The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
type: Item
instance of: scholarly article
title: The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
zbMATH Open document ID: 1225.00001
DOI: 10.1007/978-3-7091-0445-3
author: M. Kauers
author: Peter Paule
published in: Texts \& Monographs in Symbolic Computation
publication date: 2011-01-31T00:00:00Z
review text: This is a book on techniques for solving problems concerning infinite sequences. The authors have three goals. The first goal is to give an overview of some of the most important mathematical questions concerning infinite sequences which can be answered by a computer. The second goal is to explain how the algorithms work and on what principles they are based. The third goal is to describe some techniques which are suitable for traditional paper and pencil resoning rather than for modern computer calculations. The authors have included problems on which the techniques explained in the book can be tested. They prefer concrete examples over abstract theorems and informal explanations over formal proofs wherever this seems to be in the interest of readability, assuming basic algebraic notions such as rings, fields, etc., linear algebra in finite-dimensional vector spaces, and some complex analysis in one variable. The authors treat mathematical concepts which play a great role in many different areas of mathematics, such as symbolic sums, recurrence (difference) equations, generating functions and asymptotic estimates, and study their key features in isolation or in combination, their mastery by paper and pencil or by computer programs, and their application to problems in pure mathematics or to ``real-world problems''. These concepts are closely connected with each other: a recurrence equation has been deduced from a symbolic sum, a generating function from a recurrence and asymptotic estimates can be deduced when the generating function is available. The authors call these connections the ``concrete tetrahedron''. The book can be considered as an algorithmic supplement to [\textit{R. L. Graham}, \textit{D. E. Knuth} and \textit{O. Patashnik}, Concrete mathematics: a foundation for computer science. 2nd ed. Amsterdam: Addison-Wesley Publishing Group (1994; Zbl 0836.00001)].
reviewed by: Dan-Mircea Borş
Mathematics Subject Classification ID: 00A05
Mathematics Subject Classification ID: 00-01
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 5842882
zbMATH Keywords: infinite sequences
describes a project that uses: Guess
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-7091-0445-3
OpenAlex ID: W4243410516
description: scientific article; zbMATH DE number 5842882