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Books > Science & Mathematics > Mathematics > Algebra
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Recurrent Sequences - Key Results, Applications, and Problems (Hardcover, 1st ed. 2020)
Loot Price: R1,733
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Recurrent Sequences - Key Results, Applications, and Problems (Hardcover, 1st ed. 2020)
Series: Problem Books in Mathematics
Expected to ship within 10 - 15 working days
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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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