Mathematics for the Analysis of Algorithms [Paperback]

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.

This monograph collects fundamental mathematical techniques required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present major paradigms used in the precise analysis of algorithms.

A quantitative study of the efficiency of computer methods requires an in-depth understanding of both mathematics and computer science. This monograph, derived from an advanced computer science course at Stanford University, 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 terse enough for easy reference yet detailed enough for those with little background. Approximately half the book is devoted to original problems and solutions from examinations given at Stanford.

 

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 ClusteringAsl#-