Beauty of Mathematics (Third Edition)

This book grew out of the "Beauty of Mathematics" series that its author, Wu Jun, serialized on the Google China blog. The series drew millions of hits and was then substantially rewritten for print, explaining the mathematical principles behind communications, natural language processing, search, and machine learning in accessible language and through concrete cases. The book's main thread is "how to turn complex problems into simple ones": beginning with the origins of writing and numbers, it proceeds through statistical language models, Chinese word segmentation, hidden Markov models, information entropy and mutual information, Boolean algebra and indexing, graph theory and web crawlers, PageRank, TF-IDF, finite state machines and dynamic programming, the law of cosines and news classification, matrix operations and singular value decomposition, information fingerprints, cryptographic principles, search engine anti-spam, maximum entropy models, pinyin input methods, Bloom filters, Bayesian networks, conditional random fields, the Viterbi algorithm, the expectation-maximization algorithm, logistic regression and search advertising, MapReduce and cloud computing, and artificial neural networks, closing with a discussion of computational complexity. The third edition adds three chapters to the second, introducing the mathematical foundations of blockchain (elliptic curve encryption), the mathematics of quantum key distribution, and Hilbert's tenth problem and the limits of machine intelligence. What readers take away is less a set of formulas than a method of "dissecting engineering problems with mathematical thinking."