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 the 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 understand 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 already entered the society, the perfect 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 who graduated from the same class, everyone knows each other more or less.
Especially the freshmen in the School of Physics. Many freshmen know that this year’s NTU Physics Department has a top scorer in the college entrance examination.
where Ω(A) is the set of features.”
"Considering the Banach algebra generated by A, B, I, we have that A is commutative, so we get:
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.
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.
"What are the important decompositions in linear map decomposition?"
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.
Chen Zhengping had greeted him two days ago, so he wanted to test Xu Chuan's basic mathematics skills.
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).
"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.”
For Xu Chuan, in the first few days of class, there were always girls coming to him and asking for wv and contact information because of his handsome appearance, which really caused him a lot of trouble.
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.
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
Already."
"Now 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).”
Although the textbook is not thick, with only eight chapters in content, it brought him a lot of knowledge and inspiration.
I had just taken out the book and hadn't read it for two minutes when a voice sounded 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.
Seeing Xu Chuan write out the answer smoothly, Zhou Hai was stunned for a while and then said: "Not bad, very solid foundation."
Because Emperor G passed away last year, that is, in November of 2014, and left the world forever to calculate mathematics for God.
This also made him sigh.
With that said, Xu Chuan turned over the paper for the quiz, picked up the pen and paper and wrote in the blank area.
The spectral radius of bounded linear operators can be calculated directly without thinking. This is a very solid foundation. I am afraid that most graduate students do not have such a solid foundation.
The various theorems in this book and information compiled by others are enough for a college student to spend most of a semester studying.
For example, "Factorization of Linear Operators and Geometric Properties of Banach Spaces" written by Pisier.
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.
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 smoothly.
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.
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.
In Xu Chuan's view, the most important part of this book is probably the introduction to Grothendieck's theorem.
After the freshman orientation ceremony, military training, and a series of tedious matters related to freshman enrollment, the campus of Nanjing University gradually entered a regular routine.
However, these contributions are simply insignificant in Emperor G's mathematical career, not even a drop in the bucket.
As for Xu Chuan, apart from his daily classes, he basically spent the rest of his time in the library.
""Factorization of Linear Operators and Geometric Properties of Banach Spaces"? Where did you see this book?"
"It's almost finished." Xu Chuan replied honestly.
And so far, there are still many ideas in Grothendieck's writings that are not fully understood.
There is a popular saying in mathematics majors: After learning real variable functions ten times, functional analysis will make you feel uncomfortable.
Both conceptual questions were answered fluently, which made Zhou Hai more interested and aroused his deeper curiosity, so he asked the question directly.
"Then how to judge whether a problem is a linear transformation?" Zhou Hai then asked.
Once again, since I have chosen to major in mathematics, I must lay a good foundation in mathematics and there are many things to learn.
G Huang’s wife is really too strong.
However, as time passed, everyone's enthusiasm dissipated and gradually calmed down.
You must know that functional analysis is a difficult course not only for undergraduates, but also for graduate students in mathematics.
"Spectral decomposition, polar decomposition and singular value decomposition."
Although Nanjing University is also a top university, it is undeniable that there is indeed a gap compared with the two T0-level universities, Shuimu P University.
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.
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.
The duality between continuity and discreteness, the Riemann-Loch-Grothendieck theorem, and the introduction of the concept of outlines reduce algebraic geometry to commutative algebra and topology.
Any one of the various great contributions would be enough for a mathematician to spend a lifetime studying and researching.
His mathematics is pretty good, but he is only strong in some areas, and is far less comprehensive and systematic than physics.
It is a pity that Xu Chuan could not meet the Pope of mathematics either before or after his rebirth.
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.
This shows how difficult this course is.
Zhou Hai is now really envious of Chen Zhengping. He has accepted a good student. He doesn't know his achievements in physics, but his mathematical ability is definitely not bad.
Why would such a student study physics? It would be great to study mathematics instead.