By Ilwoo Cho

This ebook introduces the research of algebra brought on by means of combinatorial items referred to as directed graphs. those graphs are used as instruments within the research of graph-theoretic difficulties and within the characterization and answer of analytic difficulties. The ebook provides fresh learn in operator algebra conception attached with discrete and combinatorial mathematical items. It additionally covers instruments and techniques from a number of mathematical parts, together with algebra, operator concept, and combinatorics, and gives quite a few functions of fractal concept, entropy thought, *K*-theory, and index theory.

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