Xu Chuan came to power, and there was a commotion in the gymnasium.

"Is this this year's perfect score god?"

"So handsome! I'll go and ask for the WX number later! ”

"Oh, I'm still alive!"

"If I get the top score in the college entrance examination, I will go to Shuimu P University, I don't know why I came to NTU."

"The physics department of NTU is not bad."

The small exchanges in the gymnasium are buzzing, and for ordinary people who have entered the society, the perfect score champion may not be so concerned, even if it is on the hot search, it is probably just a glance.

But for the high school students who graduated in the same class, everyone knows more or less.

Especially for the freshmen of the School of Physics, many freshmen know that the Department of Physics of NTU has a perfect score in the college entrance examination.

It's just that many people don't quite understand why this kind of champion didn't go to Shuimu and P University but came to Nanda.

Although NTU is also a top university, it is undeniable that there is indeed a gap between it and Mizuki P University, two T0-level universities.

.......

After the opening ceremony of the freshmen, the military training, and a series of tedious things for the admission of the freshmen, the campus of NTU has gradually entered the formal middle school.

For Xu Chuan, in the first few days of class, there were always girls who came over to ask for wv and contact information because of his handsome appearance, which really caused him a lot of trouble.

However, as time passed, everyone's enthusiasm dissipated and gradually calmed down.

As for Xu Chuan, in addition to his daily classes, he basically spent the rest of his time in the library.

In mathematics, he has a lot of things to learn, but basically he doesn't teach in mathematics classes at the undergraduate level, and many materials and textbooks can only be found in the library.

For example, Pisier's "Factorization of Linear Operators and the Geometric Properties of Banach Spaces".

As for the calculus, linear algebra, and probability statistics taught by the teacher in the freshman class, he had already finished learning them in high school.

His mathematics is okay, but his strength is only in some areas, and it is far less comprehensive and systematic than physics.

Once reborn, since you choose to major in mathematics, you have to lay a good foundation in mathematics and have a lot to learn.

......

In the classroom, after completing the differential test in his hand, Xu Chuan found out "Factorization of Linear Operators and the Geometric Properties of Banach Space" from his school bag.

This is what he borrowed from the library, and he has been looking at it for nearly a week, and the rest will be almost ready in two days.

Although the textbook is not thick and the content is only eight chapters, it brings him a lot of knowledge and inspiration.

In Xu Chuan's view, the most important part of the book is probably the introduction of Grothendieck's theorem.

This also made him sigh.

Grothendieck is the Pope of mathematics, not only in the field of algebraic geometry, but also in the field of functional analysis.

The theorems in this book compiled by others alone are enough for a college student to spend most of the semester studying.

However, these contributions are simply insignificant in Emperor G's mathematical career, and they are nothing at all.

The duality of continuity and discreteness, the Riemann-Loch-Grothendieck theorem, the introduction of the concept of generalizations to reduce algebraic geometry to commutative algebra, topological theorem, ......

Any one of the great contributions of all kinds is enough for a mathematician to spend a lifetime studying and researching.

And to date, there are still many ideas in Grothendieck's writings that have not been fully understood.

But this does not prevent it from producing many big results, such as the Delin proof of the Wey conjecture and the birth of the K theory.

Emperor G is really too strong.

It's a pity that neither before nor after his rebirth, Xu Chuan was unable to meet the pope of mathematics.

Because Emperor G had passed away last year, that is, in November of the 14th year, he left the world forever to calculate mathematics for God.

......

"Factorization of Linear Operators and the Geometric Properties of Banach Spaces"? Where did you read this book? ”

I had just touched the book out and hadn't read it for two minutes when a voice sounded in my ears.

Xu Chuan looked up and saw that it was Professor Zhou Hai, who was presiding over the test, and he was staring at him with interest at the moment, to be precise, at the book in his hand.

"I'm almost done." Xu Chuan replied honestly.

"What are the important decompositions in linear mapping decomposition?"

Zhou Hai asked with interest, he knew the student in front of him, a full-score player in the college entrance examination, and a new student admitted by Academician Chen Zhengping of the Academy of Physics.

Chen Zhengping also greeted him two days ago, so he wanted to test Xu Chuan's basic mathematical skills.

"Spectral decomposition, polar decomposition, and singular value decomposition."

"So how can you tell if a problem is a linear transformation?" Zhou Hai then asked.

"For a transformation A in linear space V, to verify whether it is a linear transformation, it is sufficient to see whether any element in V α, β and any k in the field P, have A(α+β) = A(α) + A(β) and A (kα) = kA(α)."

The two conceptual questions were answered fluently, which made Zhou Hai more interested and aroused his deeper curiosity, so he directly came up with the question.

"Then there are now two commutative operators A and B, their spectral radius r(A), r(B), how to prove that the spectral radius of the exchangeable bounded linear operator in Banach space satisfies r(A+B)≤r(A)+r(B)."

This was one of the questions he had written to him a few days ago in a course on functional analysis for graduate students, and he didn't believe that the student in front of him could solve it smoothly.

Xu Chuan thought for a while and said: "The spectral radius has nothing to do with the Banach subalgebra where the element is located, so you only need to consider the commutative Banach subalgebra generated by A and B, and use Gelfand's (Gellfand's theorem) to represent it. ”

As he spoke, Xu Chuan turned over the manuscript paper of the quiz, picked up the pen and paper and wrote it in the blank space.

"Considering the Banach algebra generated by A, B, I, we have A commutative, so we get:

σ(A)={τ(A):τ∈Ω(A)}，σ(B)={τ(B):τ∈Ω(A)}

......

⇒r(A+B)=sup{τ（A+B）：τ∈Ω(A)≤r（A）+r（B）。

where Ω (A) is a collection of features. ”

Watching Xu Chuan write out the answer smoothly, Zhou Hai was stunned for a while, and then said, "Yes, very solid foundation." ”

The radius of the bounded linear operator spectrum can be calculated directly without thinking, which is not only a solid foundation, but I am afraid that most graduate students do not have such a solid foundation.

You must know that the course of functional analysis is not only in the undergraduate, but also in the graduate mathematics, which is a difficult course.

There is a saying in mathematics majors: real variable functions are studied ten times, and functional analysis is chilling.

Therefore, functional analysis is also known as quantum mechanics in mathematics, and it is difficult for ordinary college students to learn this course, let alone use it freely.

A few years ago, the mathematics department of a normal university once offered an elective course on functional analysis and real functions, but no one in the class passed.

You can see the difficulty of this course.

Zhou Hai is really envious of Chen Zhengping now, he has accepted a good student, he doesn't know his achievements in physics, but his mathematical ability is definitely not bad.

How can such a student study physics? How good it is to learn math.

.......