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Difference equations. From rabbits to chaos. (English) Zbl 1085.39002
Undergraduate Texts in Mathematics. New York, NY: Springer (ISBN 0-387-23233-8/hbk; 0-387-23234-6/pbk). xiii, 400 p. (2005).
As the authors point out in their introduction this is a textbook for undergraduate students taking introductory courses on discrete mathematics.
The text is quite elementary, written for an audience with a preference for computational aspects of mathematics and modelling real world phenomena. This is also reflected by the exercises at the end of each chapter.
Starting with simple examples (Fibonacci rabbits) the reader is lead to basic notions and theorems of basic linear algebra and analysis. Proofs are worked out accurately, an understanding requires some more experience with mathematical reasoning.
Along the main stream – difference equations – the book exemplifies various mathematical topics such as power series, convolution, generating functions, graph theory, Perron-Frobenius matrices, modular recurrences, discrete (fast) Fourier transform. The last section deals with stability of nonlinear recurrence relations and the route to chaos.

MSC:
39A05 General theory of difference equations
39-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations
68R01 General topics of discrete mathematics in relation to computer science
65T50 Numerical methods for discrete and fast Fourier transforms
65Q05 Numerical methods for functional equations (MSC2000)
Software:
Mathematica
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