rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Discrete Calculus
    sub title: Methods for Counting
  name:
    name part: Mariconda, Carlo.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Tonolo, Alberto.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXI, 659 p. 66 illus. online resource.
  abstract: 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.
  table of contents: 1 Let’s Learn to Count -- 2 Counting Sequences and Collections -- 3 Occupancy Constraints -- 4 Inclusion/Exclusion -- 5 Stirling Numbers and Eulerian Numbers -- 6 Manipulation of Sums -- 7 Formal Power Series -- 8 Generating Formal Series and Applications -- 9 Recurrence Relations -- 10 Linear Recurrence Relations -- 11 Symbolic Calculus -- 12 The Euler-Maclaurin Formulas of Order 1 and 2 -- 13 The Euler-Maclaurin Formula of Arbitrary Order -- 14 Cauchy and Riemann Sums, Factorials, Ramanujan Numbers and their Approximations -- 15 Tables and Formulas -- 16 Appendix A.
  note: by Carlo Mariconda, Alberto Tonolo.
  subject:
    topic: Mathematics
  subject:
    topic: Approximation theory
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Approximations and Expansions
  classification: QA164-167.2
  classification: 511.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: UNITEXT, 103
  identifier: 9783319030388
  identifier: http://dx.doi.org/10.1007/978-3-319-03038-8
  record info:
    record creation date: 161201
    record change date: 20161202001016.0
    record identifier: 978-3-319-03038-8