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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.

Mathematics for the Analysis of Algorithms

Preface
Binomial Identities.- Summary of Useful Identities.- Deriving the Identities.- Inverse Relations.- Operator Calculus.- Hypergeometric Series.- Identities with the Harmonic Numbers
Recurrence Relations.- Linear Recurrence Relations.- Nonlinear Recurrence Relations
Operator Methods.- The Cookie Monster.- Coalesced Hashing.- Open Addressing: Uniform Hashing.- Open Addressing: Secondary Clustering
Asymptotic Analysis.- Basic Concepts.- Stieltjes Integration and Asymptotics.- Asymptotics from Generating Functions
Bibliography
Appendices.- 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 Solution
Index