I really just want to be a scholar

Chapter 271 Create your own brand-new Olympiad theory system!

Throughout the opening ceremony, the biggest highlight was the speeches of several mathematics masters who won the Fields Medal, the Wolf Prize in Mathematics, and the Abel Prize.

Compared with the half-hour long speeches of domestic scholars, each of them gave a speech of no more than 5 minutes, which is very concise. In contrast, there is not much content. It is nothing more than a simple summary of the history of IMO. Best wishes It is not too much new to see that the candidates get good grades in the exam and contribute to the future of IMO, etc.

Only Professor Martin, an Austrian Filipino award winner, mentioned a few words that touched Qin Ke:
"I appreciate the reform of this IMO, it has made great efforts in the direction of innovation. Mathematics is an interesting thinking game, because it can always bring forth new ideas, and you can always find the joy of 'creation', Even if it is a very simple theory, when you look down from a high level, you can still find different mathematical aesthetics and have different gains.”

"The direction of my research is mainly the theory of stochastic partial differential equations. However, in the past two years, I have been invited to assist the motherland in revising textbooks for middle school students. I have tried to find a new way of thinking, which can help middle school students better understand mathematics and learn Math, solve math puzzles..."

Professor Martin's words also only lasted about 3 minutes, but they touched Qin Ke greatly, because they coincided with his recent thoughts and also inspired him to a certain extent.

In the past two days, he has been studying the S-level knowledge "Exploration and Detailed Explanation of the Nonlinear Partial Differential Equation 'Navier-Stokes Equation' (Part [-]), (Part [-])" in his spare time. Have new experiences and perceptions.

The biggest insight is the change in the way of thinking. The reason why the "first part" and "the second part" are complicated is not only because many theories are very profound and require extremely high levels of mathematics and physics, but also because its levels stand very high. high.Its thinking mode is not limited to a certain direction of a certain subject, but directly integrates the knowledge of these subjects from a higher level of the combination of theoretical science and practical science, and transforms theory into practice.

Qin Ke re-examined his "theoretical achievements", whether it was the few papers he had written, or the set of "The Wonderful Mathematical Journey of Kitten Lemon and Puppy Keke (First Part)" written by him and Ning Qingyun , and the "New Knowledge System of Mathematical Olympiad" expounded during the special training for Ning Qingjun and the Mathematical Olympiad training team. Efficient and easy.

Can my newly formed Olympiad theory system be optimized and improved?
The answer is yes, that is to innovate in the way of thinking, integrate the knowledge of Mathematical Olympiad with a higher perspective, and form a new, more scientific, and more concise theory.

However, Qin Ke's current Olympiad level has reached the peak that all high school students in the world can achieve. In other words, he has also reached a bottleneck period. How easy is it to make progress?
Until the end of the opening ceremony, Qin Ke was still immersed in this kind of thinking, but he had no inspiration or breakthrough for a while, so he had to give up for the time being and planned to study after the game.

After passing the security check and certificate inspection, Qin Ke stepped into his own examination room after high-fiving Ning Qingyun, Wang Changai and other four team members at the entrance of the examination room, and Liang Shaoping was in the same examination room as him.

The layout of the examination room of each IMO is in the charge of the venue, and this year is naturally arranged by the University of Oslo.Qin Ke was lucky, and was actually arranged to take the exam in a simple and elegant auditorium.

The auditorium is huge and can accommodate nearly [-] examinees. Qin Ke quickly found his seat. A small bag of biscuits, a piece of chocolate, and a small bottle of mineral water have been prepared on it. They are prepared for temporary supplementation of nutrients during the five-hour exam without frequent trips to the bathroom.

Some of the candidates around looked at the biscuits and chocolates very freshly, and at first glance they were newcomers to the competition for the first time; some were indifferent, looking through the reference materials they carried calmly, they should be veterans who participated in the competition last year.

According to Deng Hongguo, the Asian named Hill in this year's US team was the gold medalist the year before and the champion last year, because last year he used two different and very creative new methods to solve the last big problem. , was unanimously recognized by the judges, and he was specially designated as the champion.

Deng Hongguo regards him as a strong enemy of Qin Ke and Ning Qingyun.

Coincidentally, Qin Ke recognized Hill at a glance and sat three rows in front of him.

At this time, Hill was turning the pen in his hand with extremely delicate movements, and his expression was relaxed, even smiling.

His nimble movements of turning the pen make people unconsciously marvel.His finger movements are as precise as a machine, turning back and forth hundreds of times in succession, the speed is astonishingly fast, but he has never missed it. Judging by his state, as long as he doesn't want to stop, he can turn forever.

Not to mention anything else, just by looking at the precise control of his fingers, he can know how superb his brain is in controlling fine movements. Such a person must have a superb IQ.

Another thing that caught Qin Ke's attention was a tall man from Xiongguo, with blue eyes and fair skin. Unlike Hill's movement, he was another extreme of quietness.

He sat quietly on the spot, as quiet as a rock, without a trace of tension or anxiety, and did not show any boredom, as if he was letting himself go, and he seemed to be meditating.

As expected of IMO, the most high-end event gathered by Olympiad masters from all over the world made Qin Ke a little bit fighting.

Ten minutes later, the DAY1 competition was about to start. The test papers were issued 5 minutes earlier in order for the examinees to check the papers in advance to see if there were any mistakes or omissions, so they could only read and not write.

Qin Ke finished reading the paper in 3 minutes. The questions are really difficult. If it is just a conventional solution, Qin Ke is confident that he can finish it within 35 minutes. However, if he adopts a new solution, he needs further thinking, and it will take about 50 minutes. up.

Why don't we just use three solutions to complete the entire paper?

Qin Ke decided to give himself a new challenge.

First, it will make this IMO more interesting, and second, it will ensure that the champion of this year is in his arms.

——IMO has always encouraged the use of multiple solutions, because it has always advocated "creativity", but it is difficult for the vast majority of candidates to complete the entire test within the specified time, only a very few geniuses, like last year Hill of the U.S. team was able to figure out two brand new solutions to a certain big problem with ease.

Before the exam officially started, Qin Ke held up the sign with "HELP", and immediately a young brown-haired invigilator came over and asked in English, "Excuse me, this student, what do you need?"

Qin Ke said softly: "Can you give me two more answer sheets?"

The invigilator said in astonishment, "Is there something wrong with the answer sheet in your hand?"

"No, I'm afraid it won't be able to write my answer."

Because there are two more questions in this year's IMO, the organizing committee specially prepared a larger answer sheet, which can be folded in half and can be written on four sides. Normally, it is enough. Unexpectedly, there are students who have proposed to add more questions early. paper, and two sheets at a time.

It was the first time for the invigilator to encounter such a situation. He couldn't make up his mind, so he ran to ask the invigilator in the examination room. The invigilator accidentally glanced at the national flag on Qin Ke's desk. This student was from Xia Guo. player?Xia Guo used to be a first-rate strong team, but unfortunately, it has been going downhill in the past ten years, and now it is about to be reduced to a third-rate weak team.

He shook his head and said: "The ancient country likes to play tricks like this, so give it to him."

The invigilator got the instruction, and quickly fetched two answer sheets for Qin Ke.

Basically, not many people care about the little things that happen here. Everyone is hurrying to review the questions. Even if they can't start writing, they must first look for ideas to solve them.

At this time, the melodious bell rang for the start of the exam, and only nearly one-fifth of the candidates in the exam room began to pick up their pens and rushed to the first threshold question.

Hill of the US team and Xiong Guo's meditation candidates were naturally one of them, and they picked up their pens to do the questions without any haste.

The rest of the candidates were all bitter, and some were scratching their heads in anxiety, apparently stumped by the first threshold question at the beginning.

In fact, according to the usual practice, the questions on DAY1 will be easier than those on DAY2, and the first question is the easiest among all the questions on DAY1. However, the difficulty of this IMO has increased a lot, which puts forward higher requirements for the flexibility of thinking. The difficulty of the questions is also randomly distributed. Unfortunately, this threshold question is the most difficult in the entire test, so it stumps four out of five people.

"1. n is a given positive integer, S={(x, y, z)|x, y, z ∈ {0, 1, 2,..., n}, x+y+z is greater than 0} is a three-dimensional space A set of (n+1)^3-1 points in the middle. Try to find the minimum value of the number of planes whose union contains S but does not contain (0, 0, 0)."

Qin Ke didn't start writing either. This question was not difficult for him. It only took him five seconds to come up with a solution and two slightly innovative solutions.

But just when he picked up the pen and was about to write the answer, an inspiration flashed through his mind.

Inspiration is like a naughty child. When you look for it everywhere, it always hides left and right, but when you don't look for it, it will appear naughty in front of your eyes again.

Qin Ke suddenly thought of the fourth solution to this question. As long as the difference method is used, the answer can be made very simple, but it requires the use of Lagrangian mean value theorem and partial derivative theory, which are the knowledge level of university mathematics. It's beyond the scope of high school students.

According to the rules of IMO, you can only solve the problem with mathematics knowledge of high school and below, otherwise you will not get points.If you insist on using university knowledge theorems to solve problems, it is not completely impossible. The premise is that you use high school knowledge to complete the derivation of the theorems before you can quote them.

Let Qin Ke first deduce the relevant knowledge points of Lagrangian median value theorem and partial derivatives. Think of this solution, just because it is "simple".

Can you use the thinking mode of college mathematics and the knowledge points of high school to write the most concise solution?

This inspiration skipped Qin Ke's brain like an electric spark, and he slowly closed his eyes, trying to catch the slightest bit of inspiration.

By the way, why don't you try it yourself?
Isn't this exactly what I have been thinking about these days, using a higher-level vision and a higher-level way of thinking to combine and optimize low-level knowledge points to form a more efficient, concise, and easier-to-understand new Knowledge system?
Qin Ke put down his pen, and in the darkness in front of him, he began to use this trace of inspiration to create and perfect his own brand-new Olympiad theory system!

　Make up for the second update from the day before yesterday.

　　I'm sorry, I just got home after overtime at one o'clock in the morning. I was so tired that I fell asleep right away. This chapter was coded around six o'clock in the morning.

　　Yesterday's two updates, try to make up before 2 pm.

　　Thank you for the recommended monthly tickets, and thank you "Uji" and "Daily K" for the rewards, I am so touched!
　　Try harder today!More chapters!
　　Continue to ask for monthly tickets, starting from today, double monthly tickets!Anyone with a monthly pass will come here!
　　
　
(End of this chapter)