Discrete Calculus

Methods for Counting

  • Carlo Mariconda
  • Alberto Tonolo

Part of the UNITEXT book series (UNITEXT, volume 103)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 103)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Carlo Mariconda, Alberto Tonolo
    Pages 1-26
  3. Carlo Mariconda, Alberto Tonolo
    Pages 27-64
  4. Carlo Mariconda, Alberto Tonolo
    Pages 65-82
  5. Carlo Mariconda, Alberto Tonolo
    Pages 83-104
  6. Carlo Mariconda, Alberto Tonolo
    Pages 105-151
  7. Carlo Mariconda, Alberto Tonolo
    Pages 153-191
  8. Carlo Mariconda, Alberto Tonolo
    Pages 193-273
  9. Carlo Mariconda, Alberto Tonolo
    Pages 275-318
  10. Carlo Mariconda, Alberto Tonolo
    Pages 319-354
  11. Carlo Mariconda, Alberto Tonolo
    Pages 355-417
  12. Carlo Mariconda, Alberto Tonolo
    Pages 419-463
  13. Carlo Mariconda, Alberto Tonolo
    Pages 465-534
  14. Carlo Mariconda, Alberto Tonolo
    Pages 535-578
  15. Back Matter
    Pages 619-659

About this book

Introduction

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified.

Keywords

combinatorics finite sums and their approximations generating functions power series recurrences

Authors and affiliations

  • Carlo Mariconda
    • 1
  • Alberto Tonolo
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di PadovaPadovaItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di PadovaPadovaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-03038-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-03037-1
  • Online ISBN 978-3-319-03038-8
  • Series Print ISSN 2038-5714
  • About this book