From small town academic to chief scientist

At this moment, the entire examination room was silent.

The students who originally answered a lot of real questions and listened to a lot of lectures by teachers did not start writing at all.

Inside I was all about who I was, where I was, and why I wanted to participate in the math competition.

Why are these math questions different from the previous ones, and why are they so much more difficult?

Even the first question, many people cannot understand the question.

There are six major questions in the entire test paper.

Questions 1, 2, 3 and 5 are all worth 15 points each, and question 46 is worth 20 points.

Generally speaking, students in the examination room only need to solve one question to get a prize, the third prize at the municipal level.

That’s right, you only need to solve one question to win the prize.

This was mentioned by Professor Tang Ping during class.

You can imagine how difficult the questions in the mathematics competition are.

Compared with practice questions, compared with the real questions in the postgraduate entrance examination for mathematics majors, it is more difficult than the so-called counting of one, two and three.

In addition, there are many big names participating this year, and the hand of the question maker is trembling, and the questions are much more difficult than in previous years.

At this moment, Li Xiaodong, the seventh-ranked academic in Class 1, was holding the paper and looking at the first question.

The first question:

[Suppose S is an ellipsoid in three-dimensional Euclidean space, P is a fixed point in the space, and P is not on S.

For any X ∈S, let X* be the midpoint of the line segment PX. Question: What is the trajectory formed by all such points X*? Justify your conclusion. 】

After reading it, I couldn't help but sigh, "Oh my god, these are some magical questions."

Why can’t I understand the meaning of some questions?

Am I really a math major?

Do I really know math?

Am I really suitable for this major?

Even when I asked the first question, I had no clue.

Many people used the topic to scold you. Who the hell do you know what your trajectory is?

I won’t do this question anymore, let’s move on to the next question.

I don’t believe I can’t know the next question!

Generally speaking, analytic geometry has the best scores and is also the simplest. If you cannot get any points for this question, it means that you will most likely miss the prize in this competition.

Of course, we do not rule out the possibility that people who are good at high-level math can get points from the questions about high-level math.

At this moment, in the quiet examination room, only the Book of Changes in the middle is written with vigour. How dare you come up with this kind of question?

The first big question requires no thinking, it’s an instant kill!

This time I didn’t think about Zhou Yi, I’m not good at it!

Zhou Yi made a crazy cry in his heart.

After writing hundreds of pages of papers and reading so many books, there was never a time when I didn’t need to think. Every time I thought about it, Zhou Yi realized that he had not yet reached the realm of teleportation. He was still a piece of cake.

But today, I, Zhou Yi, can finally let out a cry,

I don’t need to think, I’m not good at it!

The whole table made a sound when the signature pen was used.

Zhouyi directly wrote:

[Suppose the equation of the ellipsoid in the O-xyz rectangular coordinate system is x/a+y/b+z/c=1,

line break,

Set point P = (α, β, γ), then for any X = {x, y, z}∈ S, the meaning of the question is:

X*=1/2(X+P).;

Therefore, it can be seen that the curved surface formed by X* is an ellipsoid with the center point {α/2, β/2, γ/2)}. 】

Not long after, Zhou Yi wrote down the first answer eloquently.

Zhou Yi took a look at the neat rolled surface. There was no stain on it, and he immediately felt that it was perfect.

so easy!

When all the students in the examination room heard the sound of Zhou Yi writing, they all panicked in their hearts.

This boss doesn’t need to think about it.

Mr. Zhou, do you know that every time you write, the sound you make, and the answers you write are not answers to the test paper, but a torture of my soul.

Why am I such a badass?

We are in the same school, in the same math college, taught by the same teacher, and have the same scores. Why is the gap so big?

The crucial test paper didn't even give me multiple-choice questions, and it didn't even give me a chance to do metaphysics.

After Zhou Yi finished writing, he stopped writing. Everyone was relieved when they heard that Zhou Yi was not writing.

Fortunately, it seems that the question is still difficult, at least Mr. Zhouyi stopped writing and thinking.

Otherwise it would be too unreasonable.

Zhou Yi stopped writing only because he started to read the second question, rather than thinking about it.

The second question is about calculating integrals. This is a question about fractions.

[∫0 to +∞ (x-x+x^3-x^4-x^2018)/(x+1)^2021dx. 】

Zhou Yi has finished reading, and the ideas in his mind took shape instantly without thinking for a second.

Just pick up the pen and write,

[It is easy to know that I_k=∫0 to +∞, x^k/(1+x)^2021dx converges, so x=1/t can be set

It can be obtained from the linear operation of the integral that the integral is 0. 】

At this time, the sound of Zhou Yi writing down the pen made another sound appear in the silent examination room. Each sound seemed to be as heavy as a thousand stones, hitting the hearts of the twenty-nine candidates hard.

After writing the Book of Changes, continue reading the third answer question.

An advanced question, still an instant kill,

No difficulty.

The fourth question is still an algebra-oriented question. It is not difficult at all and will kill you instantly.

For four consecutive questions, Zhou Yi hardly stopped writing except for the pause when reading the questions.

Until the fifth question, analyze the questions inside together.

At this time, the students in the examination room breathed a sigh of relief again.

Now you can finally delay the time you stop writing in Zhouyi to more than 10 seconds.

Thankfully, it made me realize I'm not a loser.

Everyone guessed it from the three-second pause. It was probably because Zhou Shen was reading the question, so he stopped writing.

What does it mean that it has stayed for more than ten seconds now?

It shows that Zhou Shen also has issues to think about!

This fifth question also needs to be considered by top academics.

What does it mean to think about it?

Means dish!

I think, therefore I cook, a truth that has been spread forever in the Department of Mathematics.

So: I = food,

Zhou Shen = dish,

Derivation: I = God of Zhou!

Perfect logic, I am worthy of being a leader in mathematics.

The reason why Zhou Yi stayed for more than ten seconds was not because he was thinking, but because two ideas came to his mind instantly, indicating that there are two ways to solve the problem. So which one should he write?

Each one has its own merits, why not just write two?

What if it counts as a violation for me, but there are two ways not to write it down and not let me show off. I feel so uncomfortable.

After struggling for a while, Zhou Yi decided to write a method with less writing on the blackboard.

[Suppose the upper and lower limits are L and l respectively, then s＜l＜L＜1. According to the recursive formula,..., it can be proved that the limit exists, and the limit is equal to 2021^ (1/2021). 】

After finishing writing, Zhou Yi let out a long sigh,

well.

It's a pity that I don't dare to take the risk of writing two solutions, otherwise I would write both.

The second solution requires more writing on the blackboard and uses more methods.

First of all, the first step is to use mathematical induction. After getting the derivation, we need to use the monotonic bounded convergence theorem.

It is concluded that the convergence is 1, and finally the jia and b theorems must be used.

There are so many mathematical things used in this, and the amount of calculations is also large. It is really not worthwhile and a waste of my pen refills.

A pen refill costs one yuan. Wouldn't it be nice to buy a meat bun with this one yuan?

Zhou Yi immediately decided to eat a meat bun for lunch to reward his wit.

Use the least money to get the highest scores, get the biggest rewards, and get the strongest glory. This is very operational research.