ABSTRACT

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.

chapter Chapter 1|12 pages

Words and languages, numbers and information

chapter Chapter 2|51 pages

Natural language processing—From rules to statistics

chapter Chapter 3|11 pages

Statistical language model

chapter Chapter 4|8 pages

Word segmentation

chapter 5|9 pages

Hidden Markov model

chapter Chapter 6|10 pages

Quantifying information

chapter Chapter 7|8 pages

Jelinek and modern language processing

chapter Chapter 8|6 pages

Boolean algebra and search engines

chapter Chapter 9|6 pages

Graph theory and web crawlers

chapter Chapter 10|5 pages

PageRank: Google's democratic ranking technology

chapter Chapter 11|5 pages

Relevance in web search

chapter Chapter 13|4 pages

Google's AK-47 designer, Dr. Amit Singhal

chapter Chapter 14|8 pages

Cosines and news classification

chapter Chapter 16|10 pages

Information fingerprinting and its application

chapter Chapter 19|7 pages

Discussion on the importance of mathematical models

chapter Chapter 21|10 pages

Mathematical principles of Chinese input method editors

chapter Chapter 22|5 pages

Bloom filters

chapter Chapter 23|6 pages

Bayesian network: Extension of Markov Chain

chapter Chapter 24|9 pages

Conditional random fields, syntactic parsing, and more

chapter Chapter 25|9 pages

Andrew Viterbi and the Viterbi algorithm

chapter Chapter 27|4 pages

Logistic regression and web search advertisement

chapter Chapter 28|18 pages

Google Brain and artificial neural networks

chapter Chapter 29|20 pages

The power of big data

chapter |3 pages

Postscript