, undergraduate, second-term, Discrete-Mathematics course, ii) for a first, or preferably, second-year stand-alone text for graduate students specializing in dynamical systems, combinatorics, or discrete systems, or iii) for researchers in these areas. … The book presents close to 200 references most of which are post-2000. Anyone wanting to read further will find what they need here.” (Russel Jay Hendel, MAA Reviews, April 10, 2022)
“This book teaches numerous fundamental facts and techniques which are central in mathematics. It is both a research monograph and a delightful problem book, which I feel will spark the interest of a wide audience, from mathematics Olympiad competitors and their coaches to undergraduate or postgraduate students, or professional mathematicians with an interest in recurrences and their multiple applications.” (Michael Th. Rassias, EMS Magazine, Issue 119, March, 2021)
Authors and Affiliations
About the authors
Dorin Andrica is a Professor of Mathematics at the Babeș-Bolyai University of Cluj Napoca, Romania. He has obtained a PhD in Pure Mathematics in 1992 with a thesis on critical point theory with applications to the geometry of differentiable submanifolds. His interests include differential topology (critical point theory with applications, Morse theory with applications), differential geometry, geometry, Lie groups and Lie algebras with applications in geometric mechanics, number theory, discrete mathematics, and mathematics for competitions. Dorin has co-authored Springer textbooks on various topics in mathematics, as well as problem books for olympiad training.
Ovidiu Bagdasar is an Associate Professor in Mathematics at the University of Derby, United Kingdom. He holds PhDs in Applied Mathematics (University of Nottingham, 2011), and Pure Mathematics (Babeș-Bolyai University, 2015), the latter with a thesis entitled "On the geometry and applications of complex recurrent sequences". His research is at the boundary between Mathematics and Computer Science, encompassing areas like number theory, optimization, computational, discrete and applied mathematics. He is the author of the SpringerBriefs volume Concise Computer Mathematics Tutorials on Theory and Problems.
Bibliographic Information
Book Title: Recurrent Sequences
Book Subtitle: Key Results, Applications, and Problems
Authors: Dorin Andrica, Ovidiu Bagdasar
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-030-51502-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-51501-0Published: 24 September 2020
Softcover ISBN: 978-3-030-51504-1Published: 25 September 2021
eBook ISBN: 978-3-030-51502-7Published: 23 September 2020
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XIV, 402
Number of Illustrations: 2 b/w illustrations, 65 illustrations in colour
Topics: Discrete Mathematics, Number Theory, Algebra, Geometry