Finite Markov chains and algorithmic applications /

As compared, say, with the physical sciences, the undergraduate mathematics curriculum seems rather insulated from research-level breakthroughs. High-level mathematical research usually runs to great complexity and undergraduate teaching traditions provide little quarter for summary or merely descriptive overview. Occasionally, however, one sees the very rafters of a mathematical discipline shaken by a fundamental new idea, simultaneously very simple and yet extremely profound. A case in point is the Propp-Wilson algorithm for exactly simulating the equilibrium distribution of certain Markov chains, which precipitated a small revolution in the field of stochastic processes. Here Haggstrom (Goteborgs Universitet) takes the beginning student from the first definitions concerning Markov chains even beyond Propp-Wilson to its refinements and applications, all in just a hundred or so generously detailed pages. If an undergraduate reading this book comes away saying "I should have thought of that!" then the psychological barrier between school mathematics and research will have begun to break down. Few mathematical monographs provide a comparable opportunity. General readers; lower-division undergraduates through professionals. D. V. Feldman University of New Hampshire