Chapter 69 Zhou Hai’s Appreciation
Xu Chuan came on stage, and there was a commotion in the gymnasium.
"Is this this year's top scorer?"
"So handsome! I'll ask for my wx number later!"
"Oh God, he's 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 Nanjing University."
“The Department of Physics at NTU is not bad either.”
The small exchanges in the gymnasium were buzzing. For ordinary people who have entered the society, the top scorer may not be that concerned. Even if it is on the hot search, it is probably just a glance.
But for high school students graduating from the same class, everyone knows more or less.
Especially the freshmen in the School of Physics. Many freshmen know that NTU’s Physics Department has a top scorer in the college entrance examination this year.
It's just that many people don't quite understand why this top pick came to Nanjing University instead of going to Shuimu and P University.
Although NTU is also a top university, it is undeniable that there is indeed a gap compared with the two T0-level universities, Shuimu P University.
After the opening ceremony for freshmen, military training, and a series of tedious matters related to freshman admission, the campus of Nanjing University has gradually entered a regular routine.
For Xu Chuan, in the first few days of class, there were always girls coming 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, apart from daily classes, he basically spent the rest of his time in the library.
In mathematics, he has a lot to learn, but most of it is not taught in undergraduate mathematics courses. 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, probability and statistics taught by the teacher in the freshman class, he had already completed them in high school.
His mathematics is pretty good, but he is only strong in some areas, and is far less comprehensive and systematic than physics.
Once again, since I choose to major in mathematics, I must 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 Spaces" from his schoolbag.
He borrowed this from the library and has been reading it for nearly a week. The rest of it will be finished in the next two days.
Although the textbook is not thick, with only eight chapters in content, 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 introduction to Grothendieck's theorem.
This also made him sigh.
Grothendieck is worthy of being the Pope in the field of mathematics. Not only his contributions to algebraic geometry are profound and profound, but his contributions to the field of functional analysis are equally huge.
The various theorems in this book and information compiled by others are enough for a college student to spend most of a semester studying.
However, these contributions are simply insignificant in Emperor G's mathematical career, not even a drop in the bucket.
The duality between continuous and discrete, the Riemann-Loch-Grothendieck theorem, and the introduction of the concept of outlines reduce algebraic geometry to commutative algebra and topology.
A random selection of various huge contributions would be enough for a mathematician to spend a lifetime studying and researching.
And there are still many ideas in Grothendieck's writings that are not fully understood to this day.
But this does not prevent it from producing many big results, such as Delin's proof of Weil's conjecture and the birth of K theory.
G Huang is really too strong. It is a pity that Xu Chuan could not 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 did you see this book?"
I had just taken out the book and hadn't read it for two minutes when a voice rang in my ears.
Xu Chuan looked up and saw that Professor Zhou Hai, who was presiding over the test, was staring at him with interest. To be precise, he was staring at the book in his hand.
"It's almost finished." Xu Chuan replied honestly.
"What are the important decompositions in linear mapping decomposition?"
Zhou Hai asked with great interest. He knew the student in front of him. He was a perfect scorer in the college entrance examination and a new student accepted by Academician Chen Zhengping of the Academy of Physics.
Chen Zhengping had greeted him two days ago, so he wanted to test Xu Chuan's basic mathematics 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 check whether for any element α, β in V and any k in the number field P, there is A(α+β)=A (α) + A (β) and A (kα) = kA (α) are enough. ”
Both conceptual questions were answered smoothly, which made Zhou Hai more interested and aroused his deeper curiosity, so he asked the question directly.
"Then there are two commutative operators A and B with their spectral radii r(A) and r(B). How to prove that the spectral radius of the commutative bounded linear operator on Banach space satisfies r(A+ B)≤r(A)+r(B)”
This was one of the questions in the postgraduate functional analysis course that he wrote to him a few days ago, and he didn't believe that the student in front of him could solve it successfully.
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 (Gelfand's theorem) to express it and you can solve it ”
With that said, Xu Chuan turned over the paper for the quiz, picked up the pen and paper and wrote in the blank area.
"Considering the Banach algebra generated by A, B, I, we have that A is 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 the set of features. ”
Watching Xu Chuan write out the answer smoothly, Zhou Hai was stunned for a while and then said: "Not bad, very solid foundation."
The spectral radius of bounded linear operators can be calculated directly without thinking. This 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 functional analysis is a difficult course not only for undergraduates, but also for graduate students in mathematics.
There is a popular saying in mathematics majors: After learning real variable functions ten times, functional analysis will make you feel uncomfortable.
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 mathematics department of a normal university offered elective courses on functional analysis and real variable functions. As a result, no one in the class passed.
This shows how difficult this course is.
Zhou Hai really envied Chen Zhengping now. He had accepted a good student. He didn't know his achievements in physics, but his mathematical ability was definitely not bad.
Why would such a student study physics? It would be great to come and learn mathematics.
A little late, sorry.