Takishima Comet: Considering that the group leader will have an Olympiad competition in the near future. So I think the group leader can learn the mathematical theorems of functions first!

Shelton: That's right, the Olympiad often has functional questions.

In mathematics, the inverse theorem gives sufficient conditions for a vector-valued function to have an inverse function in an open region containing a point in a defined domain. The theorem also states that the full derivative of the inverse function exists and gives a formula. The inverse function theorem can be generalized to mappings defined on manifolds, as well as on infinite-dimensional Banach spaces (and Banach manifolds). Roughly speaking, the C1 function F is reversible at point p if its Jacobian matrix JF(p) is reversible......

Xiao Jun: It's too troublesome to type, let's voice in groups!

Sheldon: Good!

The Xueba chat group also has the function of video call and voice call.

If you use group voice, it is more convenient to teach. It is equivalent to online live teaching.

In the next few days, Xiao Jun was frantically irrigated with all kinds of mathematical esoteric knowledge by Takishima Comet and Sheldon. Fortunately, he has the ability to remember and does not cause dizziness.

It doesn't matter if you can understand it or not, whether you can understand it or not. Let's keep it in my head first!

When you have time later, you can tidy it up slowly.

The three days passed quickly.

In the past few days, although Xiao Jun has not thoroughly understood a lot of esoteric mathematical theorems and other knowledge, he has also learned a lot of knowledge. This kind of knowledge is not learned in high school classrooms.

After all, these esoteric things are taught by these two top students, and its profundity and diversity are definitely not available in high school classrooms.

Although he didn't understand a lot of knowledge, Takishima Comet and Hilton poured a lot of mathematical knowledge into his brain. These are all things that he didn't understand thoroughly, but he kept them in his mind.

"It will come in handy in the future, but now I have time to learn more. Xiao Jun said secretly in his heart.

The next day, Xiao Jun and Yang Qianqian, led by Chen Jianyong, came to Jiangcheng, the capital of Jiangbei Province, again.

Xiao Jun and Yang Qianqian were going to gather here with six other people from other high schools for a few days of emergency math training. Because in a few days, I will go to Tianhai City to participate in the National High School Mathematics Olympiad!

This time, the venue of the National High School Olympiad is in Tianhai No. 1 High School!

This high school is also one of the top 20 high schools in the country.

In the car, Chen Jianyong said to Xiao Jun and Yang Qianqian: "I heard that this time we have a total of 6 places in Jiangbei Province to participate in the National Olympiad Competition!"

Yang Qianqian asked in a coquettish voice, "Is it the top three in the last provincial mathematics competition?"

"That's right! It's the two of you from Wucheng No. 3 Middle School, two from Jiangbei High School, and two from Jiangbei University High School! You six of you can also be called members of the Jiangbei Provincial Olympiad Provincial Team. You represent our Jiangbei Province in the National Mathematics Olympiad!" Chen Jianyong explained.

"Of course, although the six of you are called the provincial team. But at that time, the National Olympiad will not be a team competition, but an individual competition. Each person has a test paper, and it depends on who does well in the test, and who can win the award. Of course, if all six of you win. Then when all the provincial teams in the country are ranked, it will highlight that our Jiangbei Province is at the top of the ranking!"

"I see!" Xiao Jun nodded.

"This time, the National Mathematics Olympiad lasts for 5 days, the first day is the opening ceremony, the second and third days of the exam, the fourth day of academic reports or visits, and the fifth day of the closing ceremony, announcing the results of the examination and awarding of awards. ”

"The National Mathematics Olympiad is a complete simulation of the International Mathematics Olympiad, with 3 questions a day and a limit of four and a half hours to complete. Each question is worth 21 points (3 times the questions of the International Mathematics Olympiad, which is in line with the score cognitive habits of Chinese people), and the full score of 6 questions is 126 points. Set up first, second and third prizes!"

"The top 60 players with the highest scores will form the Huaxia training team to participate in this year's International Mathematics Olympiad. Chen Jianyong said slowly.

"Teacher, are you saying that as long as we get the top 60 places in this National Olympiad competition, we can enter the national Olympiad team for training and selection?" Yang Qianqian said.

"Yes, but even if you can get into the top 60, don't think it's okay to be in the National Mathematics Olympiad. In other words, after some training and selection of 60 of you, only 6 people will be selected to participate in the International Mathematics Olympiad. These six people are the real members of the National Mathematics Olympiad team!" Chen Jianyong said in a deep voice.

"That's it! It's cruel. Xiao Jun smacked his lips.

"Also, I would like to tell you a good news, that is, if you can win a prize in the International Mathematics Olympiad, then the winners can be admitted to Beijing University, Jinghua University, Fudan University, Nanjing University, Huaxia University of Science and Technology, Shajiang University, Shanghai Jiaotong University and other first-class universities in China. ”

"Oh~ That's good!" Yang Qianqian didn't show much excitement after hearing this. After all, it is difficult to say whether it can enter the top 30 of the national Olympiad competition. Not to mention participating in the International Mathematics Olympiad.

In the afternoon, Xiao Jun and others came to the middle school attached to Jiangbei University.

This three-day intensive training was held here. On the fourth day, we set off for Tianhai City! On the fifth day, we will see the opening ceremony of the National Mathematics Olympiad.

After coming here, Xiao Jun met with members of the other two schools.

Among them, the two people in Jiangbei High School are still a man and a woman, the male is called Wu Junhua, and the female is called Zhou Xiaoyu. A girl was able to participate in the National Mathematics Olympiad. It's rare, indeed. Generally speaking, the field of mathematics is generally the world of boys. Girls are inherently disadvantaged.

Even Yang Qianqian, if Xiao Jun hadn't taken her to fly, she wouldn't have been eligible to participate in the National Mathematics Olympiad at all!

The other two classmates from the High School Attached to Jiangbei University are named Wang Qiang and Chen Feixiang.

This was followed by three days of emergency training.

Those who can get the top three in the last provincial mathematics competition are basically level.

Therefore, the teachers of the training will no longer talk about the basic problems, but will pick some difficult and miscellaneous Olympiad knowledge to explain, and also pick some national Olympiad questions for them to practice.

Three days passed in such an intense training.

On the morning of the fourth day, everyone followed the heads of the provincial team and began to take the bullet train to Tianhai City.

The drive is just over two hours, which is not very far!

When I arrived at the station, there was a special bus waiting, and then we came to Tianhai No. 1 High School together.

Tired travel, eating and resting. Before I knew it, a day had passed.