I Am the President of the University

"Elbow, who do you think will be the teacher who will teach us later?"

"How would I know..."

Lu Zhou rolled his eyes at Zhang Lei, really not wanting to pay attention to this wise man.

It was their first time at MIT, how would he know who would be the teacher who would teach them!

Seeing that Lu Zhou ignored him, Zhang Lei went to find Zheng Tianyu again.

"Tianyu, you..."

"Get lost!"

After being humiliated twice in a row, Zhang Lei calmed down awkwardly, stroking his student ID lightly with his hand, feeling very proud.

The American university student ID is actually equivalent to the campus card in China. The upper left corner of the front is the three big letters "MIT", followed by the full English spelling "Massachusetts Institute of Technology".

The bottom is divided into two parts, the left side is the student's name and MIT ID, and the right side is a one-inch photo.

The back of the card is a barcode, entry, and other information.

This is the student ID of the Massachusetts Institute of Technology!

Zhang Lei took a photo of the front of his student ID card with his phone, and then sent it to the school group to show off. Not only that, he also posted a circle of friends.

[The texture of this card is so-so. I feel that the one from my school feels more comfortable. Sigh, I'll just use it for now. Picture.JPG]

Within a few minutes of posting it on the circle of friends, more than a dozen reminders appeared, and a group of people were scolding Zhang Lei for showing off.

Before class, except for Zhang Lei who had time to play with his phone, the other 7 people were either nervously waiting for the teacher to come, or doing questions like Lu Zhou.

Until the time was close to 10 o'clock.

A white-haired old man walked in from the door of the classroom. Even in the July weather, he was wearing a decent shirt and trousers and walked in with a cup of coffee in his hand.

Putting the coffee on the table, the old man looked around and said, "Good morning, students. I am Sean Stevens, the teacher who teaches you [Algebra and Number Theory]. You can just call me Professor Steven." (Steven is a first name, not a last name, so I'll just leave it as it is...)

As he said that, he turned around, picked up the chalk and wrote his name and email address on the blackboard.

Most of the courses at MIT are similar to those in China, using PPT projection to assist teaching, but math classes are different, which mainly rely on chalk and blackboard.

"Sean Steven?" Lu Zhou muttered in his heart, and then memorized the email number under the other party's name.

For some reason, I always feel that this Professor Steven seems familiar?

Lu Zhou frowned slightly, and after thinking for a long time, he still couldn't remember who the other party was.

But it was not a big deal, and Lu Zhou quickly put it behind his mind.

After all, it was the first class, and the first thing to do was to introduce themselves.

Eight students from Guanghua University introduced themselves in English one by one.

Several students started talking, and when it was Lu Zhou's turn, Professor Stephen's attention was instantly drawn to him. With a smile on his face, his eyes fell on Lu Zhou, as if he was looking at something. Since it was at MIT, the whole course was naturally taught in English. Fortunately, when the list was released before, the school had conducted intensive English training for this batch of students selected for the summer course. It was still a bit difficult, but I could still understand it. Time continued to pass, and in a blink of an eye it had been more than an hour. It must be said that Professor Stephen's level was indeed very high, and he explained the knowledge points of algebra and number theory very plainly and straightforwardly. Professor Stephen glanced at his watch, then smiled and said, "I will give you an algebra problem in the last minute." Lu Zhou picked up the chalk and looked at the blackboard intently. With the sound of "swish swish" of chalk friction, the problem on the blackboard gradually became clear. [Let n be a positive integer. Let e=（1，1···, 1）^T be an n-dimensional column vector. Let A=（aij）be an n-order matrix, where the elements of the i-th row and j-th column are aij=1/（2i）2-（2j-1）2, let the n-dimensional column vector f satisfy Af=e, find e^t·f. 】（Figure in chapter）

This is a classic algebra problem, which is a little difficult, but not a big problem.

Lu Zhou looked at the problem and began to deduce it frantically in his mind.

Just as Lu Zhou's eyes lit up and he was about to pick up the pen to start solving the problem, Professor Stephen on the podium suddenly spoke.

"Are there any students who want to come up and solve the problem?" Stephen smiled.

Zhang Lei was eager to move, but he had no idea to solve the problem!

He turned his head to look at Zheng Tianyu beside him. Perhaps sensing Zhang Lei's gaze, Zheng Tianyu looked up and looked at him.

Seeing Zheng Tianyu shaking his head slightly, Zhang Lei's heart sank.

Guanghua University has two summer programs, and the main force is their mathematics group. Among the eight people who came to MIT summer school, Lu Zhou is the strongest, followed by Zheng Tianyu, and then him.

If none of the eight people can do it, wouldn’t it be a loss of face for the school?

Guanghua can connect with MIT entirely because of the president’s face.

We can’t let the people from MIT look down on our students at Guanghua University!

And the only hope...

Zhang Lei gritted his teeth, and looked in the direction of Lu Zhou with trepidation. Seeing Lu Zhou raise his hand, he couldn’t help but exhale.

This is stable!

Professor Stephen on the stage also smiled inadvertently when he saw this.

Lu Zhou picked up the chalk and almost didn’t stop, and started writing directly in the blank space next to it.

[Suppose f=(y1, y2···, yn)^T. For i=1, 2···, n, we have:

y1/(2i)2-12+y2/(2i)2-32+···+y1/(2i)2-(2n-1)2=1 (1)

Suppose Q(t)=(t-12)(t-32)···(t-(2n-1)2),

With P(t)=y1(t-32)(t-52)···(t-(2n-1)2)

+y2(t-12)(t-52)···(t-(2n-1)2)

+···

+yn(t-12)(t-32)···(t-(2n-1)2)

(The items containing yk in P(t) do not include (t-(2k-1)2).)

By dividing both the left and right sides of the equation in (1), we can get:

P(22)=Q(22), P(42)=Q(42),..., P((2n)2)=Q((2n)2).] (The picture is in the chapter)

Seeing this, Professor Stephen couldn't help but nodded. Basically, this algebra problem is about to be solved.

Students who have scored full marks on the math test should know that math problems are actually quite easy. As long as you find the correct idea for solving the problem, there will basically be no problems later.

Zhang Lei looked at what Lu Zhou wrote and instantly patted the back of his head.

He said angrily: "Damn, why didn't I think of that!"

No matter what other people were thinking, Lu Zhou's chalking still didn't stop.

【therefore

S(t)=(t-22)(t-42)···(t-(2n)2).

thereby

P(t)=Q(t)-S(t)=···Shortly···

After getting the expression of P(t), you can get it by comparing the coefficients of the t^n-1 term: e^t·f=n(2n+1).】

Lu Zhou put down the chalk, turned around and said seriously to Professor Stephen:

"Professor, the answer to this question is n(2n+1)."

ps: All the formulas are typed by hand, which is too tiring...

There is another chapter today, please recommend and vote, please vote o(╥﹏╥)o