Recurrent Sequences : Key Results, Applications, and Problems. 1st ed. 2020

種類:

電子ブック

責任表示:

by Dorin Andrica, Ovidiu Bagdasar

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Andrica, Dorin.
• Bagdasar, Ovidiu.
• SpringerLink (Online service)

シリーズ名:

Problem Books in Mathematics ;

ISBN:

9783030515027 [3030515028]    

注記:

1. Introduction to Recurrence Relations -- 2. Basic Recurrent Sequences -- 3. Arithmetic and Trigonometric Properties of Some Classical Recurrent Sequences -- 4. Generated Functions -- 5. More Second Order Linear Recurrent Sequences -- 6. Higher Order Linear Recurrent Sequences -- 7. Recurrences in Olympiad Training -- 8. Solutions to Proposed Problems -- Appendix A. Complex Geometry anhd Number Theory -- Appendix B -- References -- Index.
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 th

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