id: 06300907
dt: b
an:
au: Mariconda, Carlo; Tonolo, Alberto
ti: Discrete calculus. Methods for counting.
so: Unitext 103. La Matematica per il 3+2. Cham: Springer (ISBN
978-3-319-03037-1/pbk; 978-3-319-03038-8/ebook). xxi, 659~p. (2016).
py: 2016
pu: Cham: Springer
la: EN
cc: K25
ut:
ci:
li: doi:10.1007/978-3-319-03038-8
ab: Preliminary review / Publisher’s description: 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.
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