Technical books and Mathematics Education

Author: Meng Yan

From: http://blog.csdn.net/myan/archive/2006/02/24/608422.aspx

When I go home during the Spring Festival, I will naturally have to attend a gathering of old students. When the old students get together, they will naturally have to compare and reflect on their respective life paths. This kind of comparison and reflection, especially when high school students meet. In those years, I had a hard time reading from the same window, and there was not much mutual communication between them. I still remember that when I filled in my volunteer information before the college entrance examination, a group of Children Aged seventeen or eight talked about the huge impact this incident may have on their own life. When the pen and ink are not lost, the infinite possibilities of the whole life are still in front of everyone. After the pen and ink are fixed, most possibilities will disappear. This was not until more than a decade later that we gradually realized it. So this year's reunion became a hot topic for discussion: What kind of major would you choose if God gave you a chance to come back?

I have an answer to this question for a long time. Because of a small misunderstanding, I gave up a valuable opportunity to study at a top Chinese University in applied mathematics, which became a lingering knot. Therefore, my answer is simple. I can select another one and read mathematics. What I did not expect was that my answer received the response and approval from many old people. Many people have responded that the deeper they are at work, the more they feel the resistance and troubles brought to themselves by the weak mathematical foundation. The more they feel the importance of mathematics. However, when I was in the same class in college, a classmate jumped out to question me. Based on his precise memory, he revealed that my mathematics class in college was not serious. "If you don't even take those math classes seriously in college, why do we believe that you will do well as a mathematics student ?"

This is a fatal impression. I have to admit that I didn't fully understand the importance of a series of basic courses, including mathematics and algorithm analysis. Not only did I not understand it when I was a student, but I also did not know it when I started to work on software development. This is because I have almost never encountered a time in my life or work that is associated with the profound mathematical formulas in textbooks. I can't even imagine a four-dimensional space. Why do I need to care about the law in a multidimensional space? When we really need to use relevant algorithms, a large number of off-the-shelf libraries and tool books should be enjoyed by me. Why should we be so ourselves? For such a precious period of time, I was not sure about the importance of mathematics. In addition, I did not recognize the importance of mathematics education in college. Therefore, I did not seriously study mathematics that year. Maybe my classmate is right. Even if I went to study mathematics, I would not be a good student. In the case of unclear motives, I can't do it.

The gradual understanding of the importance of mathematics comes from practical work practices. When developing mobile device software, you need to develop basic algorithms by yourself because of the lack of ready-made toolkit and graphics-related programs. At this time, my weaknesses in mathematics were fully exposed and I felt the pressure from practice for the first time. Later, I began to do some research work. Through some practices, I realized that mathematics is both the foundation and the commanding heights in modern technology-related work.

I know that there are still a lot of disputes over the importance of mathematics among millions of college students and young technicians in China, especially software development technicians. I am afraid that many people, like me in the past, lack of understanding about the importance of mathematics, as well as motivation and enthusiasm for learning mathematics, have missed the precious opportunity to lay a good foundation, waiting for the boss to be sad.

Of course, I think the main responsibility for this situation is undoubtedly the current education method, including the mainstream mathematics textbooks. However, to truly change our education, after all, there is still a long way to go. Before that, we still have a lot of useful work to do. For example, starting with some practical technical books and combining specific applications in these books, I think it may be a good way to improve the quality of mathematics for readers.

This is very beneficial. The first is to fully motivate readers. When reading practical technical books, readers are more enthusiastic and active than reading pure theoretical books. The content in the books on application technologies is practical and clear, and readers are usually more active. If the author is good at mobilizing the reader's enthusiasm for knowledge and using this positive State to introduce the corresponding basic mathematical knowledge, on the one hand, it can help the reader better understand the application technology itself, on the other hand, it can help readers understand the power of mathematics and improve their mathematical level.

Secondly, it conforms to the cognitive pattern from concrete to abstract, and the pattern of true knowledge in practice. We do not deny that there are some natural mathematical talents who can swim in the big section and fully abstract mathematical arguments without getting angry or changing colors. But for more people, it is at least not easy to grasp modern mathematical knowledge from real-world experience. However, this does not mean that these "ordinary" people cannot master mathematics, they cannot use good mathematics-they only need to be guided in a step-by-step and "normal" manner that is more in line with their cognitive habits, from concrete to abstract. Generally, mathematical textbooks written by professional mathematicians tend to be in a self-intoxicated manner, which is difficult for ordinary readers to keep up with and thus to learn. Many people who could have mastered mathematics are swallowed up. However, when this kind of high pure mathematical writing method was questioned, mathematicians were always busy declaring the independence, abstraction, and high position of mathematics, defending them, it seems that this kind of rejection style is necessary to maintain the holy position of mathematics thousands of miles away. We imagine that if the Grouch family is not centered on teaching students, but the truth of combat is used to beat the students, even if the students are mathematical geniuses, it will surely feel angry with your nose face. Many mathematical talents refuse to take readers as the center, reject the obligation to educate readers, and honor such rejection. Isn't it strange? Note: Mathematics may be the only holy thing in the universe, but for the textbook authors, the interests of the readers are at least equally sacred. At this point, the authors of technical books generally perform better. This may also be because they are closer to ordinary people than mathematical talents. Therefore, mathematics in technical books, if well spoken, may help readers learn mathematics more than mathematics textbooks, and even guide readers to understand the harmony and power of mathematics, and then interest, become a technical expert in mastering modern mathematical tools. From this point of view, if the author of an Application Technology book can write the mathematical content, it may be very good.

However, this is a kind of expectation after all. The reality is that most technical books can either avoid mathematics, or develop their own style, from the books of mathematical talents, Tian Ma xingkong is further abstracted, streamlined, and summed up more cloud-based things to be perfunctory. See the "Appendix" below many technical books. The authors also have a reason. After all, the focus of the application technology books is not here. Extracting some mathematical content is better than nothing. It has already broken this point. Readers should be satisfied and whether they can really understand it, it depends on creation.

Of course, after all, there are only a few of them. Therefore, the poor readers have to continue to become mathematical illiterate in the ways of pushing and pushing talents.

Maybe the authors of technical books should take the initiative to assume the responsibility of some mathematics education. It is not only a major improvement in the quality of books, but also a good thing for readers. The author's contribution to readers beyond each share will receive a double response from readers.

I recently read a book that provides a good example in this regard. Computer Graphics-detailed explanation of geometric algorithm tools translated and published by the Electronic Industry Publishing House itself is positioned as a "algorithm prescription" tool book. As long as the algorithm objectives and program code are listed, the score is completed. However, the author believes that it is not enough to provide readers with a dozen pieces of code for plagiarism, but also to help them fully understand these algorithms. This goal can be achieved only by allowing readers to have a solid grasp of the necessary mathematical knowledge. Therefore, the book uses five chapters, two directories, and nearly 1/4 of the length to fully describe the basic mathematical knowledge related to the book, which covers ry, linear algebra, numerical computation, and other fields, it is concise, accurate, and appropriate in depth. It fully integrates the application knowledge related to computer graphics, which not only provides a solid basic mathematical knowledge for readers to understand related algorithms, in turn, this helps readers better understand the relevant mathematical basics. As a result, although this book was not famous after its publication, it soon became a secret weapon of some professional graphic developers. Some graphic technology development companies even bought it collectively, with one hand.

Now I often think that I am a common person in the final analysis. Even if I went to the mathematics Major that year, I may not be able to become a positive result. On the other hand, if I have been diligent in reading those technical books, I can write some mathematics carefully. I may have been interested in it for a long time, in this way, you can learn mathematics quite well.

----------------------- Related comments --------------------------------

In fact, it is just a special case in mathematics.
The status quo in China is not conducive to people's personal pursuit. Some people have never established their own pursuits since childhood and follow the path chosen by their parents blindly.
The most common ideal for Chinese students in their compositions is "to be a scientist". Chinese children do not know whether they want to be a scientist, whether they want to be a scientist, or whether they want to be a scientist.
Will be praised by the teacher.
Even if some people set their own pursuits and goals, we are sorry to see how many people are forced to make a living when they grow up, due to secular vision, I gave up my pursuit.
The reality is cruel. How many people can endure poverty, be willing to be alone, and devote themselves to research on basic science without short-term benefits?
In a country, the culture of a nation tends to be impetuous "market economy". The weakness of basic scientific research is not just a matter of course.

 

Why are chinese people smarter than Americans (which has been demonstrated in many places and not cited here), but far worse in scientific achievement than Americans? I think this is the case. In fact, the scientific achievements of the United States are closely related to practice. Technology is more dependent on practice. For example, Microsoft's top windows experts, even though they were not cainiao before they started working on windows, I believe they will not be better than China's. However, after so many failures, people finally succeeded. Their strength actually went up. We don't have such a practice here, so we can't catch up with it any more. The disconnection between theory and practice on the Chinese side is an important reason for limiting the level and achievement. So the first thing we need to do is focus and focus for a long time. You don't have to think about playing with an operating system today, having another compiler in a few months, and having another DBMS in a few months. Then, even if you are a good guy, you just make toys. But here we are keen on making small toys. Do we want to know if there are too many talented people?
So your learning should also focus on practice. Not only because of limited time and energy. This is also because learning can be learned through practice. The most taboo thing is to look at mathematics today. It's good. It's good if you have learned it. (It's hard if you have learned it.) Tomorrow, it's good to look at physics. The day after tomorrow, life Sciences cannot be pulled down. Take it easy, boss.
The second question I want to talk about is the division of labor. Everyone is proficient in one item and is a strong team. But there are a lot of people here who want to solve all the problems on their own. The results do not work well. Everyone is doing this, and it is also a bunch of cainiao.

 

The gap between China and the US in Computer Level actually comes from culture. If we don't even know the history of the computers we use today (Note: personal computers), then everything will be too impetuous ~