The number of gold coins borrowed from him on 15 is: 1(20), 2(2 1), 4 (22), 8 (23), 16 (24), 32 (25), 64. 16384(2 15) In this way, the gold coins borrowed by Afan are:1+2+4+8+8222+16384 = 32767 (pieces). The gold coins that should be returned to him within 15 days are:1000×15 =15000 (pieces). According to this calculation, the usurer also lost 17767 gold coins.
After reading this story, I began to associate mathematics with my daily life. One morning, my mother kept busy: making tea for my father for 5 minutes, boiling water for 3 minutes, washing vegetables 1 minute, taking dry powder and ingredients 1 minute, frying eggs for 3 minutes, and boiling dry powder 15 minutes. How much time did mom spend in the morning? First of all, we can make good use of time by connecting with real life. When boiling water, you can wash vegetables, get dry powder and ingredients, and help dad make tea and fry eggs when boiling dry powder. Then only 15+3= 18 (minutes) was used. I told my mother this idea, and she said, actually, it won't be so clever. There must be some errors, but the algorithm is correct. It seems that we must apply what we have learned in order to make mathematics serve our lives better.
Mathematics is like a mountain peak, soaring into the sky. I felt relaxed at first, but the higher I climbed, the steeper the peak became, which made people feel scared. At this time, only those who really like mathematics will have the courage to continue climbing. Therefore, people who stand at the peak of mathematics all like mathematics from the heart. Remember, people standing at the foot of the peak can't see the summit.
The second type
Mathematics, as a science that studies the quantitative relations and spatial forms in the real world, has always been closely related to the actual needs of people's lives in its long history of emergence and development. Mathematical modeling, as the first step to solve practical problems by mathematical methods, naturally has a long history as mathematics. Euclidean geometry founded more than two thousand years ago and Newton's law of universal gravitation discovered in17th century are all successful examples of mathematical modeling in the history of scientific development.
Talking about mathematical modeling from my own experience, I think the closer I get to it, the easier I will be attracted to it. Taking part in the competition, although very tired, in a short time, we got much more than we paid, which made us feel extremely satisfied and fulfilled. Speaking of winning the prize, I think there are mainly the following aspects:
First of all, prepare before the game. Everything is established in advance, and it's useless not to plan, so a good start is very important.
I would like to thank the school and brothers and sisters for holding pre-competition training courses every year before the competition, introducing experience to more students and explaining the basic ideas and common models of mathematical modeling. We all have the basic knowledge of mathematics, but it is impossible to write a good paper without a few models in our minds to solve problems with the idea of models.
With a good environment, reference books are more important. No matter how useful our brains are, we can't remember so many formulas and models. It is necessary to prepare several good reference books. Before the competition, learn as many outstanding papers that won prizes in the past as possible, summarize the algorithms and models used in the papers, and see if there are any ready-made examples to use after the competition. Previous test questions and papers were downloaded from the Digital Model Forum.
Secondly, make more use of the Internet. Because the modeling competition is semi-closed, we should use the network to consult documents and exchange information as much as possible during the competition, such as the school's electronic library, QQ group, forum and so on. In the process of communicating and discussing with others, a casual sentence from others may make you have a whim and produce some new ideas. Of course, sharing doesn't mean sharing everything, ideas can be exchanged, and sometimes conclusions can be compared with each other, but the specific process should be kept secret, but don't be too conservative. After all, communication is mutual, and you should believe that your efforts will be rewarded.
Third, the mentality in the game. The network will provide us with information, but it will also bring us pressure. As far as we are concerned, when we learned that the conclusion of others' first question in this competition was far from ours, we were nervous for a while, because the competition time was over half, but we still failed to solve the first question and fell far behind others. At this time, tell yourself that the most important thing now is to solve the problem, do your own problems in a down-to-earth manner, and don't compare with time, let alone with other teams. After cooling down, we finally got a better solution than other groups.
Fourth, the division of labor among players. A team of three people doesn't need everyone to be a master, but they must have their own strengths. Our division of labor is a debugging program, a main attack algorithm and a special preparation. However, the division of labor is not separate, so we must cooperate with each other, discuss and discuss more, so that the competition can be carried out in a compact and harmonious atmosphere.
Finally, briefly talk about the writing of the paper, so I won't go into details here. First of all, the paper must be organized, clear and concise, otherwise the content is no matter how good, and no judges like to review it; Secondly, because this is a mathematical modeling competition, it is logical, and the proof of definitions, theorems and propositions, the derivation of formulas and the recursion of algorithms must be well founded; Then there must be a mathematical model in the paper, and abstracting the actual problem into a model is the first and most important step in modeling; Don't give up every solution in the competition easily (unless the solution is completely wrong). It is necessary to write it in the paper, either as a model hypothesis or as an algorithm demonstration, at least let the teachers know that you think so. Maybe it's also a good solution, but it didn't come to the end.
Mathematics is a profound subject. Mathematical modeling has narrowed the distance between us and mathematics, brought mathematics into our study and life, and made everything simpler and more interesting.
Third, I love math.
Mathematics is always so wonderful, so magical, it is like my good friend, which makes me get a lot of happiness in my study.
Tonight, my mother and I compete to do oral arithmetic. After I finished, it took me 1 1 minute, while my mother only took 9 minutes. I asked my mother curiously, "How do you count so fast?" Mom said, "I use multiplication and division for simple operations." After my mother taught me this method, I suddenly realized that some calculation problems are like the face-changing of traditional Chinese opera. They always appear as ordinary faces, but there are hidden mysteries in their hearts. Take 450 ÷25 as an example! We should use 450× 4 = 1800 first, then 25× 4 = 100, and finally1800 ÷100 =18. In division, divisor and divisor expand or contract the same coset at the same time. Using this property, many such calculation problems can be simplified. I'm really glad to try to do more correct questions.
As long as you understand the laws of mathematics and master its temper, you will be handy when doing problems.
The fourth kind
I have studied mathematics for more than 20 years. I have never been afraid of math exams from primary school to middle school to college for so many years, but I still remember one time, which was the most stressful time for me for so many years. It was in the examination room of advanced mathematics for graduate students. The envelope containing the advanced mathematics test paper was cut from the tail at the beginning of the exam (cut from the seal, otherwise the test paper could not be stitched after the exam), and then the heartbeat was abnormally accelerated. What should I do? My first thought is to ask the invigilator. I asked him many times, and he only replied: You do your problem! This answer makes me more nervous. If the test paper can't be sewn in an envelope after the exam, then my subject will be invalid! What should we do? How can I calm myself down and at least continue this exam? I suddenly remembered what the junior high school math teacher said to me: For you, no matter what kind of math examination room you are in, as long as you do what you can, you can get high marks! After thinking about this sentence several times, I feel a little relaxed, but I am still very nervous. I gritted my teeth, buried my head and began to do the problem. When the scores are checked next year, the advanced mathematics test paper will not be invalid. 150 I took the test 143.
In hindsight, mathematics has never let me down after more than 20 years of study. Every exam adds weight to my total score. Every time I go to the examination room, I feel as calm as if I want to play a game. Why? Do you have a talent for mathematics or a high IQ? Are you lucky or good at the exam? Is it family reasons or strict teachers? Neither. Let me sum up myself and talk about how I studied mathematics when I was a student.
First, I have never been afraid of math. I read all the difficult and long questions. In fact, after reading it, I found that most of the questions were nonsense and there was not much useful information. Many problems are related to hot events, so changing clothes scares many people! Fortunately, I know it well.
Second, the probability that I can get the question right is over 95%. In other words, as long as you can do the problem, you must do it right, keep the score firmly in your pocket, and then solve the next problem. In the examination room, we should grasp the time and improve the efficiency of marking.
Thirdly, I like reading textbooks, even the words on the preface and cover. Especially reading textbooks before class can keep up with the rhythm of the teacher's class. This habit is something I have always adhered to.
Fourth, I like talking very much. Because of speaking well, teachers often let themselves explain math problems to everyone in class, and students often applaud their wonderful explanations, which is a virtuous circle.
Fifth, I do math problems very much like doing English problems. I read "translate" a sentence, think about what conclusion this sentence can draw, or what formula may be used, and then look at the conclusion I need or want to prove after mining the stem information. I often find that the stem analysis in front of me makes you feel natural when answering your demands.
Sixth, I like math, which has a lot to do with my math teacher. I feel that from primary school to university, most teachers who teach mathematics are very responsible, which directly affects whether I follow the teacher's rhythm to learn mathematics. First of all, I have to "like" my math teacher, so that I can accept his teaching methods, study math with him in class and dare to ask him questions.
Seventh, there are many ways to solve mathematical problems, and I have mastered one of them and mastered it. Like solid geometry, every time I encounter this kind of problem, I will set up a coordinate system and use vectors to solve it. I am very skilled and seldom make mistakes. Like multiple-choice questions, if the positive solution is a bit troublesome, I will immediately use the elimination method and substitute special values. , quickly get multiple-choice questions.
……
There are many ways to learn mathematics, but all of them must have the determination to accumulate and persevere. No matter what grade you belong to, first look at yourself objectively, make a study plan that suits you, and do all the questions that you can do right step by step, and at least get 90 points or more. Many students feel that they know nothing. They usually fail the math simulation exam and are afraid of math. I think you can talk to the math teacher. Maybe you can't keep up with the teacher's class rhythm, and it's a waste of time! Instead of this, it is better to make your own plan, focus on reviewing what you don't know, or even start learning from the content of the compulsory math course 1 chapter 1 and learn by yourself again. Little by little progress can bring self-confidence, and math scores will rise with the accumulation of math knowledge.
Cheer yourself up! Mathematics is not difficult as long as you have confidence and determination! One step at a time, when the snow in winter falls and melts into water to welcome the sunshine in early spring, you can look back and see that you have made progress. Bless you!
Fifth middle school
Many students always have a little fear of mathematics, and they have a sense of admiration for those who learn mathematics well. I always have a little lack of confidence in math. I'm glad to get the new textbook and turn it over. Fortunately, there are not many mathematical formulas. If I get a book with many mathematical formulas in the middle, I will be depressed and even want to avoid it.
No one is a math major. Why do you have to talk about the re-understanding of mathematics and repeatedly emphasize the need to learn mathematics well?
How to improve mathematics literacy? I think, as a modern college student, mathematics is inevitable. Hua said in the 1950s: "The universe is big, the particles are tiny, the speed of light and arrows is mysterious, the daily life is complicated, and mathematics is everywhere". In today's information age, it can be said that there is extremely abstract mathematics behind every high technology, and high technology is essentially mathematical technology. We want to make a difference. In order to achieve excellent results, we need necessary mathematical knowledge, better mathematical literacy and higher mathematical thinking. Please note that I use three different attributes here, and the requirements are gradually rising. Besides, you are no longer a middle school student, and your parents are not going to send you to school. You have entered a period of understanding in your life, and your self-awareness of understanding is rising. Some students are even eager for scientific research, creation and innovation, which is very good. What we learn from classes and books can only be knowledge, not foreign information. What people need to develop and build is their own consciousness and understanding. Of course, knowledge can also promote the rapid improvement of consciousness and understanding. In this spring season of life, I will review mathematics with you as a whole and have a bird's eye view. I believe it will be of great benefit to you.
First, look at mathematics from the relationship between mathematics and other disciplines
Let's discuss this problem from outside mathematics.
1, mathematics is a language, which is used in science. Without mathematical language, the universe can't be described, so it will never be understood. Any science can become a science only by using mathematics, otherwise it is imperfect and immature. The society is progressing, and its degree of mathematicization is constantly improving. Mathematical language has become an important means for human society to communicate and store information. The universe and human society is a big book written in mathematical language.
Bacon said: "Mathematics is the key to science". Ignoring mathematics will certainly hurt all knowledge, because people who ignore mathematics can't understand any other science, even anything else in the world. For thousands of years, all meaningful scientific theories and practical achievements, without exception, depend on the power of mathematics. For example, without calculus, there would be no mechanics and modern science and technology, and without Maxwell's equation, there would be no radio wave theory. Roentgen became the first Nobel Prize winner to discover X-rays with 190 1. The reporter asked him what he needed, and he replied, "The first is mathematics, the second is mathematics, and the third is mathematics."
3. Mathematics is a tool, a thinking tool. Natural philosophy holds that everything is the unity of quantity and quality, and mathematics is the science of studying quantity. It constantly discovers, summarizes and accumulates many human laws about quantity, and is a powerful tool for people to know the world. Here are two examples: one is natural science and the other is social science. We are trying to find an organ that can be accurately located in the human body without surgery.