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This introductory textbook focuses on the design and analysis of algorithms. The author uses a careful selection of topics to illustrate tools for algorithm analysis, including mathematical preliminaries, recursive algorithms, and the network flow problem.

Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema­ ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the...

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in: Combinatorics, Probability Theory, Statistics, Theory of Markov Chains, and Number Theory.