Read the beauty of Mathematics

Learning the beauty of mathematics and mathematics

Read the beauty of Mathematics

In fact, I have been preparing to read the book "The beauty of mathematics" for a long time. I remember reading "the waves of the waves" last summer, and then I met a person like Wu Jun, who liked his writing style. So I am going to read the beauty of mathematics.

Like the book "The beauty of mathematics", the book itself has a good reputation among many readers, and Dr. Wu has learned and studied it, for more people, there is also a kind of respect. After I read "The waves of the waves", there was a thick history of accumulation in the chest. I have to admit the impact of "the waves" on me.

The beauty of mathematics is actually quite different from the top of the waves. The top of the waves can be said to be a more popular scientific book, there are some profound ideas in it, while the beauty of mathematics is just suitable for readers in this field. Although Dr. Wu has written a lot of theorem in the beauty of mathematics, I think it is still difficult for a liberal arts student to understand it. Even if I have been studying advanced mathematics for a year, many specific theorem technologies are also unfamiliar. So from last year's preparation to this book, to this year's actual completion, it took a long time. I think there are also a lot of opportunities and coincidences between them. I learned some machine learning, AI, and Chinese Word Segmentation knowledge due to my work, this part of knowledge is well reflected in the beauty of mathematics.

I think I have never been a practical engineer. For some technical knowledge, I am willing to start with theoretical knowledge. First, I must understand an overall framework, then you can create a local block. This logic is basically impossible for large companies. Many systems, including organizations and the overall framework, have little knowledge about it. Most people are busy with their own products, finished is complete. It's like learning Chinese word segmentation.

After having some basic knowledge, I will feel that reading the beauty of mathematics is a very happy thing. Dr. Wu explained and described a lot of theoretical knowledge in a simple way, many times it will make you feel like a plug-in.

I think there will always be something humanistic in Dr. Wu's text. That feeling is amazing, and it will make you feel the inner feelings of a person with excellent academic accomplishments inexplicably. Just like many people described by Wu Jun, many people who have made many achievements are not closely tied to a person, or have a very strange nature or have a very unique idea, however, many people have their own persistence and attitude, which affects more people, so they will succeed and lead more people to succeed.

After reading the beauty of mathematics, I have reflected on many of my own things, right, and wrong. Sometimes I wonder why some universities are so good and some are not so good. Many people are willing to make great efforts to go to a better school, and many people who have gone to college should know that the university is more self-taught. You can communicate with instructors. The reason why I understand a good university is that it has many good teachers concentrated there, so they can focus more on it, then more excellent people are attracted, and these talented people will lead excellent people. So this will form a loop, because there are good, good, and good changes. This is a good development cycle.

Dr. Wu wrote in his Postscript: "The best scholars in the world always tell outsiders the truth in a simple way, rather than complicate the simple problem." Dr. Wu also talked about a lot of theories in the book. In many cases, you may try to simplify it and think about it in a simple way. Maybe the results will be very good, like hidden Markov models, or some scientific leader ideas.

After reading Dr. Wu's book every time, I always feel that I have never done anything (although I have read only two books ). Although the book has been read, I always think that there are many things I can think about and comprehend. I remember a word that impressed me very much: "A lot of people should not pursue the number of books, but the time you read it and think about it ."

 

I am used to attaching the directory of a book as follows:

Chapter 2 text and language vs numbers and information

Text, language, and mathematics have been compatible since their birth. Although their development was separated, they can finally come together.

Chapter 2 Natural Language Processing-from rules to statistics, human understanding of machines and natural language has taken a great turn. Early studies focused on the use of rules-based methods. Although some simple problems were solved, it was impossible to fully understand natural language. Until? Years later, people began to try to use statistical-based methods for natural language processing, so that there was a breakthrough and practical product.

Chapter 4 Statistical Language Model

Statistical language model is the basis of natural language processing and is widely used in Machine Translation, speech recognition, printed or handwritten recognition, spelling correction, Chinese Character Input and Literature Query.

Chapter 2 Chinese Word Segmentation

Chinese word segmentation is the basis for processing Chinese information. It has also taken a detour and has basically solved this problem by relying on the statistical language model.

Chapter 1 Hidden Markov Model

The Hidden Markov Model was first applied to the communication field and then extended to speech and language processing, becoming a bridge connecting natural language processing and communication. Hidden Markov models are also one of the main tools for machine learning.

Chapter 1 measurement and functions of information

Information can be quantified. Information entropy is not only a quantitative measure of information, but also the basis of the entire information theory. It has a strong guiding significance for communication, data compression, and natural language processing.

Chapter 2 gienik and Modern Language Processing

As the founder of modern natural language processing, Professor Jia linick successfully applied mathematical principles to the natural language processing field. His life is full of legends.

Chapter 2 beauty of Simplicity-Boolean algebra and index Boolean algebra of search engines are very simple, but they are the foundation of computer science. They combine logic and mathematics into one, it also gives us a new perspective on the world and opens up the digital age.

Chapter 2 graph theory and Web Crawler

Before creating an index, Internet search engines need to use a program to automatically download all web pages to the server. This program is called a web crawler. It is written based on the principles of Discrete Math.

Chapter 2 PageRank-Google's democratic voting Network Name

The web page ranking technology was an early killer. Its appearance brought the quality of web page search to a great level. The principle behind it is the matrix operation of graph theory and linear algebra.

Chapter 2 determining the relevance between a webpage and a query is a fundamental issue in Web search. It is critical to determine the importance of each keyword in a query. It is a commonly used measure of the importance of keywords. The principle behind it is information theory.

Chapter 2 Basic Technologies of MAP and local search

The Finite State Machine and dynamic planning technology are used in the limited map and local service.

These two technologies are machine intelligence and machine learning tools. They are widely used, including speech recognition, spelling and syntax correction, Pinyin input methods, industrial control, and biological sequence analysis.

Chapter 2 Google AK-47 designer-Amit Shi

The most famous among all light weapons is an assault gun, because it never gets stuck and is not easy to be damaged. It can be used in any environment, featuring high reliability, high lethality, and easy operation. According to the above

Is designed.

Chapter 2 cosine theorem and news Classification

Although computers do not understand news, they can classify news accurately.

The mathematical tool is a seemingly unrelated cosine theorem.

Chapter 2 The two classification problems in matrix operations and text processing, whether Word Clustering or text classification, can be carried out through the Singular Value Decomposition of matrix in linear algebra. In this way, the problem of natural language processing becomes a mathematical problem.

Chapter 1 Information fingerprint and Its Application

Everything in the world has a unique identifier, and so does information. Each piece of information has a specific fingerprint, which can be used to distinguish different pieces of information.

Chapter 1 what comes to mind from the TV series "Dark computing"-Principles of discussion

Cryptography is based on information theory and mathematics. Passwords without information theory guidance are very easy to crack. Passwords are truly secure only when information theory is widely used in cryptography.

Chapter 3 not necessarily gold-about search engines

The Flash is not necessarily gold, and the top web pages in the search engine are not necessarily useful web pages. The principle of eliminating these cheating pages is the same as that of filtering noise in messages. This shows that many principles of information processing and communication are the same.

Chapter 2 Importance of Mathematical Models

Correct mathematical models are crucial in science and engineering, and the ways to find correct models are often tortuous. The correct model is usually simple in form.

Chapter 1 do not put eggs in a basket-chatbot

The maximum entropy model is a perfect mathematical model. It can integrate various information into a unified model, which is widely used in information processing and machine learning. It is very simple and elegant in form, and requires profound mathematical basics and superb skills in implementation.

Chapter 2 mathematical principles of PinYin Input Method

The process of Inputting Chinese characters is communication between people and computers. Good input methods consciously or unconsciously follow the mathematical model of communication. Of course, the most effective input method should be consciously guided by information theory.

Chapter 4 Marcus, Godfather of natural language processing, and his team

Turning natural language processing from a rule-based research method to a statistical-based research method means that Mickey Marcus, a professor at the University of Pennsylvania, is indispensable. He created a corpus widely used in academic circles and trained a large number of elites.

Chapter 4 bloom Filter

In daily life, it is often necessary to determine whether an element is in a collection. Bloom filter is the best mathematical tool to solve this problem in computer engineering.

Chapter 2 extended Markov chains-Bayesian Networks

Bayesian Network is a weighted directed graph and an extension of Markov chains. From the perspective of epistemology: Bayesian Networks overcome the mechanical Linear Constraints of Markov chains, which can unify any associated events into its framework. It is widely used in biological statistics, image processing, decision support systems, and game theory.

Chapter 1 Conditional Random Field and syntax analysis

The Conditional Random Field is an effective model for calculating the joint probability distribution, and syntactic analysis seems to be something taught by an English teacher in an English class. What is the relationship between the two?

Chapter 2 Viterbi and his Viterbi algorithms

Viterbi algorithms are the most frequently used algorithms in modern digital communications and also Decoding Algorithms processed by many natural languages. It is no exaggeration to say that Viterbi is one of the most influential scientists in today's life, because today's mobile communication standards are primarily developed by Qualcomm.

Chapter 2 automatic text classification-Expectation Maximization Algorithm

As long as there is some training data, define another maximization function, adopt algorithms, and use the computer for several iterations to obtain the desired model. This is really wonderful. It may have been deliberately arranged by our creator. So I call it God's algorithm.

Chapter 2 logical regression and search advertisement

Logistic regression is an exponential model that combines different factors that affect probability. It not only plays an important role in search advertisement, but also is widely used in information processing and Biological Statistics.

Chapter 2 cracking down the foundations of algorithms and Google cloud computing

Google is the most important mapreduce tool in the mysterious cloud computing field. Its principle is the "break through" algorithm commonly used in computer algorithms, the principle is as simple as it was originally-it splits complicated big problems into many small problems for separate solutions, and then merges the solutions of small problems into the solutions of the original problems. It can be seen that a lot of useful methods are used in life.

It is often simple and simple.