Xu Xiaoyu, RDFZ school graduation. Senior High School physical training team into the league are first, followed by CMO gold, CPhO silver medal. 2014 iPhO first.
Physical training team on the last day, Xu Xiaoyu said, "leaving a person too, Yanguoliusheng" I learned so many years of competition, in terms of mentality, learning, examinations have some experience, if disappearing into memory, too some regret. Therefore, such a willingness to sort out their feelings and experiences, all heart and soul, hoping to help the majority of fellow race.
First, clear your heart, directed Conscience
Nor you can have is almost? What is called missing the original mind. - "Mencius on"
Thin a few years, the initial contact contest, third grade math is to enter Chinese schools, physically two days; and into the MO and PhO, it was all high school thing. Many people will have questions: learn so many years of competition, in the end why?
Tell the truth, elementary school when learning mathematics competition, say it points, out of ambition and self-esteem; it is the point of saying, is a good face, to hear people praise my heart happy, contented. Of course there are "interested." Attention, interest and contentment of the heart is completely consistent.
But in high school, especially after high school to enter the mind of course there is (are also called spots), but it is really more curiosity, and can be found in a number of fun competing in. I remember very clearly the first was last year's summer vacation, to attend national team training in Shanghai, there was a number of topics. There are two parameters m and k, so that you permit a conclusion. I spent an hour, has been facing m "hard", no gains; later had an idea, facing k "hard", suddenly solved. (Well, not just look like a joke original title) was particularly pleased in particular, there is a "People look for him thousands of Baidu, when I look back, that person is in, the lights dim" feeling. I think this is fun Mathematical Competition.
Of course, I studied physics competition have experienced such a process, to the sophomore summer, they began to slowly understand the physical pleasure. This is independent of the "original mind", it will be described later.
So now, I am in terms of competition, really do, "clear your heart, directed Conscience." Vanity, but more of a love for them (the reason why with love rather than love, because the two subjects with me more than I have "loved" person). I call this the favorite for the "original mind." Of course, mainly from vanity to the original mind-based, naturally have some ups and downs. Here are a few competing experience.
I start from primary school, has been the so-called lucky, all the way against the aura of "Beijing strongest current mathematics" (one), it has been to high school. Since junior high took the joint first-class, high moment full of confidence ready for the Beijing team in the CMO. Results Gaolian lost, 136 minutes, under first-class. After confirmed, there is a big problem I had proved to be right, but eat duck directly at me from the province played in the first-class. Heard the news, the complainant, to no avail, only to come to grief. Of course two or three times crying. The idea is obviously not my fault, but it takes my own bear bitter fruit. Wrong ah!
Yang Qi then is to find a teacher complained. Yang apparently twenty as good, first graders with me scolding meal, and then told me how he was wrongly year, "huge anger", the results he entered the provincial team, then stepped on his head several people have given up the race (with yellow skirt-like). Various enlighten. I think, ah, two of them apparently even worse than me, whatever the outcome, I have two years of it. Then the mood will gradually calm. Yang said, in fact, you think again, if you are strong enough strength, then even if one be mistaken, but also into the team, and that it was cattle. I think this makes sense, ah, I'm going to be much stronger next year than others, so that those false teachers even if I could stop me into the team. Then I said, in fact, I was very uncomfortable thing, that is, the students will obviously think my math is not the strongest, but some people say those words on barbed, I particularly uncomfortable. I also know that "go its own way, whatever others may say," but my level was not so high.
This is actually a very terrible thing, at least this is my own greatest weakness - the extreme self-confidence (or even own, then have to correct, but needs efforts) pride (vanity) strong. Easier said than done, I try to ignore some of the rhetoric has improved but there is still some more or less painful. Later, I comfort myself with a variety of classical, especially the "Hardships for the worst," "blessing in disguise", "non-success turned empty, still in the Castle, How Many Suns." Particularly useful.
Okay, he continued. Later, on the one hand to the above-mentioned "revenge", there is an arrogance, even if you want to misjudge the coming year but also into the team (my pride does this deep-rooted); on the other hand, problems do indeed gradually feel, and think about their own also long recognized why the school competition, it is not for others Olympiad. Then slowly bring something really negative on some. After including Romania Masters Cup unsuccessful for various reasons, failed to go into, not so painful. And this year, I feel mature a lot, a lot stronger.
And since November 2011, set a goal of their own, do every day at least one CMO true problem, insist on doing 12 sessions, feel the need to leave the title for the next year, he turned to do anything else. This year I feel really level has greatly improved. Sure enough, sophomore entered the provincial team in case of miscarriage of justice, but also took the gold medal.
Physical thing, too, took a high second-class, sophomore confidence, want to rush the provincial team, the results of the last relativity (really good question) calculated ε / μ was 2c (It is obvious that knowledge does not solid), I think there many steps are right, but for the three points, but also went into the provincial team. But this defense of my mind far more than a high, naturally not been defeated.
Having said that, I spoke mainly of a "break things" process. Truths will not say, we all experience it. One last word: do not be mistaken race career is incomplete. I hope this helps those students who had or still in the trough.
I want to say is lost from the high of the beginning, I personally feel that in an unprecedented walk downhill. But I think the real understanding of the spirit of mathematics is probably this period was in this period (I did not) really know what is to insist that there must be perseverance. Now I would like to thank a little larger than the two students, who in the course of my defeat, as they think, and I think they have the same withstood the blow of failure, only today's results, they urged me to continue go friend.
Second, the experience of learning mathematics competition
"To think."
- "Three bodies Ⅱ · Dark Forest"
I started when I was in junior high school curricular content is substantially complete, two days after the basic completion of high school curricular content. This varies, but certainly to completion as soon as possible as well. Following entered, is studying high school mathematics competition.
As we all know, MO four items, geometric algebraic number theory combination, "knowledge" is indeed more. Advice is to find a school class or race extracurricular training institutions, first race of the content over again, to reach the level of first-class high-linking. Then, is to move forward toward the CMO, CMO is the first hurdle in the true sense of the mathematics competition.
Let me talk about my experience. After three days in the exam, go to Shanghai Math Camp, knows his own talent and less learning. There even learn ten days, the feeling level rose.
A high, due to go to school, that is, the CMO Zhenti do half saw (did not do) four classic Orsay (best not to look at his portfolio and geometry). High School, into the team, the CMO true problem and some other problems MO difficult to do, and CMO. After CMO, made nearly six years of training team title, read "Mathematics Competition study course", then TST. TST after school honestly would be half a semester to go to Shanghai to attend national team training. Summer vacation and did a little single goblet teacher's booklet, as well as "inequality secret." Mainly to get physical.
After high school, during physical TST he has done it again CMO, TST, made some questions, then there is no then the. From high school to sophomore summer vacation, there are some seniors RDFZ give us lectures, feel benefited.
In short, I feel the math to see the book do not much (actually pitiful), but I feel they have a very, very big advantage is that I especially love to think and will think.
Thinking here do not refer to the title refers to the summary of the issues to do. I always like to finish after a good question, "strategically advantageous" to write reviews on a few tall, just started really bad, but there are slowly feeling can often grab the title contains the idea or tip the essence.
Zi said, "I tasted all day and thinking men, as a moment of what they have learned too." This of course makes sense, but some students are "Learning without thought is labor lost," do not do it a question, a look at the answer, "Oh, , so simple, and it would come out. " Then left, something else to question. Indeed exaggeration to say that, more often, read the answer, every step will be, just do not know how to think out the answer. In this way, the next question appears contains the same idea, still do not come out.
Every time I met did not do it, or make it feel extremely clever approach, will ask yourself the following questions: Why do think the answer? It is conditional or conclusions suggest that there is a well-known theorems, there is still a very natural eye problems I have not found? Why did not I think so? What should make the next think so? This question is inside, what skills worth learning? There is no more ideology behind this question of the nature? There is no higher in the background? Of course, it is not so much want to understand at all times, but once you think about it, there will be more profound understanding. (But do not "thought without learning is perilous.")
About recommended books, because the books I am really looking to do much, not a laughing stock. But I can give a list of previous CMO good question, of course, is my own summary, summary before the first CMO to participate as follows:
1, CMO 6-6 Football - tri-color silk - the number of vertices of discharge - is a product; analogous thereto have a triangulation type CMO5-6,3n side stroke. The key is to seize the staining characteristics, starting from the regularity staining itself. For example, the use of the color of nature with the assignment method. The other is CMO1-6, the key is to find a "better use" of existing conditions with conditions that weaken the conditions of the conversion type.
2, CMO 8-4, similar to CMO1-3, will move to the complex questions put. Die length to find the longest and complex, used to demonstrate the existence of configuration.
3, CMO 8-6, can not tell, on induction. There formally apply to the recursive nature of the subject.
4, CMO 9-3, range analysis function equation. "Amplifies the deviation."
5, CMO 9-4, using the configuration of the root. Analogy "divisible selector."
6, CMO 10-2, functional equations, the weight was observed.
7, CMO 12-5, is processing configuration FIG.
8, CMO 13-5, beautiful guides Ptolemy inequality
9, CMO 14-2, good question! We found proved by the induction attempt Equation 1, and then back to prove this equation. Back then I asked coefficient derivation relations, make full use of the previous conclusions. I was anxious, direct Kanji, is to find the law to do, not been able to find the essence of this question.
10, CMO 14-3, four exchange station group. The key is to understand "the main road." But it is to change a little out of the total number of degrees.
11, CMO 14-6, clever transformation.
12, CMO 15-6, capturing the essence. 5 is not critical, "up to three different is the" thought drawer. Of course, the back of the structure is also very clever.
13, CMO 17-2, iterative elimination "constant."
14, CMO 17.03
15, CMO 18-2, part of the argument, first find out the nature again and again, thinking and writing are good.
16, CMO 18-3, scaling techniques well. And good ideas: first place, part of the solution, while another part can go back and re-solve.
17, CMO 19-3, drawer principle point with parity; male, is covered with.
18, CMO 21-3, bear in mind that with this method. Contact: 4k 1 prime number can be expressed as x2 y2.
19, CMO 21-6, count combination, directly on the "global" counted twice, almost point; can start with good "integer" condition, "withheld" by little drawer principle.
20, CMO 22-3, wonderful! fantastic! Two odd number equal to equal launched even as the starting point, after the "slip off" wonders.
21, CMO, 24-6, constructive ideas, do first weaken the conclusion, step by step. My thought process is 2-1-3
22, CMO, 25-3, see below
23, CMO, 25-5, good question! Active segment drawer principle
24, CMO, 25-6, to take constructive large prime numbers; Fermat's Little Theorem Remainder Theorem
25, CMO, 26-2, geometry guides try, a total round to look for the condition to be together.
26, CMO, 26-3, Abel transform, reasoning clear. Xuanming inspection object, so the question is more than min and their respective number.
27, CMO, 27-2, with "block" will be described, to examine the minimum is not "block." Select the "pole" for management.
28, CMO 28-? Announced tomorrow.
29, CMO 29-5 patchwork of questions, but not too bad.
30, CMO 30-6, is indeed a good question. I did three hours, knew from the start that the drawer principle, but always wanted to find something like arithmetic, the results can not be found. As a negative example, to tell you, do not start off to strengthen and conclusions have been doing things in accordance with the strengthened.
Third, the mathematics competition experience
People look for him thousands of Baidu, when I look back, that person is in, the lights dim.
- "Qing Yuan Lantern Festival ·"
The prerequisite for a few fun on Mathematical Competition. In fact, Wang Guowei Three Realms any knowledge of any cause are applicable. I want to emphasize the most crucial point is to have the "eye" in math contests, see that topic in the end you want to do. Do not speak great truths, here are a few examples. Deep.
For example, there is a small conclusion, is that an irrational number for a, for any ε> 0, there exists an integer B, such that {ab} <ε. Such a conclusion, in my mind, on the one hand there is a villain in a flat garden walk, walked away, walked away, each step a fixed distance away, never to return home, so there are always some moments he can close from the origin; the other hand, after a long walk, his footsteps in particular dense circle. Then look at such a question: "Prove: 2 and the power of numbers is not the last of the" This, naturally think of reductio ad absurdum, "Suppose the world", how to find a bigger it? If there is a power of 2, its appearance is a 1 followed by a bunch of 0, and then a bunch of other, making it a bunch ride back after the existing digital and maximum power of the 2, followed by a bunch does not affect previous 1 multiplied by the power of the existing 2, the previous 1 multiplied by the power of the number 2 and is the "largest", we are not behind 0, on the line. How to get power behind a pile 0 1 2 it? Use lg2 is an irrational number, plus the aforementioned conclusions on ok.
In the above ideas, the evidence to the contrary is natural, then find a bigger, it is also very natural looking 100 ..., all fall into place. We can understand what there is of ideas.
As another example, there is a training camp before the team's title: "Proof: arithmetic sequence of length 40 does not exist, so that each of its times can be expressed as a power of 2 and 3 and a power followed" Although at first glance a look at the index may be a little less, a little more indices, and let them count the same, but in fact, as the number of distributed meaning of the title is "sparse" can be found from the contradiction size. Exponential growth too fast is a major contradiction.
As another example, the 2010 CMO third question, put it as a function, and then look at its "trend" (ie derivatives), found most likely to take extreme value at the border, after some "wish to set up" ( set b, c is a real number) can be found bz cz2 a pattern is symmetric about the x-axis, any point on the boundary to claim -a distance is less than 1, might then be a real number. Such abc are real numbers, and behind like to do. Or consider, z around the unit circle, "walk around", bz cz2 also walk around, to select a boundary of a so bz cz2 -a distance to any point of not greater than 1, then the distance between two points bz cz2 boundary took no more than 2 , ... take appropriate Z is a method.
For these examples, mainly I want to say, to understand that when we do question this question in the end let you do, know there is a figurative, to see more clearly the more in-depth, the more likely the problem to make it.
The following points are more important.
Know some "known" conclusion, such as CMO fifth title in 2013, apparently pieced together two old questions, obvious traces. At this time, knowing the nature of some small little conclusion would be helpful. The so-called sea tactical, in addition to the brush proficiency, is to a number of well-informed. Of course, I am not used the "sea of exams," My advice is, at least make some of the most classic conclusion know. Two former league sent a summary, will be referred to the conclusion, not go into here.
To triage questions. In fact, with just said "eye" like, but there is more bias refers to the conditions from the start and conclusion, find some breakthrough. For example, this year's CMO sixth question, the conclusion is clearly related to the drawer principle, we should begin to think drawer side (of course, also need further observation). Flexible thinking. A road leads nowhere (of course, usually over a lack of progress in one hour or more) may consider trying other ways.
Fourth, physical contest learning experience
Said predecessors thus prepared.
- "Yueyang Tower"
We recommend much, just two: early start slowly learn, to lay a solid foundation. Another is to think about, like mathematics, not to say.
This really is not much recommended, because to be honest, my focus was more on top mathematics. The choice to go to a physical team, mainly because after the completion of the four, feel mathematics competition is relatively narrow, and hope to learn some college courses, just into the national team in the future can justifiably go to the University mathematics and physics.
Compare the Mathematics and Physics Team below.
Mathematical Physics derogatory praise: 1, physical training, although some courses are not good, but there are some good lessons. For example treatment forces, thermal systems, atoms. However, the mathematical training team of "training" has lost its meaning, most of the players will not listen to most of the training class. The reason is that too many auditors, to become masters. 2, physical training team, because we will be together in class, far more than the exchange of mathematical training team. I attended the physical, met at least half of the people. But after the math, basically people do not realize other provinces. 3, the physical learning environment is much thicker than mathematics.
Derogatory praise mathematical physics: 1, the physical custody of a little too strict. Not out of school, not absenteeism, Alice can not study hall. But there is no mathematical custody. Of course, this also resulted in the mathematical training team loose. Both hope to be able to improve it. 2, physical examination of the learning content from large deviations in international competitions. Of course, this is strictly a physical contest weakness, it can not be regarded as physical training team.
Differences: As mentioned above, the physical TST school, the university entrance exam content. TST math test mathematics competition deeper content. Height and depth, a matter of opinion.
Finally, a brief talk about my life generally. Since 7 am, bunk moment, wash, downstairs breakfast (breakfast giant black, a small bun a dollar. Later, some people buy bread and the like. I went downstairs just to buy milk eggs, and then bring their own bread), go to classrooms, 8:30 class, no class or study hall. Generally I learned a half-hour rest 10min, reading a novel. 11:30 self-study class or, cafeteria lunch, back to the room to take a nap. 2-5 pm, after dinner, after 6-10 study hall. Then back to the room and began to write essay.
Puguang, 5 days. Li force seven days. Thermal systems, for 7 days. Quantum, for 6 days. Electric, five days (before self over again). Mathematical & atoms, rapid self-reading in teacher then, one day. Cumulative whole month, basically from scratch finish school physics basic course University.
Fifth, physics competition experience
Love was the view, get almost no different?
- "Yueyang Tower"
First of all, basically general physical problems have become column-wise solution of the equation, whether ordinary differential equations or equations, anyway, is the first column-wise solution and then nothing. Algebra skills with math contest, it will not be difficult. So, what is the problem then? Is the new model, the formula is not easy to list the title, or the wrong column on the solution of the equation is not out of the question, or solving equations in tricky question, or contains advanced physics background, it must be thorough understanding of the physics knowledge the problem (in particular, the theory of relativity). Model depends on physical literacy (IQ), solution of the equation depends on skilled and mastery of a few tips. Of course, the level of understanding of their own physical improvement, these points have helped.
Here is the application of mathematics competition in physics :( I found so far only one application, must learn to understand the competing Guoshuo). Laplace's equation with inversion of invariance. Inversion here is not to say that physical which often take the opposite number, which is often said that a mathematical geometric transformation. This conclusion is my own to discover and prove (to get rid of Tsai's a difficult problem), can be proud of. Feeling should be a corollary of higher theorem. To prove it, with inversion of the conformal transformation and scaling in the neighborhoods of a point equal proportions to. Conclusion This thing ... is to solve some of the electric potential distribution problems arc-shaped conductor. I do not go into details.
Six, "and" tactics
"Young Brothers, your martial arts tricks very much, I'm not presuming to say, of course, very wonderful gathering house, but can not help but heterogeneous impure. You do best effort in the end is what door?"
- "evil"
Kingland His Holiness senior master is really, really good to say. While doing math and physics competition in two subjects, a corresponding put any effort will be greatly reduced in both, not to mention the main items of mine from high school is not two but four - mathematics, physics, abroad (TOEFL, SAT, App) , curricular learning, and bluntly said, there are four aspects are three peak strength (strength abroad test can only be considered the top). The dependence is two words: time dedicated professionals.
First, there must be "when" may "use." I'm not saying we have to stay up till the early hours every day - I am usually is never in after 10:00 learning. I'm talking about, we must first be made. I also wanted to have fun, especially like reading novels, but fortunately both have self-discipline, not fallen down. Too many examples come to grief because of fun and competition, should take warning.
Then is the "use" of the technique. It is actually very simple: What is the most urgent thing, you do something. Do one thing, we devote, to do it. For example, when I do the usual high school competition, but that was before school examinations concentrate on school curricular, carefully review, so that a high four exams dominating the first three grades.
A high TOEFL test before the summer holidays, there are half a month, every day is a xdf class, go home with a "machine Classic" (it turns out, only twelve oral questions by a little, there are a bunch wrong) began mad that a pass. Later SAT words to be, that is the day was 3-4 hours, at a rate of 3 list per day in advance.
High School into a mathematical Beijing team, physically put for a year, get a year in math, do the previous CMO and TST topic. Sophomore summer, especially after August, due before mathematics into the training team, do not worry about mathematics Gaolian missed, and began efforts to get a physical until the training team. My high school years (or two and a half) is so over, at least for me to do both of these items is still very balanced. As long as "the right time to do the right thing", you should be able to coordinate.
Of course, just one example, unless there is a foundation confident are interested, it is not advisable to do with too many items.
However, the above said "and" does not allow students to one read only the books of sages. I still have some recreational activities, such as hobbies reading novels, read this three times per Jin Yong, Wen Jui novels are read, Liu Cixin are read, tomatoes in the previous year also saw ... There Bridge, body It is a bridge team Zong Jiaotou under HU Ji-seat super teacher. And although I do not play bridge well, but the cards did give me a lot of fun.
Seven, then it would not pull a few
These days there are some students asked on everyone. First, someone asked, how can suddenly "resuscitation." Express my own maths never felt the "sudden resuscitation." Is a little bit of learning, learning skills, and then slowly some perception, skills near Road.