Titlebook: Discrete Calculus; Methods for Counting Carlo Mariconda,Alberto Tonolo Textbook 2016 Springer International Publishing Switzerland 2016 com

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Textbook 2016nly 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

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,Let’s Learn to Count,though its contents are elementary, we warmly suggest to take a look at the chapter. Our approach consists in trying to describe every combinatorial problem by means of sets of (ordered) sequences, or (unordered) collections, and their dual concepts of sharings and compositions. Computations are suc

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Stirling Numbers and Eulerian Numbers, an application of the concepts discussed here we state Faà di Bruno chain rule for the .-th derivative of a composite of .-times differentiable functions on .. In the last section we discuss Eulerian numbers and as an application we solve the famous problem of the Smith College diplomas, and we est

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Manipulation of Sums,screte analogue of differential calculus. The discrete primitives are the tool that enable to compute finite sums. We examine in detail the case of the sums of powers of consecutive natural numbers: quite surprisingly this leads to the Stirling numbers of second kind. A section is devoted to the inv

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Formal Power Series, on their algebraic properties and basic applications to combinatorics. The reader must not be confused by the many technical, though simple, details that are needed in a book to justify rigorously every step. In Chap. ., we have learned how to count sequences and collections with occupancy constrai

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