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