Chapter 423

The University of Cambridge is a school that is not weaker than the Massachusetts Institute of Technology in terms of the overall strength of the school or the ranking of individual subjects in mathematics.

According to the 2021 QS World University Rankings by Subject - Mathematics, the University of Cambridge is ranked second.

The Massachusetts Institute of Technology (MIT) is in third place.

Professor Hans from Cambridge University, Professor Fresnel did not know this person, but to be qualified to be invited to this dinner by Professor Maas is certainly not an ordinary person.

Moreover, the information of all the faculty and staff of Cambridge University is published on the Internet, and it is clear that there is no need for this person to deceive.

Since there is an idea of letting Cheng Nuo not be confined to one place and study in another place, then Cambridge University in Yingguo is undoubtedly a good choice.

"Cheng Nuo, what do you think?"

Although Professor Fresnel had this idea in his mind, he still needed to consider Cheng Nuo's opinion in the end.

Go to Cambridge as an exchange student?

Cheng Nuo touched his chin, groaned for a while, and finally nodded slowly, "I have no opinion!"

A gimmicked look of joy crossed Professor Hans's face.

He shook Cheng Nuo's hand violently and said kindly, "Cheng Nuo, on behalf of our school, I welcome you to come and communicate." ”

When Cheng Nuo, a talented and hard-working student, comes to their school, it may bring a lot of new atmosphere.

Professor Hans said to Professor Fresnel, "Mr. Fresnel, I will immediately contact the school to confirm the specific matters related to the exchange students, and our school will also send an excellent graduate student to exchange with Cheng Nuo." ”

Professor Fresnel nodded, "Decide the exchange time for the next semester, I'm afraid it's too late, and there will be no need for Cheng Nuo to go to Cambridge for the exchange by then." ”

Hans was stunned for a moment, and then suddenly suddenly. He shrugged his shoulders and smiled, "No problem. I hope to see Cheng Nuo in the classroom at Cambridge University next year. ”

"I am also looking forward to the arrival of your exchange students. Fresnel smiled indifferently.

The two raised their glasses and touched them, looking at each other and smiling.

............

As soon as Christmas passed, Cheng Nuo's life returned to normal.

Exchange students go to Cambridge University in the second half of the semester, and Cheng Nuo still has some time to prepare.

Just finished a "big" project, and Cheng Nuo did not stay at MIT for a long time, Professor Fresnel did not arrange a new project for Cheng Nuo.

So Cheng Nuo's daily routine is to come to the office slowly and leisurely at work time, help several other assistants answer small questions, and after seeing that no one is looking for help, he sneaks to the school library to eat books.

In the previous research topic, under that kind of high pressure, although he was physically and mentally exhausted, Cheng Nuo's harvest was undoubtedly quite huge.

Taking advantage of this free time, Cheng Nuo was also able to absorb and consolidate again.

Anyway, there is Professor Fresnel by his side, and sometimes some questions that he doesn't understand can be asked at any time.

And Professor Fresnel is naturally knowing everything because Cheng Nuo is about to leave him for half a semester.

In this way, Cheng Nuo felt that his mathematical level was improving at a speed visible to the naked eye.

............

Graduate students at the Massachusetts Institute of Technology do not have a final exam, but a final exam. The difference between the two is that one is officially agreed by the school, and the other is carried out by the teacher alone.

The format of the final exam is determined by the instructor.

There are two main types: in-class tests and final papers.

Cheng Nuo's choice of basic mathematics direction, there are no compulsory courses, but there are still credit requirements, so Cheng Nuo directly chose the courses that need to be taken half of the credits at the graduate level.

If you do the math, there are 10 courses.

Although there are many courses, I haven't been to a few classes.

He also didn't have time, since the beginning of the school year in September, he has been wandering between one topic after another, and he also took time to go to the International Congress of Mathematicians in the middle.

So much so that Cheng Nuo didn't know which professor was the teacher of which course.

But luckily, the instructor doesn't care about that.

MIT is a fairly liberal school, and it will not force you to sit in your seat, but will just submit a withdrawal application if you fail multiple subjects.

Of the 10 courses, three are tested in the last week of the course, and the other seven courses require a final thesis.

Compared with the final paper, Cheng Nuo still prefers the form of the exam.

Why?

That's seven papers?!

Although it is only a final paper, the quality requirements are not as high as SCI papers, but there are so many quantities and hard rules on the number of words, which makes Cheng Nuo also have a headache.

In the library, Cheng Nuo sat by the window, looking at the brand-new "Group Theory Algebra", writing and drawing on the paper on the side.

This book is one of the ten courses he took this semester, and in Cheng Nuo's impression, it seems that he showed his face in one class, and the remaining dozen classes were all absent.

But this is not an undergraduate level, it is not an exaggeration, this kind of course, Cheng Nuo has no need to listen to it at all.

Perhaps, it would be fine to just let him stand on the podium and give a lecture.

It's just a simple final paper, and Cheng Nuo, with his current level of mathematics, can naturally complete one in one day.

But a paper written in this way is soulless!

Unless there is really no time, Cheng Nuo will not do this, but now, Cheng Nuo, who does not have any problems on his side, can say that he has a lot of time.

So, Cheng Nuo came to the quiet place of the library and started his work.

"Group Theory Algebra" is a course of algebra, Cheng Nuo first spent more than an hour to comb through more than 100 pages of textbooks from beginning to end, write down important knowledge points, and after pondering for a while, he chose an entry point as the title of the final paper: "Universal Envelope Algebra of τ-Lie Algebra and Its PB Theorem".

To determine the topic of the paper, Cheng Nuo first performed the calculations on the scratch paper, then opened the laptop and crackled on the keyboard.

In the paper, Cheng Nuo discusses a class of generalized Lie algebras as generalizations of Lie algebras, Lie superalgebras, and ε Lie algebras: τ-Lie algebras and the universal envelope algebra U on τ-Lie algebra L.

In order to further explain the structure of U, this paper defines the split-conjunctive algebra G and L related to U: τ-symmetric algebra S, and by constructing a representation ψ of τ-Lie algebra L, the PB theorem, an important result of universal envelope algebra about Lie algebras, is extended to τ-Lie algebra, and the PB theorem of τ-Lie algebra is obtained: the sub-conjunctive algebra G and S are isomorphic.

The algebra problems discussed by Cheng Nuo are not clichés, but the research content determined according to the latest trends in the discipline after listening to the conversations of several bigwigs after that dinner.