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© 2011

The Concrete Tetrahedron

Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates

Textbook

Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Manuel Kauers, Peter Paule
    Pages 1-16
  3. Manuel Kauers, Peter Paule
    Pages 17-41
  4. Manuel Kauers, Peter Paule
    Pages 43-61
  5. Manuel Kauers, Peter Paule
    Pages 63-86
  6. Manuel Kauers, Peter Paule
    Pages 87-112
  7. Manuel Kauers, Peter Paule
    Pages 113-136
  8. Manuel Kauers, Peter Paule
    Pages 137-164
  9. Back Matter
    Pages 165-203

About this book

Introduction

The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.

Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.

Keywords

asymptotics formal power series recurrence equations symbolic computation symbolic summation

Authors and affiliations

  1. 1.Research Institute for Symbolic Computation (RISC)Johannes Kepler University LinzLinzAustria

Bibliographic information

  • Book Title The Concrete Tetrahedron
  • Book Subtitle Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates
  • Authors Manuel Kauers
    Peter Paule
  • Series Title Texts and Monographs in Symbolic Computation
  • DOI https://doi.org/10.1007/978-3-7091-0445-3
  • Copyright Information Springer-Verlag/Wien 2011
  • Publisher Name Springer, Vienna
  • eBook Packages Computer Science Computer Science (R0)
  • Softcover ISBN 978-3-7091-0444-6
  • eBook ISBN 978-3-7091-0445-3
  • Series ISSN 0943-853X
  • Edition Number 1
  • Number of Pages IX, 203
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
    Discrete Mathematics
    Number Theory
    Algebra
  • Buy this book on publisher's site

Reviews

From the reviews:

“The Concrete Tetrahedron is suitable for advanced undergraduate students in mathematics or computer science who have had some exposure to elementary concepts in abstract algebra and complex analysis. … The volume’s numerous problems together with selected solutions definitely make it appropriate for an independent reading course for the motivated student. Summing Up: Highly recommended. Upper-division undergraduates.” (D. M. Ha, Choice, Vol. 49 (11), July, 2012)

“The book deals with a blend of continuous and discrete mathematics, applying continuous methods to discrete problems. … Those who are interested in the subject matter of Concrete Mathematics will enjoy The Concrete Tetrahedron for an independent perspective, some more recent results, and for new applications.” (John D. Cook, The Mathematical Association of America, March, 2011)