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Details for:
Knuth D. Mathematics for the Analysis of Algorithms 3ed 2008
knuth d mathematics analysis algorithms 3ed 2008
Type:
E-books
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1
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3.6 MB
Uploaded On:
Oct. 6, 2022, 10:41 a.m.
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andryold1
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9B18638D73CEB03D3037E965B63F018DB27B8E16
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Textbook in PDF format This monograph is derived from an advanced course in computer science at Stanford University on the analysis of algorithms. The course presents examples of the major paradigms used in the precise analysis of algorithms, emphasizing some of the more difficult techniques. Much of the material is drawn from the starred sections of The Art of Computer Programming, Volume 3 [Knuth III]. Analysis of algorithms, as a discipline, relies heavily on both computer science and mathematics. This report is a mathematical look at the synthesis--emphasizing the mathematical perspective, but using motivation and examples from computer science. It covers binomial identities, recurrence relations, operator methods and asymptotic analysis, hopefully in a format that is terse enough for easy reference and yet detailed enough to be of use to those who have not attended the lectures. However, it is assumed that the reader is familiar with the fundamentals of complex variable theory and combinatorial analysis. Winter 1980 was the fourth offering of Analysis of Algorithms, and credit is due to the previous teachers and staff--Leo Guibas, Scott Drysdale, Sam Bent, Andy Yao, and Phyllis Winkler--for their detailed contributions to the documentation of the course. Portions of earlier handouts are incorporated in this monograph. Harry Mairson, Andrei Broder, Ken Clarkson, and Jeff Vitter contributed helpful comments and corrections, and the preparation of these notes was also aided by the facilities of Xerox corporation and the support of NSF and Hertz graduate fellowships. In this third edition we have made a few improvements to the exposition and fixed a variety of minor errors. We have also added several new appendices containing exam problems from 1982 and 1988. Binomial Identities Summary of Useful Identities Deriving the Identities Inverse Relations Operator Calculus Hypergeometric Series Identitieswith the Harmonic Numbers Recurrence Relations Linear Recurrence Relations Finite History Constant Coefficients Variable Coefficients Full History Differencing By Repertoir e Nonlinear Recurrence Relations Relations with Maximum or Minimum Functions Continued Fractions and Hidden Linear Recurrences Doubly Exponential Sequences Operator Methods The Cookie Monster Coalesced Hashing Open Addressing: Uniform Hashing Open Addressing: Secondary Clustering Asymptotic Analysis Basic Concepts Notation Bootstrapping Dissecting Limits of Limits Summary of Useful Asymptotic Expansions An Example from Factorization Theory Stieltjes Integration and Asymptotics O-notation and Integrals Euler's Summation Formula An Example from Number Theory Asymptotics from Generating Functions Darboux's Method Residue Calculus The Saddle Point Method Bibliography Appendices A Schedule of Lectures, B Homework Assignments C Midterm Exam I and Solutions D Final Exam I and Solutions E Midterm Exam II and Solutions F Final Exam II and Solutions G Midterm Exam III and Solutions H Final Exam III and Solutions I A Qualifying Exam Problem and Solution
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Knuth D. Mathematics for the Analysis of Algorithms 3ed 2008.pdf
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