"Yu Lei, if this conjugate equation has the same characteristics as v=Ulogr+V, and U and V are continuous in region R, what is U(ε,ζ)?"
It was the third day of training for the Olympic Math national team. Cadre Liu tapped the blackboard with an eraser. Today it was his turn to teach algebra; he was the coach in charge of the subject.
"It equals... 1?" Yu Lei answered uncertainly.
"Why did you take so long to think?" Cadre Liu scolded him. "Yu Lei, I really don't know how you got selected for the National Training Team. Fine, U(ε,ζ)=1. If I enclose (ε,ζ) in a circle, then remove it from the region of integration, what do we get as the circle shrinks to (ε,ζ), according to the generalized Green's theorem?"
"We get, we get, we... we get?" Yu Lei stammered, dumbfounded.
"Idiot!" Cadre Liu roared. "What do we get?"
Yu Lei: "We get, we get... we get, we get..."
"Forget it. Sit down. At this level, you'll only embarrass yourself at the international competition." Cadre Liu shook his head in disappointment.
Yu Lei sat down, looking dazed, still stammering under his breath. "We get, we get..."
"Ugh." Shen Qi sighed, unable to bear it. That's it. The guy's gone mad.
"Zhou Yu'an!" Cadre Liu called another team member.
Zhou Yu'an stood up nervously.
Cadre Liu asked, "Continuing from the previous question, if the function v is a Green's function, and we add to its definition the condition that v equals zero on the boundary of R, what can we get?"
Zhou Yu'an scratched his head, utterly stumped.
"Zhou Yu'an, I asked what we can get!" Cadre Liu bellowed furiously.
Zhou Yu'an went from nervous to terrified, then, bizarrely, broke into a grin. "Hehe."
"What do we get?" Cadre Liu's expression darkened.
"Hehe, hehehe." Zhou Yu'an giggled foolishly.
"Forget it. Sit down. The Olympic Math national team is ashamed to have you." Cadre Liu was angry and exasperated.
Zhou Yu'an sat down, looking just like the village idiot from some rural movie. "Hehe, hehe, hehehe."
"Ugh." Shen Qi couldn't bear to watch. That's it. Another one's gone stupid. Cadre Liu was ruthless. One algebra class, and he'd driven one team member crazy and made another an idiot. Was this a training camp or a concentration camp?
"I'm going to have a heart attack... I... I... Wait, let me take some medicine." Cadre Liu felt a dull ache in his chest. He hurriedly took out a bottle and swallowed a heart-protecting pill.
"I can't get worked up, I can't get angry, and I can't take any more shocks. My brilliant students, I'm begging you—could you please do me proud?" Cadre Liu was frustrated by their lack of ambition, so he tried goading them instead.
Swish, swish, swish!
Cadre Liu grabbed a piece of chalk and wrote a new equation on the blackboard with quick strokes.
"Who can tell me the simplest and most effective way to transform this second-order equation into a first-order one? Raise your hand if you know." Cadre Liu no longer called on individual team members; he addressed the whole group.
Five seconds passed. No one raised a hand.
"You bunch of... idiots!" Cadre Liu launched into a group-wide scolding.
Ten seconds passed. Shen Qi raised his hand.
"Shen Qi?" Seeing him volunteer first, Cadre Liu said, "Wait a moment."
After swallowing another heart-protecting pill, Cadre Liu felt much more relaxed. "Go ahead, Shen Qi. Or you can come up and write it out."
"I'll write it." Shen Qi walked up to the podium, picked up half a stick of chalk, and began writing.
$ax^m dx^p = y^n dy^{p-2} d^2y$
Proceed as follows:
We obtain dy/dx
Set the constant α
Thus we eliminate the exponential factor...
Then make the substitution z=dv/dt
Convert the second-order equation into a first-order one
Q.E.D.
Shen Qi finished the solution, gently placed the chalk in the blackboard tray, then returned to his seat.
"We get, we get... we got it!" Yu Lei, who had been stammering all along, suddenly brightened up and returned to normal.
"Hehe... hehehe, oh! So that's another way to transform it!" Zhou Yu'an stopped giggling. Shen Qi's solution had given him an idea.
"Not bad. Shen Qi's got a sharp mind." Cadre Liu had taken his medicine, so he was feeling better. He praised Shen Qi highly without showing the slightest sign of heart trouble.
At last, the algebra training class was over. No other team members went crazy or stupid.
At lunch, Yu Lei and Zhou Yu'an sat on either side of Shen Qi, flanking him.
"Shen Qi, you're something else. You're a national finals gold medalist, after all. You're incredibly good," Yu Lei said.
"Not only a gold medalist, but a perfect scorer, too," Zhou Yu'an added.
Shen Qi wasn't arrogant, but he didn't downplay himself either. "I'm all right. What about you two? Why didn't I see you at this year's national finals?"
"I got onto the training team through the Math Elite Cup," Yu Lei said.
"I competed in the Wisdom Cup and won," Zhou Yu'an said.
"Oh, Yu Lei, you won the Math Elite Cup too, right?" Shen Qi asked.
"Yeah." Yu Lei nodded. "But the Math Elite Cup and the Wisdom Cup aren't on the same level as the national finals. Your perfect-score gold medal at the national finals is worth the most, Shen Qi."
China was vast and populous, with an enormous number of students. The national math league wasn't the only high school math competition.
If the national league was the English Premier League of top-tier competitions, then the Math Elite Cup and the Wisdom Cup were more like the Dutch Eredivisie or the Portuguese Primeira Liga—slightly lower in rank.
The champions from the different leagues had gathered together to form this Olympic Math national training team.
"Speaking of which, this kind of national team training is pretty brutal. It's only a fifteen-day crash course, but if it went on for a whole month, I don't think anyone would make it out of this camp alive." Shen Qi really disliked this kind of national team training, but he chose to endure it for a chance to make the IMO team.
"I hope it'll all be over soon," Yu Lei said, looking a little tired.
"Me too." Zhou Yu'an shared his misery.
"Since we're here, we may as well stick it out to the end." Shen Qi took a bite of rice.
After a short lunch break, the afternoon session was Probability Theory.
Then, in the evening, they took the daily test.
The test was an exam. After each day's training, every team member had to complete a paper, with a maximum score of 100.
After three days of exams, Shen Qi ranked first among all the team members with a score of 297.
He'd finally slipped up once. In yesterday's test, he'd lost three points and failed to get a perfect score.
Over the next week, two more team members left.
One had health problems, and the other had psychological problems.
Seventeen team members were still holding on.
Across the ten tests so far, Shen Qi continued to lead with a total score of 985.
Shen Qi found it increasingly difficult to get perfect scores. The tests got harder as they went on, and the coaches could always find some fault to deduct a few points.
At last, the fifteen-day intensive training came to an end. Fourteen team members had lasted until the end.
Of those fourteen, the six with the highest total test scores would make the official Olympic Math national team roster.
Shen Qi's name was on the list.
On July 23, a group of more than ten people from the Chinese Olympic math team boarded a plane for Britain.
New challenges awaited, and Shen Qi was ready.
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