Methods in Algorithmic Analysis: Chapman & Hall/CRC Computer and Information Science Series
Autor Vladimir A. Dobrushkinen Limba Engleză Paperback – 16 iun 2017
A flexible, interactive teaching format enhanced by a large selection of examples and exercises
Developed from the author’s own graduate-level course, Methods in Algorithmic Analysis presents numerous theories, techniques, and methods used for analyzing algorithms. It exposes students to mathematical techniques and methods that are practical and relevant to theoretical aspects of computer science.
After introducing basic mathematical and combinatorial methods, the text focuses on various aspects of probability, including finite sets, random variables, distributions, Bayes’ theorem, and Chebyshev inequality. It explores the role of recurrences in computer science, numerical analysis, engineering, and discrete mathematics applications. The author then describes the powerful tool of generating functions, which is demonstrated in enumeration problems, such as probabilistic algorithms, compositions and partitions of integers, and shuffling. He also discusses the symbolic method, the principle of inclusion and exclusion, and its applications. The book goes on to show how strings can be manipulated and counted, how the finite state machine and Markov chains can help solve probabilistic and combinatorial problems, how to derive asymptotic results, and how convergence and singularities play leading roles in deducing asymptotic information from generating functions. The final chapter presents the definitions and properties of the mathematical infrastructure needed to accommodate generating functions.
Accompanied by more than 1,000 examples and exercises, this comprehensive, classroom-tested text develops students’ understanding of the mathematical methodology behind the analysis of algorithms. It emphasizes the important relation between continuous (classical) mathematics and discrete mathematics, which is the basis of computer science.
Toate formatele și edițiile | Preț | Express |
---|---|---|
Paperback (1) | 589.61 lei 6-8 săpt. | |
CRC Press – 16 iun 2017 | 589.61 lei 6-8 săpt. | |
Hardback (1) | 1556.35 lei 6-8 săpt. | |
CRC Press – 3 noi 2009 | 1556.35 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781138118041
ISBN-10: 1138118044
Pagini: 826
Ilustrații: 54
Dimensiuni: 178 x 254 x 42 mm
Greutate: 0.45 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Computer and Information Science Series
ISBN-10: 1138118044
Pagini: 826
Ilustrații: 54
Dimensiuni: 178 x 254 x 42 mm
Greutate: 0.45 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Computer and Information Science Series
Public țintă
UndergraduateCuprins
Preliminaries. Combinatorics. Probability. More about Probability. Recurrences or Difference Equations. Introduction to Generating Functions. Enumeration with Generating Functions. Further Enumeration Methods. Combinatorics of Strings. Introduction to Asymptotics. Asymptotics and Generating Functions. Review of Analytic Techniques. Appendices. Bibliography. Answers/Hints to Selected Problems. Index.
Notă biografică
Vladimir A. Dobrushkin is a professor in the Division of Applied Mathematics at Brown University and a professor in the Department of Computer Science at Worcester Polytechnic Institute.
Recenzii
…helpful to any mathematics student who wishes to acquire a background in classical probability and analysis … This is a remarkably beautiful book that would be a pleasure for a student to read, or for a teacher to make into a year's course.
—Harvey Cohn, Computing Reviews, May 2010
—Harvey Cohn, Computing Reviews, May 2010
Descriere
Accompanied by more than 1,000 examples and exercises, this comprehensive, classroom-tested text presents numerous theories, techniques, and methods used for analyzing algorithms. It includes basic material on combinatorics and probability that can be used for students with weak backgrounds. It presents information on asymptotics not usually found in similar books, including Rice’s method, the Euler and Boole summation formulas, and recurrences. The author offers tutorials throughout the text on topics as diverse as continued fractions, functions of a complex variable, numerical calculations, and Stieltjes integration. An appendix contains a comprehensive collection of useful formulas.