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Kauers, Manuel; Paule, Peter

The Concrete Tetrahedron Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates (Kartoniert / Broschiert / Paperback)

Springer-Verlag KG, Januar 2011


203 S. - Sprache: Englisch - 20 schwarz-weiße Abbildungen, 20 schwarz-weiße Tabellen - 237x160x13 mm

ISBN: 3709104440 EAN: 9783709104446

The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates. Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.

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Produktdetails

Concrete mathematics from a computer algebra perspectiveInformal style: as simple as possible, as complicated as necessaryIncludes notivating applications from combinatorics, computer science, number theory, special functions

Inhaltsverzeichnis

1 Introduction1.1 Selection Sort and Quicksort1.2 Recurrence Equations1.3 Symbolic Sums1.4 Generating Functions1.5 Asymptotic Estimates1.6 The Concrete Tetrahedron1.7 Problems 2 Formal Power Series 2.1 Basic Facts and Definitions2.2 Differentiation and Division2.3 Sequences of Power Series2.4 The Transfer Principle2.5 Multivariate Power Series2.6 Truncated Power Series2.7 Problems 3 Polynomials3.1 Polynomials as Power Series3.2 Polynomials as Sequences3.3 The Tetrahedron for Polynomials3.4 Polynomials as Solutions3.5 Polynomials as Coefficients3.6 Applications3.7 Problems 4 C-Finite Sequences4.1 Fibonacci Numbers4.2 Recurrences with Constant Coefficients4.3 Closure Properties4.4 The Tetrahedron for C-finite Sequences4.5 Systems of C-finite Recurrences4.6 Applications4.7 Problems 5 Hypergeometric Series5.1 The Binomial Theorem5.2 Basic Facts and Definitions5.3 The Tetrahedron for Hypergeometric Sequences5.4 Indefinite Summation5.5 Definite Summation5.6 Applications5.7 Problems 6 Algebraic Functions6.1 Catalan Numbers6.2 Basic Facts and Definitions6.3 Puiseux Series and the Newton Polygon6.4 Closure Properties6.5 The Tetrahedron for Algebraic Functions6.6 Applications6.7 Problems 7 Holonomic Sequences and Power Series7.1 Harmonic Numbers7.2 Equations with Polynomial Coefficients7.3 Generalized Series Solutions7.4 Closed Form Solutions7.5 The Tetrahedron for Holonomic Functions7.6 Applications7.7 Problems Appendix A.1 Basic Notions and NotationsA.2 Basic Facts from Computer AlgebraA.3 A Collection of Formal Power Series IdentitiesA.4 Closure Properties at One GlanceA.5 SoftwareA.6 Solutions to Selected ProblemsA.7 Bibliographic Remarks

Kritikerstimmen

From the reviews:"The Concrete Tetrahedron is suitable for advanced undergraduate students in mathematics or computer science who have had some exposure to elementary concepts in abstract algebra and complex analysis. ... The volume's numerous problems together with selected solutions definitely make it appropriate for an independent reading course for the motivated student. Summing Up: Highly recommended. Upper-division undergraduates." (D. M. Ha, Choice, Vol. 49 (11), July, 2012)"The book deals with a blend of continuous and discrete mathematics, applying continuous methods to discrete problems. ... Those who are interested in the subject matter of Concrete Mathematics will enjoy The Concrete Tetrahedron for an independent perspective, some more recent results, and for new applications." (John D. Cook, The Mathematical Association of America, March, 2011)

ISBN 3-7091-0444-0

ISBN 978-3-7091-0444-6

Alternative Antiquarische Bücher / Angebote Auf Buchfreund
The Concrete Tetrahedron

Kauers, Manuel and Peter Paule.
The Concrete Tetrahedron Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates. Texts & Monographs in Symbolic Computation
Wien, Springer, 2011. 216 Seiten 23,5 cm, Softcover, Taschenbuch EAN: 9783709104446 (ISBN: 3709104440)


Englischer Text. Einband nur minimal berieben. Sehr gut bis fast wie neu. 9783709104446
Schlagworte: informatik, sonstiges mathematik

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