Rapidly Settling In
"Mathematical Physics, a magical and wonderful world." Muller nodded in approval, expressing satisfaction with Shen Qi's choice of Depth.
"And what about the auxiliary direction?" Muller asked again.
As is customary in Princeton University's Mathematics Department, after students choose their major, they also need to determine a secondary research area, namely Breath.
Shen Qi's Breath should naturally be in Professor Muller's area of expertise. In addition to Mathematical Physics, Professor Muller also has considerable strength in Algebraic Geometry, number theory, and Group Theory.
Shen Qi immediately made a decision. "I choose Algebraic Geometry as my secondary direction."
"Algebraic Geometry, a magical and wonderful world." Muller nodded in approval, also expressing satisfaction with Shen Qi's choice of Breath.
The German old man had a limited English vocabulary, and the words "magical" and "wonderful" appeared frequently in his speech.
"Mathematical Physics and Algebraic Geometry very profound fields. I admire your courage, young man." Muller's first meeting with Shen Qi took place in a friendly and harmonious atmosphere.
"I also Muller Mr. Muller's extensive knowledge and academic achievements, after all, you are a renowned professor who teaches Mathematical Physics and Algebraic Geometry," Shen Qi said.
"I originally thought you would choose number theory," Muller said.
Shen Qi replied, "My girlfriend studies number theory; I can't take her job."
"That's a very good reason! What a wonderful and magical couple." Professor Muller gave Shen Qi a thumbs up. His personality didn't seem like that of a German; he was more like a Frenchman or an Italy.
"Would you like a cup of coffee? Sugar, please?" Muller picked up the coffee pot and offered Shen Qi a cup of coffee. They chatted amiably.
"Regular drinking water is fine, thank you," Shen Qi said Shen Qi. "I just arrived in the United States and I'm not used to drinking coffee."
"Alright then, plain water is healthier." Muller poured Shen Qi a glass of plain water.
Shen Qi had never met such a kind and easy-going German.
Of course, Shen Qi hadn't met many Germans. When he was studying at Yenching University, he met a German exchange student who had a rigid, poker-faced expression and was meticulous and self-disciplined.
"Professor Muller, what should I do next?" Shen Qi asked.
Muller typed Shen Qi's information into the computer and said after a while, "You need to earn 45 credits each semester. When you have 225 credits, you will have a Master's degree in the Princeton Mathematics Department. Then you can choose to pursue a PhD with me, or with another advisor, no problem."
"So I need five semesters to earn enough credits."
"Normally it doesn't take that long; three to four semesters is the average time to get a master's degree. The fastest record here is held by Tao and Yun, who both got their master's degrees in two semesters and then went on to pursue their doctorates. Shen, you should have heard of Tao and Yun, right?"
"Of course." Shen Qi nodded. Tao refers to Terence Tao, and Yun refers to his senior brother Yun Wei.
Having met with my advisor and chosen Depth and Breath, I need to complete 225 graduate credits as soon as possible, then pursue a PhD.
Shen Qi knew exactly what he needed to do next.
The Mathematics Department admitted a total of 12 graduate students this fall, including 3 from the United States and 9 from 9 different countries around the world.
Princeton Mathematics Department is quite selective in its admissions process, admitting only a small number of graduate students each season. Shen Qi is the only student from all over China to pursue a master's degree there.
All 12 Mathematics Department students admitted this fall are male; there are not a single female student.
Princeton has strict admission requirements, and it's even stricter for female students.
It's unexpected that the phenomenon of favoring sons over daughters would occur in the United States, a country that prides itself on democracy and equality, especially at Princeton, which is ranked No. 1 in the country.
Whether she's an undergraduate, graduate, or doctoral student, if she's a girl, she must be exceptionally outstanding, world-classly outstanding.
Shen Qi and the other graduate students in the Mathematics Department who enrolled at the same time all had advisors, and they also needed to attend classes.
Simply attending classes and taking exams, or just doing research projects and writing papers, is not enough to earn the required 225 graduate credits.
The combination of attending classes and writing papers is what Mathematics Department graduate students will be required to complete, with a maximum of five semesters and a minimum of one semester (theoretically).
The current fastest record is two semesters, jointly held by Terence Tao and Yun Wei.
Designed by the renowned Chinese-American architect I. M. Pei, the Spelman Hall is a teaching building where most of the Mathematics Department's graduate courses are held.
In one of the classrooms in the Spelman Hall, a class on Algebraic Geometry was being taught. Ten students, all graduate students in the Mathematics Department, were seated in the classroom.
Shen Qi was also here; this was his first class after arriving at Princeton.
Algebraic Geometry was Shen Qi's Breath, and he selectively chose to attend this course.
The ten Mathematical Research in the classroom had enrolled in different years and seasons.
There is no strict distinction between first-year and second-year graduate students here. It is all based on a mentor system, and graduate students can choose which courses to take based on their own needs.
"As we all know, for an m-th degree algebraic surface with isolated and ordinary polycentric lines, a certain m-4-th degree surface should act as an m-3-th degree adjoint curve on an m-th degree curve." The professor of Algebraic Geometry paused here, tapped the blackboard, and said, "If we want this double integral to remain finite in the two-dimensional domain of the four-dimensional surface, how should we do it?"
Professors ask questions, students discuss – this is the Princeton teaching model.
"Clearly, Q is an m-4 degree polynomial, and Q=0 is an adjoint surface," a Canadian graduate student said.
"Let me add that there is a multiline passing through f=0, and at every k-order multiline where f=0 there is a multiline of at least order k-1," an Israeli graduate student added.
"Wow, that's a very good argument." The professor, a Romanian, applauded.
There was one professor and ten students in the classroom, only one of whom was American. This is a characteristic of Princeton University's Mathematics Department: there are more foreigners than Americans.
"Experts, they're all experts," Shen Qi smiled slightly. "The Canadians and Israelis are quick-witted, sharp-minded, and logically rigorous. They've said everything I wanted to say."
"Then I'll add something," Shen Qi chimed in, "The first kind of double integral is similar to the first kind of Abel integral; we just need to substitute N=m-4."
"Very good!" the Romanian professor praised Shen Qi, then asked, "Child, what's your name?"
"Shen Qi."
After finishing this Algebraic Geometry class, Shen Qi immediately went to listen to a class on the analysis of Navier-Stokes equations, a course in the field of Mathematical Physics.
"Your answer is perfect. What's your name?" the professor of the Navier-Stokes equations asked.
"Shen Qi."
Then, Shen Qi went to attend a number theory class, since there were no other Mathematical Physics, or Algebraic Geometry classes that day.
"May I have your name?"
"Shen Qi."
"May I have your name?"
"Shen Qi."
In the week or so after the start of the semester, Shen Qi listened to all the courses that Mathematics Department graduate students could attend. He listened attentively, actively participated in class discussions, rarely made mistakes, and presented clear and logical viewpoints, leaving a deep impression on the professors of many courses.