Chapter 360

Chapter 363

when the message arrived at Cheng Nuo, he had already received an offer from Princeton.

As one of the top universities of mathematics department in the world, it is the dream of many mathematics lovers to be one of them.

The number of 13 fields award winners is the third in the world.

A lot of mathematics big cattle also teach in this school, academic exchange atmosphere is strong.

But Massachusetts Institute of technology in the United States is no worse.

In the newly released QS World University professional ranking in 2022, the two mathematics majors are third and fourth!

Although there are only six fields awards, that's only because they were founded late. And the fields awards, which are still teaching at present, are the same in two universities, with three in each.

Generally speaking, but from the mathematics major, the two universities are Lu Ben Wei.

For Cheng Nuo, it doesn't matter which one the two universities choose.

It's just that if you choose MIT, you'll get an additional position as assistant to the fields prize winner. With the suggestion of the professor above, Cheng Nuo thought about it for a while and then chose this option.

The premise, of course, is to stand out from a competitive group of 12.

Cheng Nuo has that confidence.

Those competitors, at most, have the level of doctoral students. If this kind of person still can't make sure, then what kind of force king is he?!

…………

After a week of preparation for the war, under the leadership of Professor Fang, Cheng Nuo came to a room for testing.

By the time Cheng Nuo entered, the other eleven had reached the full.

Cheng Nuo glanced faintly.

Seven men and three women are generally three or four years older than Cheng Nuo.

Especially the two boys, the top of the head has become a little bald, a look is not a good role to provoke.

The other three women doctors, almost in the same dress. Thick lenses, horsetail in the back of the head, plain face.

Cheng Nuo dignified to go to sit on as.

When Cheng Nuo looks at other opponents, others are also looking at Cheng Nuo.

After all, it is a real competitor. Twelve in one is quite cruel.

For Cheng Nuo, what surprised them most was their age.

At this age, should still be studying undergraduate? How to run here to compete with a group of doctoral students?

Is it By the back door?

But it shouldn't be. If you come in through the back door and let an undergraduate face a group of doctoral students, it's still useless!

Although the heart is puzzled, but no one is free to ask this.

Aggressive but confident eyes, one by one looking at each other.

Suddenly, the door was pushed open, and a man in a suit and a portly man came in carrying a briefcase.

He glanced at the classroom, found that all the people, then from the briefcase out of a pile of papers, one by one sent.

Taking the test paper, Cheng Nuo took a look.

There are only two questions in the whole paper.

It is a well-known theorem that the fewer questions, the higher the difficulty.

After the examination paper was issued, the man with a big stomach and a big stomach coughed and said slowly, "open book examination, the examination time is four hours, you can hand in the paper in advance!"

With that, he moved a chair to the front of the room and cocked up his legs to play with his mobile phone.

Cheng Nuo shrugged, spread the test paper on the desk in front of his chest and read it carefully.

Since it is such a test, there must be a considerable difference between the test items and the test items.

The difficulty is at least equal to the level of doctoral thesis.

After all, this is an assistant in selecting Professor Fresnel.

Suppose (n, g) is an N + 1-dimensional Riemannian manifold, M is its n-dimensional submanifold, and ψ is a given smooth function on n. Whether there is such embedding φ: m → n, so that f (x) = ψ.]

not only the questions are few, but also the questions stem is not short.

However, the difficulty is comparable to a lot of nonsense outside. The mathematical problems of setting situations and compiling stories are not in the same plane.

Seeing the topic at the first glance, Cheng Nuo has a feeling: This is a stubble!

Obviously, this is a problem in the domain of Riemannian manifolds.

Since Prof. Fresnel's major subject is geometry, it is reasonable to ask this question.

What is a Riemannian manifold?

In other words, the manifold is equipped with a symmetric positive definite second-order covariant tensor field, that is, a positive definite quadratic form is equipped on the tangent space of each point. Given the measurement, we can measure the length, the area, the volume, as in elementary geometry.

There is a natural metric DS ^ 2 = (DX) in n-dimensional Euclidean space_ 1)^2+...+(dx_ n)^2。 Its matrix representation is identity matrix.Submanifolds in Euclidean space naturally induce a metric. In the differential geometry of curves and surfaces, we regard curves and surfaces as Submanifolds in three-dimensional space, so we naturally endow them with metric structure.

Looking at the title of the test paper, Cheng Nuo thought deeply.

After reading the title, other players are taking out their mobile phones and searching for information in a hurry, but Cheng Nuo doesn't have to.

One is that it is impossible to find the correct answer on the Internet; the other is that all the information about Riemannian manifolds has been printed in his mind.

A week of preparation time, Cheng Nuo is not unprepared.

One minute, two minutes, three minutes

In his mind, Cheng Nuo's thoughts fly.

A group of formulas are combined in series to form a complete chain of proof.

Ten minutes later, Cheng Nuo's closed eyes slowly open.

Then, write.

Cheng Nuo is going to solve this problem with the predetermined curvature of Hypersurfaces of Riemannian manifolds.

The principal curvature of hypersurface φ (m) under induced metric is k = (K1, K2, K3 ）In particular, if f (k) = ∑ ki or F (k) = Πki.]

[suppose n = R ^ n + 1, when n is a curved Riemannian manifold, there exists an n-dimensional Riemannian manifold (m, D, σ ^ 2) and differentiable function H: I → R ^ 2, such that n = I * m, and the metric of N can be written as DS ^ 2 = DT ^ 2 + H ^ 2 】

…………

As time ticked by, Cheng Nuo also wrote a line of formula on the test paper.

The train of thought is in the brain, so Cheng Nuo writes fluently.

In the outsider's view, Cheng Nuo seems to have not thought about it, a formula leaps to paper.

There exists an n-dimensional manifold m and differential homeomorphism, where I = (a, b) is the development interval of R, a, B ∈ R 】

done, perfect!!

Excited, he subconsciously snapped a finger.

Then, several other people in the classroom looked at him, showing suspicious eyes.

Cheng Nuo put his hands together. After several people turned their heads, he shook his head and gently laughed.

To tell you the truth, if the elaboration process of this topic is expanded into a piece of thesis, it will not be a problem to participate in the graduation defense of graduate students.

In other words, Cheng Nuo spent more than half an hour on the research content of a doctoral student from half a month to a month.

This is hard power.

Cheng Nuo's mouth slightly tilted, looking at the second question.

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