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Unitext Ser.: Discrete Calculus : Methods for Counting by Carlo Mariconda and Alberto Tonolo (2016, Trade Paperback)
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Discrete Calculus by Carlo Mariconda, Alberto Tonolo. Author Carlo Mariconda, Alberto Tonolo. This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums.
- Buy It NowDiscrete Calculus: Methods for Counting by Carlo Mariconda (English) Paperback B
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About this product
Product Identifiers
PublisherSpringer International Publishing A&G
ISBN-10331903037X
ISBN-139783319030371
eBay Product ID (ePID)18038563110
Product Key Features
Number of PagesXxi, 659 Pages
LanguageEnglish
Publication NameDiscrete Calculus : Methods for Counting
SubjectNumerical Analysis, Calculus, Mathematical Analysis, Discrete Mathematics
Publication Year2016
TypeTextbook
Subject AreaMathematics
AuthorCarlo Mariconda, Alberto Tonolo
SeriesUnitext Ser.
FormatTrade Paperback
Dimensions
Item Weight358.8 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
Dewey Edition23
Reviews"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)
Series Volume Number103
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515.62
Table Of Content1 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.
SynopsisThis primer covers a remarkably wide range of topics in discrete calculus, from combinatorics to recurrence relations. With examples and exercises throughout, the text's clarity and rigor are informed by extensive teaching experience and academic discussion., This text deals with combinatorics, finite calculus, formal power series and generating functions, recurrence relations, symbolic calculus and approximation formulae for finite sums. There are several books on these arguments, even though few are covering all of them. This books wants to be an introductory text which leads the reader from basic knowledge to deeper insights into specific topics, while maintaining an accurate mathematical style. The aim here is to provide a strategy in order to classify and solve problems, avoiding tricks and ad hoc solutions, thanks to a rigorous and at the same time user-friendly, mathematical setting. The basic of every concept is clearly introduced and is accompanied by several examples. The reader will appreciate the effectiveness of being precise. In addition, depending on the needs of different courses, various paths through the text can be adopted., 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.
LC Classification NumberQA297.4
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