universal data

Chapter 420 Closing Essay
423 chapter

Cambridge University, this is a school that is not weaker than the Massachusetts Institute of Technology in terms of the overall strength of the school or the single-subject ranking of mathematics.

According to the 2021 QS World University Rankings for Mathematics, the University of Cambridge ranks second.

The Massachusetts Institute of Technology came in third.

Professor Hans from Cambridge University, Professor Fresnel did not know this person, but he must be an unusual person to be invited by Professor Masi to this dinner.

What's more, the information of all the faculty and staff of Cambridge University is public on the Internet, and it is easy to find out that there is no need for this person to deceive.

Since Cheng Nuo had the idea of ​​not being limited to one place and studying in another place, Cambridge University in Yingguo was undoubtedly a good choice.

"Cheng Nuo, what do you think?"

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

Going to Cambridge University as an exchange student?

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

A look of joy appeared on Professor Hans' face.

He grabbed Cheng Nuo's hand and said kindly, "Student Cheng Nuo, on behalf of our school, you are welcome to come and communicate."

When Cheng Nuo, a talented and diligent student, came to their school, it might bring a lot of new atmosphere.

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

Professor Fresnel nodded, "Set the exchange time for the next semester? I'm afraid it will be too late, and Cheng Nuo will no longer need to go to Cambridge for exchange."

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

"I'm also looking forward to the arrival of the exchange students from your school." Fresnel smiled lightly.

The two raised their wine glasses, touched each other, and smiled at each other.

…………

After Christmas, Cheng Nuo's life returned to normal.

The exchange students will 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's time at MIT was not too long, Professor Fresnel did not arrange new projects for Cheng Nuo.

So Cheng Nuo's daily routine was to slowly come to the office during working hours and help other assistants answer small questions. When no one asked him for help, he sneaked into the school library to read books.

Although the last research topic was exhausted physically and mentally under such high pressure, Cheng Nuo's harvest was undoubtedly quite huge.

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

Anyway, Professor Fresnel, a big boss, is by my side, and sometimes I can ask for some questions that I don't understand.

Professor Fresnel, because Cheng Nuo was about to leave him for half a semester, naturally told him everything he knew.

Just like that, Cheng Nuo felt that his math 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 approved by the school, and the other is carried out by teachers alone.

The format of the end-of-course examination is determined by the instructor.

There are generally two types: class tests and final papers.

Cheng Nuo's choice of basic mathematics did not require any required courses, but there were still credit requirements. At the beginning, Cheng Nuo directly chose courses that required half of the credits at the graduate level.

If you count it down, there are ten courses.

Although there are many courses, it is enough that Cheng Nuo has not attended a few courses.

He also has no time. Since the beginning of school in September, he has been wandering between one topic after another, and even found 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 fortunately, the teachers don't care about these.

MIT is a fairly free school. It will not force you to sit on the seat to attend lectures, but will submit an application for withdrawal when you fail many subjects.

There are ten courses, three of which are in-class tests in the last week of the course, and the other seven courses need to submit end-of-course papers.

Cheng Nuo still prefers the form of exams to final papers.

why?
That's seven papers? !
Although it was just a final paper, the quality requirements were not as high as SCI papers, but with such a large number and strict rules on the number of words, Cheng Nuo also had a headache.

In the library, Cheng Nuo was sitting by the window, flipping through the brand-new "Algebra of Group Theory", writing and drawing something on the side of the paper.

This book was one of the ten courses he took this semester. In Cheng Nuo's impression, it seemed that he showed up in one class and was absent from the remaining dozen classes.

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

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

It's just a simple end-of-class paper. With his current level of mathematics, Cheng Nuo can naturally finish one in one day.

But a paper written in this way has no soul!
Cheng Nuo wouldn't do this unless he really didn't have time, but now, Cheng Nuo, who didn't have any projects to deal with, could say he had plenty of time.

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

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

After deciding on the topic of the thesis, Cheng Nuo first did the calculations on the draft paper, then turned on the laptop and tapped on the keyboard.

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

And in order to further explain the structure of U, a graded associative algebra G related to U and a graded associative algebra on L are defined: τ-symmetric algebra S, and by constructing a representation ψ of τ-Lie algebra L, the Lie The important result of general enveloping algebra—PBW theorem, is extended to τ-Lie algebra, and the PBW theorem of τ-Lie algebra is obtained: graded associative algebras G and S are isomorphic.

The algebra problem that Cheng Nuo discussed was not a cliché, but a research content determined according to the latest trends in the subject after listening to the conversations of several bigwigs after the dinner.

(End of this chapter)