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Discrete Calculus

Methods for Counting

  • Textbook
  • © 2016


  • A new and efficient way to learn combinatorics
  • Includes effective problem-solving methods
  • Efficient didactical approach, taking care of the reader
  • An original collection of important aspects of discrete mathematics, rarely presented in the same book
  • Includes numerous examples and exercises
  • Based on the extensive teaching experience of and fruitful discussions between the different authors

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

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (14 chapters)


About this book

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.


“Discrete Calculus is an introductory text to combinatorics and finite calculus. … the work is well organized, and its massive size is also a strength since an interested reader will be  able to find any related topic with the assistance of its comprehensive index including symbols, helpful appendixes, and markers indicating what information is most and least important. … Summing Up: Recommended. Graduate students, researchers, and faculty.” (A. Misseldine, Choice, Vol. 54 (11), July, 2017)

Authors and Affiliations

  • Dipartimento di Matematica, Università degli Studi di Padova, Padova, Italy

    Carlo Mariconda, Alberto Tonolo

About the authors

Carlo Mariconda was born in 1964. In 1991 he received his PhD in Functional Analysis from the International School for Advanced Studies (SISSA-ISAS), Trieste, Italy. Since 1992 he has been a member of the Department of Mathematics at the University of Padova, where he is now Professor in Mathematical Analysis. His scientific interests mainly focus on the Calculus of Variations and Functional Analysis.

Alberto Tonolo was born in 1962. In 1993 he received his PhD in Algebra from the University of Florence, Italy. Since 1992 he has been a member of the Department of Mathematics at the University of Padova, where he is now Professor in Algebra. His scientific interests mainly focus on Module and Ring Theory and Homological Algebra.

Bibliographic Information

  • Book Title: Discrete Calculus

  • Book Subtitle: Methods for Counting

  • Authors: Carlo Mariconda, Alberto Tonolo

  • Series Title: UNITEXT

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Softcover ISBN: 978-3-319-03037-1Published: 15 December 2016

  • eBook ISBN: 978-3-319-03038-8Published: 01 December 2016

  • Series ISSN: 2038-5714

  • Series E-ISSN: 2532-3318

  • Edition Number: 1

  • Number of Pages: XXI, 659

  • Number of Illustrations: 66 b/w illustrations

  • Topics: Combinatorics, Approximations and Expansions

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