Description
BIRKHAUSER Mathematics For The Analysis Of Algorithms 2007 Edition by Daniel H. Greene Donald E. Knuth
This monograph collects some fundamental mathematical techniques that are required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms emphasizing the more difficult notions. The authors cover recurrence relations operator methods and asymptotic analysis in a format that is concise enough for easy reference yet detailed enough for those with little background with the material. Table of contents : PrefaceBinomial Identities.- Summary of Useful Identities.- Deriving the Identities.- Inverse Relations.- Operator Calculus.- Hypergeometric Series.- Identities with the Harmonic NumbersRecurrence Relations.- Linear Recurrence Relations.- Nonlinear Recurrence RelationsOperator Methods.- The Cookie Monster.- Coalesced Hashing.- Open Addressing: Uniform Hashing.- Open Addressing: Secondary ClusteringAsymptotic Analysis.- Basic Concepts.- Stieltjes Integration and Asymptotics.- Asymptotics from Generating FunctionsBibliographyAppendices.- Schedule of Lectures.- Homework Assignments.- Midterm Exam I and Solutions.- Final Exam I and Solutions.- Midterm Exam II and Solutions.- Final Exam II and Solutions.- Midterm Exam III and Solutions.- Final Exam III and Solutions.- A Qualifying Exam Problem and SolutionIndex