Chapter 718： 1 "easy" algebra problem

"Elder, do you think who will be the teacher who will come to teach us later?"

"How would I know……"

Lu Zhou gave Zhang Lei a blank look, and really didn't want to deal with this wisdom.

This is the first time to come to MIT, how could he know who the teacher is to teach them!

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

"Tianyu, you..."

"roll!"

After eating twice in a row, Zhang Lei calmed down embarrassedly, stroking the student ID card lightly in his hand, feeling very proud.

The US university student card is actually equivalent to the domestic campus card. The upper left corner of the front is the big three letters "MIT", followed by the English spelling "MassachusettsInstituteofTechnology".

It is divided into two parts below, the student's name and MITID on the left, and the one-inch photo on the right.

Behind the card are barcodes, entries, and other information.

This is the MIT student ID card!

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

[The texture of this card is so-so, I feel it is more comfortable to touch with the school's one, alas, let's use it for the time being. Figure.JPG]

A few minutes after it was sent out in the circle of friends, more than a dozen reminders appeared, and a group of them were scolding Zhang Lei for holding a cup.

Before class, in addition to Zhang Lei, who was still playing with his mobile phone, the other 7 were either nervously waiting for the teacher's arrival, or scribbling questions like Lu Zhou.

Until the time is approaching 10 o'clock.

A white-haired old man walked in at the door of the classroom. Even in the weather in July, 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 at everyone and said loudly: "Good morning, classmates, I am Sean Stephen, the teacher in charge of teaching you [Algebra and Number Theory]. You can call me Professor Stephen directly." (Stephen is The first name is not the last name, it can only be wrong...)

With that, he turned around and picked up the chalk to write his name and mailbox on the blackboard.

Most of MIT's courses are similar to those in China, using PPT projection to assist teaching, but the mathematics courses are different, mainly relying on chalk blackboards.

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

For some reason, I always feel that this Professor Stephen sounds familiar?

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

But it wasn't a big deal, and Lu Zhou quickly put it behind him.

After all, this is the first class, and the first thing to do is to introduce myself.

Eight students from Guanghua University introduced themselves in English in turn.

A few students spoke first, and until Lu Zhou, Professor Stephen's attention was instantly attracted.

With a smile on his face, his eyes fell on Lu Zhou, as if he was looking at something.

Since it is at MIT, the whole course is taught in English. Fortunately, when the previous list came out, the school conducted intensive English training for this group of students selected for the summer program.

It's still a bit difficult, but I can still understand it anyway.

Time continued to pass, and it was already more than an hour in the blink of an eye.

I have to say that this Professor Stephen is indeed very high-level, and he explained the knowledge points of algebra and number theory very flatly and straightforwardly.

Professor Stephen glanced at his watch, then smiled, "I'll give you an algebra problem at the last minute."

Lu Zhou picked it up and looked at the blackboard attentively. With the sound of chalk rubbing, the topics 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, in which the elements of the i-th row and the j-th column are aij=1/(2i)2-(2j-1)2, and let the n-dimensional column vector f satisfy Af=e, find e^t·f. ] (The picture is said in the chapter)

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

Lu Zhou looked at the question, and began to deduce crazy in his brain.

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

"Any classmates who want to come and solve the problem?" Stephen laughed.

Zhang Lei was just about to move, but he didn't have any ideas for solving the problem!

He turned his head to look at Zheng Tianyu beside him, perhaps sensing Zhang Lei's gaze, Zheng Tianyu raised his head and looked at each other.

Seeing Zheng Tianyu shaking his head slightly, Zhang Lei's heart froze for the most part.

There are two summer programs at Guanghua University. 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 know how to do this, wouldn't it be a loss of face for the school?

Guanghua's ability to connect with MIT is entirely because of the principal's face.

Don't let MIT people look down on our Guanghua University students!

And the only hope...

Zhang Lei gritted his teeth and looked in Lu Zhou's direction inwardly. Seeing Lu Zhou raised his hand, he couldn't help but let out a breath.

It's stable now!

Professor Stephen on the stage also smiled inadvertently.

Lu Zhou, who picked up the chalk, hardly stopped, and started writing directly in the blank space next to him.

[Let 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)

Let 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 term in P(t) that contains yk does not contain (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 figure is said in the chapter)

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

Students with full marks in the math test should know that math problems are actually quite easy.

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

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

No matter what other people think, Lu Zhou's chalk still hasn't stopped Therefore

S(t)=(t-22)(t-42)...(t-(2n)2).

thereby

P(t)=Q(t)-S(t)=・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・—

After obtaining the expression of P(t), by comparing the coefficients of the t^n-1 term, we can get: 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 all hand-typed, it's too tiring...

There is one more chapter today, asking for a recommendation ticket, asking for a monthly ticket o(╥﹏╥)o