Great Country Academician

When Xu Chuan took the stage, there was a commotion in the gymnasium.

"Is this this year's top scorer?"

"So handsome! I'll ask for the wx number later!"

"My God, I'm still alive!"

"If I were the top scorer in the college entrance examination, I would go to Shuimu P University. I don't know why I came to Nantah University."

"The Physics Department of Nantah University is not bad either."

The humming of small exchanges in the gymnasium, for ordinary people who have entered the society, the top scorer may not pay much attention to it, even if it is on the hot search, it is probably just a glance.

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

Especially the freshmen of the School of Physics, many freshmen know that there is a top scorer in the physics department of Nantah University this year.

It’s just that many people don’t quite understand why this kind of champion came to Nanjing University instead of going to Mizuki and P University.

Although Nantah University is also a top university, it is undeniable that there is indeed a gap compared with the two T0-level institutions of Shuimu P University.

After the freshman opening ceremony, military training, and a series of tedious tasks for freshman enrollment, Nantah University's campus has gradually entered into a normal state.

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

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

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

In terms of mathematics, he has a lot to learn, but most of them are not taught in mathematics courses at the undergraduate level. Many materials and textbooks can only be found in the library.

For example, "Factorization of Linear Operators and Geometric Properties of Banach Spaces" written by Pisier.

As for the calculus, linear algebra, and probability statistics that the teacher explained in the freshman class, he had already learned them in high school.

His mathematics is not bad, but he is only strong in some fields, far less comprehensive and systematic than physics.

Once you are born again, since you choose to major in mathematics, you have to lay a good foundation in mathematics, and there are many things to learn.

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

He borrowed this from the library, and he has been looking at it for nearly a week, and the rest can be finished in two days.

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

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

This also made him sigh.

Grothendieck deserves to be the pope of mathematics, not only for his extensive and profound contributions in algebraic geometry, but also for his contributions in the field of functional analysis.

Just the various theorems in this book compiled by other people is enough for a college student to study for most of the semester.

However, these contributions are simply insignificant in Emperor G's mathematical career, not a drop in the bucket.

The duality of continuous and discrete, the Riemann-Loch-Grotendieck theorem, the introduction of the concept of outlines to reduce algebraic geometry to commutative algebra, topology.

Randomly picking out one of the various great contributions is enough for a mathematician to spend a lifetime studying and researching.

And so far, there are still many ideas in Grothendieck's writings that are not fully understood.

But this does not prevent it from producing many great results, such as Deling's proof of Weil's conjecture and the birth of K theory.

Emperor G is really too strong.

It is a pity that Xu Chuan was unable to meet the pope of mathematics either before or after his rebirth.

Because Emperor G passed away last year, that is, in November of 2014, and left the world forever to calculate mathematics for God.

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

Just after taking out the book and not reading it for two minutes, a voice rang in my ear.

Xu Chuan looked up and found that it was Professor Zhou Hai who was in charge of the test, and he was staring at him with interest at the moment. To be precise, he was staring at the book in his hand.

"It's almost over." Xu Chuan replied honestly.

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

Zhou Hai asked with great interest, he knew the student in front of him, a perfect scorer in the college entrance examination, and a new student accepted by Academician Chen Zhengping of the Chinese Academy of Sciences.

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

"Spectral Decomposition, Polar Decomposition and Singular Value Decomposition."

"Then how to judge whether a problem is a linear transformation?" Zhou Hai then asked.

"For a transformation A in the linear space V, to verify whether it is a linear transformation, just look at whether there is A(α+β)=A for any element α, β in V and any k in the number field P (α)+A(β) and A (kα)=kA(α) are enough.”

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

"Now there are two commutative operators A and B whose spectral radii r(A), r(B), how to prove that the commutative bounded linear operator spectral radius on Banach space satisfies r(A+ B)≤r(A)+r(B)."

This was one of the topics in the graduate functional analysis course he wrote to him a few days ago, 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 sub-algebra where the elements are located, so we only need to consider the commutative Banach sub-algebra generated by A and B, and use Gelfand (Gelfand's theorem) to express it and then solve it. gone."

With that said, Xu Chuan turned over the draft paper of the small test, picked up a pen and paper and wrote in the blank area.

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

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 the set of features. "

Watching Xu Chuan write out the answer smoothly, Zhou Hai was stunned for a while before saying, "Not bad, very solid foundation."

The spectral radius of the bounded linear operator can be directly calculated without thinking. This is more than a solid foundation. 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 an undergraduate course, but also a difficult course in graduate mathematics.

There is a saying in the mathematics major: ten times of real variable functional analysis, functional analysis is chilling.

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

A few years ago, the Department of Mathematics of a normal university once offered elective courses of functional analysis and real variable functions, but none of the class passed.

The difficulty of this course can be seen.

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

How can such a student study physics? How nice to learn math.

A little late, sorry.