The Beauty of Mathematics in Computer Science

The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school. The book covers many topics related to computer applications and applied mathematics including: Natural language processing Speech recognition and machine translation Statistical language modeling Quantitive measurement of information Graph theory and web crawler Pagerank for web search Matrix operation and document classification Mathematical background of big data Neural networks and Google’s deep learning Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

1. Words and languages, numbers and information Information Words and numbers The mathematics behind language 2. Natural language processing|From rules to statistics Machine intelligence From rules to statistics 3. Statistical language model Describing language through mathematics Extended reading: Implementation caveats Higher order language models Training methods, zero-probability problems, and smoothing Corpus selection 4. Word segmentation Evolution of Chinese word segmentation Extended reading: evaluating results Consistency Granularity 5. Hidden Markov model Communication models Hidden Markov model Extended reading: HMM training 6. Quantifying information Information entropy Role of information Mutual information Extended reading: Relative entropy 7. Jelinek and modern language processing Early life From Watergate to Monica Lewinsky An old man's miracle 8. Boolean algebra and search engines Boolean algebra Indexing 9. Graph theory and web crawlers Graph theory Web crawlers Extended reading: two topics in graph theory Euler's proof of the Königsberg bridges The engineering of a web crawler 10.PageRank: Google's democratic ranking technology The PageRank algorithm Extended reading: PageRank calculations 11.Relevance in web search TF-IDF Extended reading: TF-IDF and information theory 12.Finite state machines and dynamic programming: Navigation in Google Maps Address analysis and Finite state machines Global navigation and dynamic programming Finite state transducer 13.Google's AK- designer, Dr Amit Singhal 14.Cosines and news classification Feature vectors for news Vector distance Extended reading: The art of computing cosines Cosines in big data Positional weighting 15.Solving classification problems in text processing with matrices Matrices of words and texts Extended reading: Singular value decomposition method and applications 16.Information Fingerprinting and its application Information Fingerprint Applications of information Fingerprint Determining identical sets Detecting similar sets YouTube's anti-piracy Extended reading: Information Fingerprint's repeatability and SimHash Probability of repeated information Fingerprint SimHash 17.Thoughts inspired by the Chinese TV series Plot: The mathematical principles of cryptography The spontaneous era of cryptography Cryptography in the information age 18.Not all that glitters is gold: Search engine's anti-SPAM problem and search result authoritativeness question Search engine anti-SPAM Authoritativeness of search results Summary 19.Discussion on the importance of mathematical models 20.Don't put all your eggs in one basket: The principle of maximum entropy Principle of maximum entropy and maximum entropy model Extended reading: Maximum entropy model training 21.Mathematical principles of pinyin input method Input method and coding How many keystrokes to type a Chinese character? Discussion on Shannon's First Theorem The algorithm of phonetic transcription Extended reading: Personalized language models 22.Bloom Filters The principle of Bloom Filters Extended reading: The false alarm problem of Bloom Filters 23.Bayesian network: Extension of Markov Chain Bayesian network Bayesian network's application in word classification Extended reading: Training a Bayesian network 24.Conditional random Fields, syntactic parsing, and more Syntactic parsing|the evolution of computer algorithms Conditional random fields Conditional random fields' applications in other fields 25.Andrew Viterbi and the Viterbi Algorithm The Viterbi algorithm CDMA technology: The foundation of G mobile communication 26.God's algorithm: The expectation maximization algorithm Self-converged document classification Extended reading: Convergence of expectation-maximization algorithms 27.Logistic regression and web search advertisement The evaluation of web search advertisement The logistic model 28.Google Brain and artificial neural networks Artificial neural network Training an artificial neural network The relationship between artificial neural networks and Bayesian networks Extended reading: \Google Brain" 29.The power of big data The importance of data Statistics and information technology Why we need big data

Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese internet users from 2006-2010. The blogs had more than two million followers. He received Ph.D. in computer science from the Johns Hopkins University and had been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded more than ten US patents during his ten-year tenure there. He became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.