A New Journey

"Yu Lei, if the behavior of this conjugate equation is the same as v=Ulogr+V, and U and V are continuous in region R, then what is U(ε,ζ) equal to?"

On the third day of the Olympic Math national team's intensive training, Cadre Liu tapped the blackboard with an eraser. It was his turn to lecture on Algebra, and he was the coach responsible for it.

"Equal to... 1?" team member Yu Lei answered with little confidence.

"Why did you take so long to think!" Cadre Liu reprimanded, "Yu Lei, I really don't know how you got selected for the national training team? Fine, U(ε,ζ)=1. Then I'll enclose (ε,ζ) in a circle and remove it from the integration region. So, as this circle shrinks to (ε,ζ), by the generalized Green's theorem, we get?"

"Get, get, get, get... get, get?" Yu Lei was dumbfounded, his voice trembling.

"Idiot!" Cadre Liu roared, and he pressed, "Get what?"

Yu Lei: "Get, get, get, get... get, get, get..."

"Forget it, sit down. Your level will only bring shame to the international competition," Cadre Liu shook his head in disappointment.

Yu Lei sat down, looking dazed, still muttering in a low voice, "Get, get, get, get... get, get..."

"Sigh," Shen Qi sighed involuntarily. It's over, this guy's gone mad.

"Zhou Yu'an!" Cadre Liu called out another team member's name.

Zhou Yu'an stood up nervously.

Cadre Liu asked, "Continuing the previous question, if the function v is a Green's function, and the condition that v is 0 on the boundary of R is added to the definition of the Green's function, what can be obtained?"

Zhou Yu'an scratched his head, unable to figure it out.

"Zhou Yu'an, I'm asking you what can be obtained!" Cadre Liu roared in anger.

Zhou Yu'an went from nervous to fearful, and finally, he actually started to laugh strangely, "Heh."

"Get what?" Cadre Liu's face darkened.

"Heh, heh-heh." Zhou Yu'an chuckled foolishly.

"Forget it, sit down. The Olympic Math national team is ashamed of you," Cadre Liu said, both angry and helpless.

Zhou Yu'an sat down, looking just like the village idiot at the entrance of the village in a rural movie, "Heh, heh, heh-heh."

"Sigh," Shen Qi couldn't bear to watch. It's over, another one has gone silly. Cadre Liu is truly ruthless. One algebra training session drove one team member mad and made another silly. Is this a training camp or a concentration camp?

"I'm so angry... I... I... Wait a moment, I need to take some medicine." Cadre Liu's chest ached faintly. He quickly took out his medicine bottle and took a heart-protecting pill.

"I can't get excited, can't get angry, can't be stimulated. My dear proud students, I'm begging you, can we show some spirit?" Cadre Liu, angered by their lack of progress, resorted to goading.

Swish, swish, swish!

Cadre Liu picked up chalk and furiously wrote on the blackboard, writing a new equation.

"Who can tell me how to transform this second-order equation into a first-order one in the simplest and most effective way? Raise your hand if you know." Cadre Liu no longer called out individual team members' names but addressed the entire team.

Five seconds passed, and no one raised their hand.

"A bunch of... idiots!" Cadre Liu began to mock everyone.

Ten seconds passed, and Shen Qi raised his hand.

"Shen Qi?" Seeing Shen Qi raise his hand first, Cadre Liu said, "Shen Qi, please wait a moment."

After taking another heart-protecting pill, Cadre Liu felt much more relaxed. "Shen Qi, you can tell us, or you can come up and write it."

"I'll write it," Shen Qi walked to the podium and picked up a piece of chalk to write.

Let ax^mdx^p=y^ndy^p-2d^2y

Perform the following calculation:

Obtain dy/dx.

Fix the constant α.

Thus, eliminate the exponential factor...

Then transform z=dv/dt.

The second-order equation is converted into a first-order one.

Solution complete.

Shen Qi finished his explanation, gently placed the chalk in the chalk trough, and returned to his seat.

"Get, get... Got it!" Yu Lei, who had been saying "get, get, get,"'s eyes lit up, and he returned to his normal state.

"Heh... Heh, oh, it can be transformed like this!" Zhou Yu'an stopped chuckling foolishly. He gained inspiration from Shen Qi's solution.

"Not bad, student Shen Qi has a very sharp mind." Cadre Liu, having taken his medicine, had some resistance and praised Shen Qi greatly. He didn't experience any cardiac discomfort.

This algebra training session finally ended, and no more team members went mad or silly.

During lunch, Yu Lei and Zhou Yu'an flanked Shen Qi on either side.

"Shen Qi, you're amazing. After all, he's a National Final gold medalist, very powerful," Yu Lei said.

"Not just gold, but a perfect score too," Zhou Yu'an added.

Shen Qi wasn't arrogant nor overly humble. "I'm okay. How about you two? I didn't see you at this year's National Final."

Yu Lei replied, "I got selected for the training team through the Math Elite Cup."

Zhou Yu'an said, "I participated in the Wisdom Cup and won the championship."

"Oh, Yu Lei, you were also the champion of the Math Elite Cup, right?" Shen Qi asked.

"Yes," Yu Lei nodded. "But neither the Math Elite Cup nor the Wisdom Cup can compare to the Math League National Final. Shen Qi, your gold medal from the National Final with a perfect score has the highest value."

China is vast and rich, with a huge population and so many students. There isn't just the Math League for high school math competitions.

If the Math League is considered the top league, like the English Premier League, then the Math Elite Cup and the Wisdom Cup are like the Eredivisie or the Primeira Liga, a tier lower.

Champions from various leagues gathered together to form this Olympic Math national training team.

"Speaking of which, this training method for the national training team is pretty brutal. This is just a 15-day intensive training; if it were extended to a month, I don't think anyone could leave the training camp alive," Shen Qi really disliked the national team's training camp model, but he chose to endure it for the sake of securing a spot in the IMO.

"I hope it all ends soon," Yu Lei sounded a bit exhausted.

"Me too," Zhou Yu'an echoed his sentiment.

"Since we're here, we have to persevere until the end," Shen Qi took a mouthful of white rice.

After a short lunch break, the afternoon session was a Probability Theory training class.

Then, in the evening, there was the daily routine test.

The test was an exam. After each day's training session, every team member would take a paper, with a perfect score of 100.

They tested for three consecutive days, and Shen Qi ranked first among all team members with 297 points.

He had finally slipped up once, losing 3 points in yesterday's test and failing to get a perfect score.

Over the next week, two more team members left.

One had physical issues, and the other had psychological issues.

There were 17 team members remaining.

In the past 10 tests, Shen Qi continued to lead with a total score of 985 points.

Shen Qi found it increasingly difficult to get perfect scores. The tests became harder and harder, and the coaches always found some minor flaws to deduct a few points from him.

Finally, the 15-day intensive training concluded, with 14 members remaining.

From these 14 members, the top six with the highest total test scores would be selected for the official Olympic Math national team roster.

Shen Qi's name was on the list.

On July 23rd, a group of over ten people from the Chinese Olympic Math competition team flew to the United Kingdom.

New challenges were on the horizon, and Shen Qi was ready.