I studied engineering at Jiaotong University (though there were not many classes). Elementary school, junior high school and senior high school participated in the math competition all the way, and the ranking was not bad. So I didn't take the senior high school entrance examination and the college entrance examination, and I came all the way. I have deep feelings for mathematics. At the same time, my girlfriend's university is also a department of mathematics, and I regret that the university chose a major that I was not interested in (Jiaotong University allowed me to choose any major at that time, but I chose shipbuilding without consulting my parents). In the process of reading this book, I found a lot of feelings about reading competition books in high school. A lot of knowledge about probability theory (inequality), graph theory and number theory mentioned in it is the focus of the re-examination of senior high school mathematics league. I learned a lot in high school, but I almost forgot it after the university was abandoned. Many theorems mentioned in the book are still very intimate.
The book is called The Beauty of Mathematics, which seems a little too big. After all, it is more about the introduction and summary of the mathematical model used by Wu Jun in Google search-related work. Most of the mentioned mathematics focuses on probability theory, graph theory, number theory and other fields, so the topic is too big. Maybe hax was right, maybe the publishing house got the name of selling books.
I have to say that Wu Jun is a great man, and his words can reveal everyone's momentum. The book is constantly interspersed with stories and even gossip of great scientists and people in the field of science and technology in history. Reading between the lines, I can feel that Wu Jun is at their level (even though he will laugh at himself as a second-rate engineer).
I won't introduce the specific models in the book, but I have learned a few things (only superficial knowledge), and I can list them all after reading them.
1. In the world of Internet, how is information quantified and what is the information entropy? What's the use?
2. In the field of search, how is language counted, especially how to divide words by probability model?
3. How does the search engine work? What's with the web crawler?
4.4 What's the matter? PageRank？ Solve what problem?
5. Mathematical models in the field of cryptography and decryption, especially all kinds of interesting stories about decryption during World War II, and the TV series "Assassination" mentioned above should be watched in time.
6. Mathematical model of pinyin input method
7. Automatic text classification model
……
The biggest feeling after reading it is:
1. Mathematical model plays a great role in promoting the development of new technology.
2. Siege master is a great profession, and it is great to be able to turn this knowledge into productivity.
3. It is mentioned in the book that many mathematical models are constantly evolving, improving and upgrading, that is to say, some people are constantly optimizing, and better models and newer technologies will appear. It may be more important to keep up with the development of technology, otherwise many people have been doing continuous optimization at a certain point, which is meaningless.
But at the same time, technology plays a huge role in solving practical problems. All kinds of mathematical models and methods mentioned in the book are aimed at solving people's needs or business needs. After all, the company is not a scientific research institute, so it is very important to pursue directly solving the user's needs through technology or making easy-to-use tools for business personnel and operators to indirectly solve the user's needs. It may not be that technicians think that 80 points is enough, but that users and users who use tools think that 80 points is an important measure.
Speaking of tools, I remembered Zhao Zhao's words: If you don't use tools well, it means you don't have tools, which may be the key point. At the same time, people who use tools must make good use of them. If you don't make good use of them, it's too sorry for technology.
Reflection on the Beauty of Mathematics 2 "The Beauty of Mathematics", mathematics in the eyes of a Google researcher who has worked for many years. What makes me feast my eyes on is that the mathematics knowledge in the university can be so widely used in the computer industry.
In the fields of speech recognition, translation and cryptography, there are many models and ideas based on probability statistics. Of course, Bayesian formula is the basis, which is applied to hidden Markov chain model and neural network model.
In search, the knowledge of probability is used in some related calculations. In news classification, some knowledge of matrix eigenvalue and similar diagonalization is used. Of course, matrix transformation is ubiquitous in image processing. In addition, there are some communication models in identification, which involve channel, bit error rate and information entropy.
I just started school recently, so I want to find some books to read, but it's best not to be too difficult or too obscure. From August to now, The Beauty of Mathematics, written by Wu Jun and published in May 2002, has been at the top of the list of science and technology books in JD.COM, Amazon and other major online shopping malls. Of course, the earlier publication "Top of the Tide" is also in a very high position. I thought that market forces should help me pick out good books, so I borrowed one from the library and didn't finish reading it until tonight.
So, I want to write something to sum up and reflect. Anyway, there's nothing wrong just after the class meeting.
Suggestion written in front: If you don't hate math, I strongly recommend this book. It can be downloaded to the electronic version online, but it still feels very different.
Needless to say, "Beauty of Mathematics" is actually a popular science book, aimed at people who have received ordinary higher education. You don't need to have deep attainments in a specific field to understand it, but you'd better know a little about linear algebra, probability statistics, combinatorial mathematics, information theory, computer algorithms and pattern recognition (although there are so many lists, it doesn't matter if some people don't understand them ...), so it's especially suitable for people in science. Most of the content is related to artificial intelligence and computers, which is not my major, but the author is good at expressing seemingly complicated principles in concise language, so the readability is still very good.
Wu Jun graduated from Tsinghua University, worked for Google before, and then went to Tencent. These articles were published on the Google blackboard and later rewritten, so the content downloaded online is different from that in the book. Because Wu Jun himself studies natural language processing and speech recognition, there may be more statistical language models, but I don't think this will hinder the whole book from showing the beauty of mathematics ... I feel that I have gained a lot and gained some knowledge, but more is still in the way of thinking. The author gives many examples to try to make people understand that the basic principles behind many seemingly complex high-tech technologies are actually unexpectedly simple (of course, it must be admitted that the first person who thought of these methods is still great ...). For example, machine translation with high accuracy seems to be that computers can understand languages of various countries, but behind it are statistical models and probability models that many people with science degrees in universities are very clear; Another example is the mathematical principle of pinyin input method. Early research mainly focused on shortening the average coding length, such as the once popular five-stroke input method, but today the really practical input method is Pinyin input method, which has a lot of redundant information and a long coding length. The author makes a simple explanation from the perspective of information theory and market. Another example is the automatic classification of news. Many people in non-IT fields may think that computers can read news and classify it, but in fact it is only the extraction of feature vectors and the calculation of vector angles in multi-dimensional space, which is very, very simple, but those who have studied a little linear algebra can certainly understand it at a glance ... Of course, the perfect realization still needs to consider many details and realistic situations, but this is not the focus of this book. The beauty of mathematics lies in simplicity rather than triviality.
In addition to the specific information technology analysis, the author also spent a lot of time telling the growth process of some outstanding people, especially comparing their growth experiences with those of China students. Although the author didn't say it clearly, there were criticisms about higher education in China and many enterprises in China between the lines. First, the utility of education, the lack of relaxed independent thinking environment, even if you learn a bunch of theories, it is difficult to apply, and naturally there is a lack of innovative results; Second, China enterprises are short-sighted, and most of them are unwilling to invest in developing new frameworks, but enjoy the research results of academic circles and foreign enterprises.
To sum up, the "beauty of mathematics" can't really improve your programming ability, nor can it significantly improve your mathematics level, but to a great extent, it can make you jump out of the shackles of textbook-style tedious details and think about the "operating principle" of the mathematical engine behind the information world from a more macro perspective, so that people can understand that what seems to be very advanced and complicated is actually not as complicated as we thought, but the "boring" mathematics we have learned can really be.
After reading The Beauty of Mathematics, I have a strong feeling that the tools must be advanced. Mathematics is a powerful tool, so is the computer. The combination of these two tools has created powerful companies, such as Google, Baidu, Amazon, Ali, JD.COM and Teng Xun. They are not a century-old shop, but they have mastered advanced tools.
Mastering advanced tools will definitely gain a competitive advantage. If you know where a group of software engineers maintain a larger computer cluster, don't hesitate to use their services, because it will give you an advantage. So we use Google search and email, shop on Amazon, JD.COM and Taobao, contact friends with QQ and Weibo, use bank cards and online banking, and use trading terminals to conduct various transactions in the global market. ...
The history of mankind is the evolutionary history of a tool. The progress of stone tools, bronze, iron, gunpowder, steam engine, internal combustion engine, telegraph, telephone, television, computer, satellite, internet and tools leads the progress of civilization. New tools are constantly eliminating old tools, just as Internet video-on-demand is eliminating TV, Weibo is eliminating newspapers and e-books are eliminating paper books.
But there are some ancient tools that people are still studying and using today, and even spend a lot of time on them. Brush is such an example. What is the significance of learning to master the backward tool of writing brush today? In fact, when we use some backward tools, we mainly learn the ideas behind them. The general principle of artistic aesthetics contained in calligraphy and painting can stand the test of specific tool changes. Oracle Bone Inscriptions, Jin Wen and Shi Guwen's understanding of spatial composition is still worth learning by modern people. Ideological tools are more powerful tools than physical tools.
Tools combine to form a more powerful new tool. Although the Markov chain mentioned in Beauty of Mathematics is a powerful tool, I have never heard the teacher mention it in math class. The most impressive examples in this book are cosine theorem and news classification. Cosine theorem is middle school mathematics, plus some not difficult multidimensional vector knowledge, which actually solves the problem of computer news classification!
Behind every tool is people's understanding of the world. Behind the steam engine and internal combustion engine is the world of mechanics. Behind the telegraph, telephone, television, computer and Internet is the information world. Mathematics is an abstract tool and the tool behind other tools. Mathematics is essential for every subject to become a science. Maybe one day people will get used to analyzing art with mathematical tools. Mathematics is a language, which originates from the concrete world and is higher than the concrete world. If language is the understanding and description of the world and mathematics is language, then it must be the language closest to God. It seems insignificant, but it can describe everything.
What's the use of learning mathematics? Feynman, a physicist, raised this question in his freshman year, and his brother suggested that he transfer to the physics department. Today, this problem is no longer a problem. Talents with a solid foundation in mathematics are entering all walks of life, such as finance. I know the owner of a publishing house. He has one condition for recruiting fresh graduates: good math.
Although the tools are good, the key is to be able to use them. Finally, we have to go back to those who have mastered advanced tools. Software algorithm engineer and computer cluster are the necessary equipment for first-class enterprises at present. Just like Mark. Anderson said that top companies in all walks of life are software companies. Excellent software algorithm engineer is the focus of talent competition. In this way, we can easily understand Google's requirements for recruiting engineers.
The increasing ability to process and transmit information is the characteristic of knowledge economy. The Beauty of Mathematics shows how Google uses mathematics and computer networks to lead us into the era of cloud computing and big data.
The work in the era of knowledge economy is to conduct scientific research in their respective fields. Scientific research should make bold assumptions and carefully verify them. Scientific research should be quantified. There should be comparative experiments in scientific research. Scientific research should have a mathematical model. Scientific research should have field investigation. Scientific research should be verified by literature. Scientific research should have peer review. The Beauty of Mathematics introduces us to the scientific research methods and processes in the field of natural language analysis.
There are countless details in any field. People who are interested will not be intimidated by these details, but will study them with great interest, thus reaching an admirable height. Teacher Wu Jun showed us these details in mathematics and algorithm, and also showed the height he reached. It's worth learning.
I saw on the Internet that Dr. Wu Jun's The Beauty of Mathematics was recommended. Although I study social science, I have always respected mathematics, so I bought it. My real experience, as Dr. Wu Jun said in the postscript of the book, has raised my realm to a higher level.
So, for me, what level has it improved?
First of all, it must be the ideological realm. Before reading this book, I knew that there are only two ways for human beings to express the information set formed by events in this world, one is numbers and the other is language. The whole set of real numbers is infinite and each number is unique; There are infinite events in the whole world, and each event is unique, so the number set in mathematics and the event set in the world constitute a one-to-one correspondence, so studying the relationship between numbers is actually studying the relationship between events in the world. Concepts in language can also correspond to events in the world, but the problem is that the set of concepts in language is limited, so its correspondence with the set of numbers can obviously only be partial.
With the development of computer science, human beings need to process language into numbers. Because computers can only recognize digital signals, the digitalization of language has become the fastest-growing and most innovative field since computers came into being. Many China scientists have become top experts in this field, such as Kai-Fu Lee and Dr. Wu Jun, who are outstanding scientists. At this point, I feel that in the computer-dominated world, informatization is digitization, and the most difficult and successful digitization is the digitization of human natural language, because almost 100% of human information is carried and spread by language. If a computer wants to talk to people and become an intelligent machine, the first thing to be solved is the digitalization of language. However, when we freely input words on the computer, or talk with a mobile phone, we don't realize that those outstanding linguists have already converted our language into digital signals, and through input, processing and decoding, we can communicate and work without obstacles.
I seem to think that the relationship between language and numbers is the interface between man and nature. Apply the Pythagorean school of ancient Greece, plus my understanding, that is, number is the source of everything and language is the source of mankind!
Dr Wu Jun seems to be improving my understanding of the method. The way of thinking in scientific research is used to following essential, regular and continuous thinking. In the early days of linguistic research, in order to make computers recognize languages, human beings adopted the method of establishing language rules and language rules database, but both ended in failure (1950s-1970s). Since 1970s, scientists have adopted the language statistical model, and the research has made rapid progress. The victory of the language statistical model once again proves the belief of the quantum model of the universe, that is, the world is composed of discontinuous random particles, and the language system evolved by thousands of years of human civilization is a dynamic random probability event. Secondly, physical thinking has been unable to escape Newton's classic essential thinking method, that is, to find the law of 100% certainty, while information theory thinking is to study how to grasp uncertain phenomena, and using probability statistics is the only way. Third, language is essentially information dissemination. Only from the perspective of communication model can we truly understand the functions of computers. The encoding, processing, transmission and decoding of language are the strengths of computers, and computers can never understand the meaning of language.
In The Beauty of Mathematics, Dr. Wu Jun tells the experiences and anecdotes of his teachers, other disciples and colleagues, which let us know the quality of life, distinctive personality, scientific literacy and management style of these world-class scholars and technical elites. For example, Jarinik's harsh elimination of doctoral students and Marcus's generosity to students, but I feel that they have one thing in common, that is, their recognition and admiration for scientific creation, top talents, and even unconditional tolerance. Such a realm of human nature is fundamental, because great scientific creations are made by people after all, and only under the lofty humanistic spirit can top talents and first-class science and technology be created.
Looking at the domestic academic circles, the prevailing official style, corruption and human feelings are far from these first-class academic groups' appreciation of scientific creation, tolerance of personal talents and enthusiasm for scientific exploration.
It seems that we can only hope for the younger generation. I hope that the beauty of Dr. Wu's mathematics can give our students a preliminary understanding of the outstanding talents and feelings of scientific elites.