Chapter 402 Fourth Update

Due to the limited space on the whiteboard, the steps presented are as concise as possible, so the thinking process is ignored.

But everyone who studies Olympiad mathematics knows that the steps of solving a problem are just the external presentation, and what is really important is thinking ability.

Tan Jiaxu also wanted to hear how she solved the problem, how she started, and how she came up with the idea of ​​nesting lemmas to prove the conclusion.

Jiang Fuyue: "Do you all want to listen?"

"want--"

"good."

Tan Jiaxu returned to his seat, looked up at the podium, and for the first time, his eyes showed that he was looking directly at Jiang Fuyue.

Zou Hao was amazed at what he saw.

Although Jiaxu usually plays with them and they have a good relationship, there is always a sense of pride in the genius's bones.

He didn't show it on purpose, but Zou Hao could feel it.

Now, he looks at Jiang Fuyue with this kind of eyes...

It only goes to show that only the genius among geniuses can impress geniuses.

At this time, Jiang Fuyue had already picked up the pen and stood in front of the whiteboard——

"When seeing this problem, many people's first reaction is to try to find the relationship between vertices and edges."

A large number of students below nodded heavily.

That's what they think.

"We know that a connected graph, assuming it has V vertices and only V-1 edges, cannot have a cycle, otherwise the graph is not a connected graph."

"But when we have V edges, there must be a cycle. Each time we add an edge, we create a new cycle. Suppose we have V + 1 edges and there's only one cycle in the graph. Then, if we remove an edge from this cycle, there's no cycle left. But there are still V vertices in the graph, so there must be a cycle. So our assumption is wrong; there are at least two cycles in the graph..."

Talk about praising his focused gaze.

Zou Hao didn't want to listen at first, but the girl's voice was refreshing and cool, like a mountain spring in a deep stream, gurgling and tinkling.

He was attracted unconsciously.

Jiang Fuyue: "...We need to introduce a new definition here, called the remainder, which is the number of edges E minus (V-1), which equals E-V+1. It describes the amount of excess vertices in a graph, and this quantity roughly determines the number of cycles in our graph."

Tan Jiaxu's eyes lit up.

That’s right, this is the step!

He was thinking about how to bypass this proof point, but Jiang Fuyue directly introduced a new definition.

He avoids risk, while she rises to the challenge.

It’s the difference in the two people’s thought processes that ultimately makes the difference between success and failure.

So, there is a reason why he lost.

Jiang Fuyue stood on the podium, with a slim figure and outstanding temperament, but at this moment almost everyone subconsciously ignored her appearance and saw her shining wisdom, powerful logic, rigorous attitude, and her respect and devotion to knowledge.

"...Thinking further, as the number of edges in a graph increases, the number of circles will increase, and these circles will intersect with each other, and the perimeter of the circles will decrease. Returning to the question itself, it uses the description of 'finite number of counterexamples'. If we want to solve this problem head-on, the only way seems to be to constructively find two such circles in any graph..."

It turns out that some people's souls really can glow.

So brilliant that one can't take their eyes off it.

Ling Xuan stood beside him, slightly tilting his head, and this angle was just right so that the students below could not see the infatuation in his eyes at the moment.

His heartbeats were so strong that it was about to burst through his chest, making him panic and excited at the same time.

He knew that some things could not be restrained.

For example, like.

But he didn't even have the courage to say it out loud.

Jiang Fuyue is too dazzling.

He once thought that he was able to gather enough light, but now he realizes that Jiang Fuyue himself is the source of light.

Her excellence made him retreat, and her brilliance eclipsed everyone, including herself.

I want it, but I don’t dare. The dilemma of wanting it but being out of reach has become a torture.

Ling Xuan lowered his eyes fiercely and warned himself that he must be patient.

At this moment, through the half-open back door of the classroom, there was a person who was also staring at the radiant girl on the podium in a trance.

Jiang Fuyue: "...But the question also tells us that there are a finite number of counterexamples to this situation, almost telling us that this approach is a dead end. So why not try a different approach: prove the lemma, use it to derive a contradiction, and achieve proof by contradiction..."

The clear voice reveals absolute rationality and is supported by strong logic.

The man watched and listened, a smile slowly appearing in his eyes.

"Professor Xie?" Zhao Tiejun called softly.

Xie Dingyuan suddenly came back to his senses, but did not withdraw his gaze.

Zhao Tiejun went over and said with a smile, "This is the Mathematical Olympiad class. They're about to participate in the national league, so they're in training right now."

Xie Dingyuan nodded lightly.

Seeing his interest, Director Zhao couldn't help but start talking. "The girl speaking on the podium is the top student in her senior year. She's also the gold medalist and special award winner in this year's IPhO and IOI. She got full marks in both subjects. She's a promising prospect for University B and University Q..."

Speaking of this, Zhao Tiejun felt a surge of pride, and even his chest straightened up.

"Really?" Xie Dingyuan replied calmly, giving him a chance to continue.

Sure enough, Zhao Tiejun began to talk non-stop -

"This child is exceptionally talented. All her subject teachers praise her intelligence."

Xie Dingyuan: Yes, my brain is indeed quite flexible, whether it is studying or arguing with people.

"She gets along very well with her classmates. Whenever she has time, she explains the questions to everyone and sorts out the key points. Everyone calls her Yuejie."

Xie Dingyuan: Sister? She's still a little girl.

"My sports performance is also outstanding. I have trained in high jump and shot put, and I often play basketball with my classmates after class."

Xie Dingyuan: Classmate? Male or female?

"Some time ago, I published a paper on the main page of the PRL journal. The title was... eh! I forgot, but it was related to bacterial movement."

Xie Dingyuan knew it without him saying anything.

He might be the first person to see the draft of that paper, right?

"In short, Jiang Fuyue is a well-rounded student with outstanding moral, intellectual, physical, and aesthetic development. She is a shining star of No. 1 Middle School!"

Xie Dingyuan nodded, a smile flashing in his eyes, but he heard that it had already been said -

"…So, the lemma is as follows: For any positive real number a and natural number N, prove that there is a finite number of counterexamples to the statement that a graph with N vertices and (1 + a)N edges has a cycle of length less than aN…"

Just hearing the sound can make him feel happy.

"If I had to say the only bad thing about him," Director Zhao sighed, "it's that he's a bit stubborn and has a lot of ideas."

"Oh?" Xie Dingyuan raised his eyebrows.

"Some time ago, the school received admission notices from University B and University Q, telling her she could choose any major. Unexpectedly, the child rejected it out of hand, leaving no room for negotiation, and her parents joined in the antics..."

Zhao Tiejun looked regretful.

That’s B University and Q University!

I heard that Xu Jing, Meng Zhijian, and Yu Wenzhou were running around the office like crazy that day, sighing and cursing.

And what about Jiang Fuyue?

She insisted on having her own way and no one could persuade her to come back.

This was the first time Xie Dingyuan heard this: "Why did she refuse?"

Zhao Tiejun: "Is it possible that you are planning to take the college entrance examination?"

Speaking of this, he felt a little proud.

Do students from other schools have the courage to reject University of B and University of Q?

No!

But they have one!

There’s more than one!

Ling Xuan also refused. Wow, how can they still get together like this?

This year’s session is absolutely amazing!

Xie Dingyuan retracted his gaze and suppressed the faint smile on his lips: "Let's go, Director Zhao."

"Oh, okay. Is Zhong's leg almost healed?"

"Um."

"That's good, that's good. Actually, you don't have to go there in person. Just make a phone call, or have Zhong bring a handwritten, signed note from your parents when he returns to school..."

It’s better than coming in person, right?

In fact, Zhao Tiejun didn’t know why this giant Buddha suddenly appeared.

When the school sent him to pick him up, he was completely dazed.

Xie Dingyuan stepped forward, and the girl's voice behind him became smaller and smaller.

"Suppose a graph has N vertices and at least (1 + a)N edges, and all loops in the graph are of different lengths. We need to construct a contradiction to disprove this assumption when N is large enough. So, we can do this to find the shortest loop in the graph..."

After returning from a teaching and research meeting in Xujing, I suddenly found that the atmosphere in the class had become much more harmonious.

He asked the reason, but each student was more tight-lipped than the other.

"?" Curiosity got to me, and I was so anxious.

But he didn't dwell on it for too long, because harmony is a good thing.

This friendly atmosphere continued until the end of the two-week semi-closed training camp.

Soon, the National Mathematical Olympiad League came...

There’s no reason, I just want to come and see my wife.

Zhong Ziang: You use me as a cover, do you have any shame?

(End of this chapter)