This article is Academician Li Daqian speech at the School of Mathematical Sciences, Fudan University freshmen orientation Congress.
For most people, life is a middle school math most of a course: from primary to secondary school, from school to university, including graduate students to the learning phase, are learning math. Why should we spend so much time to learn math? Why we must strive to learn math it?
If you think just to implement the provisions of this learning and school teachers, just to cope with the exam and get a good result, but fared a diploma in order to come to a high-paying job, or simply to be more or less mastered Some related mathematical knowledge, even if it entered the School of mathematical sciences, will certainly take a passive attitude towards mathematics and cope with learning, learning effect is bound to be greatly affected. Therefore, this seems very trivial problem is very serious and think we deserve.
01 mathematical influence and role can be said to be ubiquitous
To find out how to learn mathematics, first to recognize the importance of the discipline of mathematics itself .
The world's number and shape everything has two sides as the study of mathematics in the real world and the relationship between the number of spatial form of science, is the exclusion of other specific properties of the material, just from the number and shape of view to study the whole world. The role and status of mathematics, it seems, can be summed up in the following few:
1. Mathematics is a kind of evergreen knowledge
As a primary school, secondary school to university compulsory course important, mathematics is essential to human knowledge, no one will doubt it. Many human discoveries like solo, from many disciplines to overthrow the previous conclusions and establish a new theory; however, the development of mathematics through the ages, not to destroy the descendants of previous results, but each generation of mathematicians in the original there are buildings on the base, then add a layer of new buildings. Thus, the mathematical conclusions tend to have eternal significance .
Euclid is two thousand years ago the ancient Greek mathematician, however, named after him Euclidean geometry are still playing an important role, in which the Pythagorean theorem, not only are not considered old out teeth and dismissive, the opposite is also known as the first theorem through the ages, has been highly praise, repeated application, it fully illustrates this point.
2. Mathematics is a language of science
Galileo once said: " Nature is a book written in the language of mathematics ...... unless you first learn to understand its language, ...... Otherwise, the book is unreadable.. " This scientific mathematical language It is very accurate, which is characteristic of a mathematical discipline.
At the same time, this language is world-wide. Subtraction, multiplication and division, power prescribing, index number, differential and integral, constant and so on, these mathematical language and symbols beginning although it may be varied, each has its advantages, but it has long been unified into a fixed pattern, common around the world, the mastery of our and it is very easy to use.
3. Mathematics is a powerful tool
Mathematics plays in people's daily life and production anytime an important role, is already obvious to all. In modern mathematics as an important weapon modernization, in many important areas more play a critical, even decisive role. Outstanding achievements of our country in the development of bombs and one satellite, the combination of a number of outstanding mathematicians of effort, is a prominent example.
4. Mathematics is a common ground
Now, not only in the natural sciences, technical sciences, but also in economic science, management science, even humanities, social sciences, in order to accurately and quantitatively consider the issue, get well-founded understanding of the laws of mathematics have become necessary an important foundation .
Left support mathematics, science-related considerable progress has been difficult to obtain, many disciplines (especially a lot of the natural sciences) even in recent years there have been trends of mathematics.
The mathematics is an important scientific
Ignoring the specific mathematical morphology and properties of matter, from a purely quantitative relations and spatial forms of view to study the real world, and it is similar philosophy, transcendent subject-specific, universally applicable characteristics, meaning all disciplines have instructive. Mathematical Sciences now has constituted a huge scientific system including pure mathematics and applied mathematics containing many branches and many emerging cross-disciplinary.
We do not think that we have learned mathematics, including mathematics already know, it is all mathematics. In fact, high school learning of mathematics, generally fall into the category of elementary mathematics and higher mathematics undergraduate learned, based on Newton, Leibniz in the seventeenth century marked by the creation of calculus and start, and it has It has been 300 years of history. Mathematics than we have seen to be colorful, to say the profound meaning of mathematics, is not too much of.
However, the more the development of mathematics, not to make things more complicated, on the contrary, deal with the problem will become more simple, people understand the world and transform the world and more and more capacity to expand, the more we learn the more you will feel mathematics charm, Yuxiang learn more science.
Past the sixth grade math class, "chicken rabbit with cage," is a top problem, saying that some of the chickens and rabbits in a cage, for example that the number of known head = 10, = 28 the number of full, ask chicken how many? How many rabbits? Because only chicken feet, while the rabbit has four legs, the problem is complicated, and requires arithmetic lesson step is to write the answer, the more difficult it is. But secondary school algebra, as long as the chicken is located only x, y is the only rabbit, a list of simultaneous equations, all of a sudden you can obtain answers to questions of meaning of the questions, how easy ah!
School plane geometry in high school, in order to prove to rack their brains to draw auxiliary lines, it is a major challenge and a test of intelligence, but learned analytic geometry, algebra and geometry will combine the past struggle to solve the problem of geometry all of a sudden a breeze.
I was in high school, how to find the center of gravity of semi mathematically became interested in this problem once, and for this spent a lot of spare time, the results came back with nothing. Later, listening to the teacher said that this issue can be resolved only with calculus, before we know the world is there such a calculus of infinite power of knowledge, but also inspired me to learn more and more mathematical curiosity and motivation. Really good mathematics, is more and more deep, more concise, more useful.
6. Mathematics is a key technology
Past a pen and piece of paper can get the math, could become a technology, it seems incredible. However, the combination of computing technology and methods of mathematical thinking and highly developed technology has indeed formed, and is a key technology that can be achieved, known as the "mathematical techniques." In this technique, since the central role of mathematics in part , it took only a pile of metal scraps.
We have seen in the hospital this advanced technology is an outstanding example of CT. Its essence, is the use of a number of plane X ray photographs taken from different angles, and restore the object in the body (e.g., tumors) three-dimensional shape, a mathematical problem entirely. Thus, the mathematical connotation materialized as computer software and hardware, has become an important part of technology and key, which can be directly translated into productivity. Now, " the high-tech nature is a mathematical technique " argument has been recognized as more and more people.
7. Mathematics is an advanced culture
Mathematics is an important foundation of human civilization. It is accompanied by the emergence and development process of human civilization, and which has played an important role, plays a decisive role. Due to the time, to name just below this count the carry a simple example will be described.
As we all know, math starts to count. 1 can only distinguish primitive and more, hit 3 felt more, three for the "public" probably comes out of this. After that came decimal, 8, 9 and 0 with these ten numbers, plus every decade a (and a decimal point), you can represent any one of the world digital. This is now aware of the fact that people from an early age, it seems only right and proper.
However, this has gone through a long historical process, is an indelible tremendous contribution to the mathematics of human civilization brings. Without it, slightly larger numbers people would be confused and disoriented, not to mention the huge astronomical or extremely small numbers, and now the financial industry or scientific experiments in a variety of complex or high-precision mathematical operations simply can not be we can have such a highly developed civilized society?
Such examples can be cited a lot, but it was enough to see from this example: mathematics was, is and will also be an advanced culture, and it led, promote, influence the course of human civilization, profoundly changing the face of the world, but also changed the thinking ability and level of understanding of humanity itself, changing people themselves. Human fully enjoy the bounty of mathematical culture, but often unaware, for granted, "the body in the fortunate."
The ancients said: "The day is not born Zhong Ni, such as vancomycin long night." Think about it, if there is no math, no progress in mathematics, people may also live in ignorance, lived a "long night as" life, we have no reason not to pay attention to math, do not attach importance to lead and nurtured culture of mathematics role in it?
In summary, for a long time, in the process of awareness and transform the world of mathematics as a precise language and a powerful tool, it has been playing a pivotal role.
Especially in contemporary mathematics as an important weapon of economic construction, as an important basis for the sciences, as an important pillar of human civilization, in many areas has played a critical, even decisive role in mathematical techniques has become a prominent symbol of high technology and an integral part of mathematics influence and role can be said to be everywhere, as its importance has been recognized by more and more people. Thus, not only in primary and secondary schools, and in many university faculties, the mathematics are among the most important required course, it is a matter of course.
02 mathematics education seems only a knowledge of education, but a quality education on nature
On the other hand, to find out why learning good at math, but also to learn mathematical knowledge of a person cultivation and growth of an important role .
Since mathematics is so important, then, to learn mathematics only purpose is to get a lot of theorems, formulas and conclusions, to understand a wide variety of mathematical methods and means will have to solve a variety of puzzles and even exercise it? no! ! !
If mathematics learning as merely accepting a lot of mathematical knowledge, even if memorize more of the theorems and formulas, may still inevitably reduced to a pile of dead dogma, it is difficult to play a role. If the quality of mathematics learning merely as "brush title" The number and speed, it can at best become a skilled craftsman mathematics.
Mathematics is a heavy thinking and understanding, strict weight training, full of scientific creativity, only to master the thinking and spirit of mathematics to deduce the ever-changing vivid conclusion by the few formulas, showing endless power.
Many of us in practical work successfully applied mathematics, has made quite outstanding achievements of alumni have such an experience: the specific branch of mathematics in the work really need to use a specific mathematical theorems, formulas and conclusions, is not necessarily lot; school learned a lot of mathematical knowledge many of them did not seem to come in useful, and some even may have forgotten, but they suffered mathematical training, the understanding of mathematical ideas and spirit, obtained mathematics education, but all the time to play an active role as the most important factor for success . I think it is very worthwhile cause everyone's attention to the voice of experience.
In fact, through careful and rigorous mathematical study of mathematical training, so that students can have some unique qualities and abilities. These qualities and abilities are irreplaceable study and practice of other courses and other areas or difficult to achieve, and even mathematical knowledge learned has been forgotten (which is often the case!), These qualities and abilities as a person mathematics education still does not disappear, will last a lifetime, has always played an active role. These qualities and abilities such as saying there:
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The number of concepts conscious. People will pay careful attention to the number of aspects of its variation of things, rather than "chest countless" seat of your pants, "racking our brains" to make decisions, do things.
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Strict logical thinking ability. People can keep clear, coherent, orderly manner to deal with the work of numerous clue.
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Highly abstract thinking ability. People face complex phenomenon, to prioritize, to seize the main contradiction in nature, highlighting things, step by step, to effectively solve the problem, but will not know what to do, do nothing, or eyebrows, beard grabbed.
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Mathematical derivation of requirements for each sign, each a decimal point can not be vague and perfunctory, help cultivate careful, meticulous style and habits .
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The pursuit of mathematics is the most useful (wide) of the conclusion, at least the conditions (costs) as well as the most concise prove, through rigorous mathematical training, will gradually excellence, and strive to perfect the habits and style .
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Focus on the ins and outs of mathematics, known mathematical concepts, methods and processes and the origin and development of the theory, will improve the mathematical model, the use of mathematical knowledge processing consciousness, faith and the ability to complex problems in the real world .
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As gymnastics and competitions, mathematics will make people an idea of enhancing the resilience and fighting spirit, through continuous analysis of contradictions, figure things out from a difficult situation, and ultimately solve the problem .
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Mathematics learning and thinking, will be open to students in the vast world of freedom to create , stimulate their spirit of exploration, innovation consciousness and ability to innovate, to make them more flexible and proactive, intelligence and play a full performance, and so on.
Thus, mathematics education seems only a knowledge of education, but a quality education in nature.
This quality education is not imposed from the outside coming in, but inherent in mathematics education. To teach and learn mathematics as the carrier, through scrupulous mathematics learning and training, it is possible by the unconscious to the conscious of these aspects of quality and ability, monasteries, personally, engraved in the heart, a habit, and gradually transform itself into mathematics education.
Really learn the math, no matter what you do for your future in which industry will make people smarter, wiser, more competitive, lifelong ever been. For the majority of our students, their future will be the most memorable, mathematics learning place to bring them the greatest grace. Of course, if you do not learn math, or just so-so half-heartedly to learn some math, can not achieve this effect, this is "the mountain of empty back to" a.
Mentioned above can be applied on these principles to all high school students, even students, everyone is certainly no exception. Today, however, we came to the Fudan University's School of Mathematical Sciences, was about to begin a mathematical system for professional learning, mathematics, science halls are stepped, when becoming a new army of mathematics, your task should not be merely conventional sense under the study, but to travel to the beautiful yet profound realm of mathematics, taste and explore mathematical sciences essence and mystery, and whom contribute to the efforts .
At the same time, both the magical and practical ideas, tools and methods but also help membership mathematics, trying to reveal the secrets and laws of nature and human society, a better understanding and awareness of the world we live in , Furthermore the state and the nation, for the benefit of mankind.
Because of this, hope that the new school of Fudan University School of Mathematical Sciences students, beginning to establish a lofty ambition, there is a beautiful dream that mathematics as his life's work, determined to own cultivate and foster a future mathematician, mathematical development and progress for the development and progress of human society to make its own achievements and contributions, further add luster mathematics Fudan University.
This is a noble and lofty aspirations, but not an unattainable goal. We are pleased to see that this year's freshmen enrolled 121 people most of them are admitted to their first choice. Consciously chosen for their volunteer mathematics, shows that we love and the pursuit of mathematics. To become a mathematician, in this century elite Fudan nurturing and nurtured, took the professor Buchin, Professor Gu Chaohao the hands of the older generation of mathematicians baton, inherit and carry forward the culture of Mathematical Sciences, Fudan University School of outstanding mathematicians cradle the fine tradition of many students should be conscious pursuit of the heart, it is worth to give full encouragement and support.
You may also have a considerable number of students, although they are interested in mathematics, but also aware of the importance of mathematics, but hope to lay a foundation of mathematics, transferred to other industries in the future play a role. It should be said this is a good way to learn mathematics and motivation, many have a good mathematical foundation and training of graduates entering all walks of life, will not only change the face of these industries fundamentally, but also for the development of mathematics itself provides a good external environment and tremendous impetus, the same should be encouraged and supported .
However, in spite of all walks of life to enter the future, you and other people are not advantages compared to other places, and in your mathematical heritage; your future in the new environment can not stand, can only rely on you mathematical advantage, rather than the other! Your future focus should be on the junction of mathematics and other disciplines intersect and integration, which is now a strong proponent of the people of Industrial and Applied Mathematics. Your goal should also be to become a mathematician, but also industrial and applied mathematicians on a real sense.
In this regard, I would like to say a few words here female students. In recent years, School of Mathematical Sciences undergraduate and graduate female student had a very high percentage. This year the proportion of female undergraduates than in previous years, although a slight decrease, but also more than 18%, while the proportion of graduate women is nearly 34%. Most female students learning seriously, good results, some of which are very good, but sometimes somewhat not confident.
Female students in the end you can not become a mathematician? The answer is yes.
No lack of some of the most outstanding female mathematician in history. To illustrate this point, I would ask the teacher in charge of school work distributed to you a brochure edited by our mathematical culture in small series to be published by e-mail, entitled "break through the barriers of prejudice and secular - On Three eminent female mathematician. " The three women are the French mathematician Germain, Sofia Kovalevskaya of Russia and Germany Knott. In the era of women do not have their basic right to education subject, yet it made such an outstanding contribution, thereby leaving a legacy for the majority of our female students, should be a great incentive and an excellent role model, I hope you find time to read a good reading, think about it.
I believe that our female students will establish enough confidence, others can do, we have, through their own efforts and dedication, we can do it! The only female math Chinese Academy of Sciences Professor Hu Hesheng in our School of Mathematical Sciences, she has set an example for us, we should redouble our efforts.
In short, for all students, set a lofty goal, and strive to learn math, learn as much as possible was outstanding, not only at this stage of your learning requirements, but also a strategic investment for your future development is not good enough for a lifetime the best . School of Mathematical Sciences, Fudan we want not only become a veritable culture of male, female mathematician cradle, and the cradle of culture man worthy of the name, female industrial and applied mathematicians. I hope we work together, and strive to create atmosphere, contribute to this goal as soon as possible.
