LEADER 04031nam 22005775 450 001 9910254090903321 005 20200706225443.0 010 $a3-319-03038-8 024 7 $a10.1007/978-3-319-03038-8 035 $a(CKB)3710000001006470 035 $a(DE-He213)978-3-319-03038-8 035 $a(MiAaPQ)EBC6315574 035 $a(MiAaPQ)EBC5592477 035 $a(Au-PeEL)EBL5592477 035 $a(OCoLC)967704161 035 $a(PPN)197455786 035 $a(EXLCZ)993710000001006470 100 $a20161201d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDiscrete Calculus $eMethods for Counting /$fby Carlo Mariconda, Alberto Tonolo 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XXI, 659 p. 66 illus.) 225 1 $aLa Matematica per il 3+2,$x2038-5722 ;$v103 300 $aIncludes index. 311 $a3-319-03037-X 327 $a1 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. 330 $aThis book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii?s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified. 410 0$aLa Matematica per il 3+2,$x2038-5722 ;$v103 606 $aCombinatorial analysis 606 $aApproximation theory 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 615 0$aCombinatorial analysis. 615 0$aApproximation theory. 615 14$aCombinatorics. 615 24$aApproximations and Expansions. 676 $a511.6 700 $aMariconda$b Carlo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0440078 702 $aTonolo$b Alberto$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254090903321 996 $aDiscrete Calculus$92105562 997 $aUNINA