Princeton is not alone in its Fields Medal winner.

It is not uncommon for students to be taught by Fields Medal winners in the classroom.

The classrooms of the winners of the Fanfei Award are basically full, and Shen Qi's functional analysis class is no exception.

Graduate students in the Princeton Department of Mathematics will choose a mentor and follow the mentor to study one or two major directions in depth.

At the same time, graduate students must also complete the necessary credits.

For example, Yu Lei, he chose Shen Qi as his supervisor. His postgraduate research focuses on function theory, including real variable functions and complex variable functions.

In addition to real variable functions and complex variable functions, Yu Lei also has to study general postgraduate courses such as functional analysis, Lie groups, Lie algebra, and partial differential equations.

Of course, more energy should be allocated to the courses of the main direction, and the study time and investment level of other courses should be appropriately allocated according to individual circumstances.

Functional analysis intersects with function theory and algebra theory, and function theory and algebra theory are the main research directions of Yu Lei and Ralph.

Not only Yu Lei and Ralph came, but also Zhou Yu'an, who is about to study for a Ph.D., also came.

Zhou Yu'an and Yu Lei traveled together, and they both lived in the postgraduate dormitory building.

The two stepped over and arrived at the classroom with one minute before class.

Unexpectedly, the seats were already occupied, and Ralph arrived 10 minutes earlier, and some graduate students arrived earlier than Ralph.

"Professor Shen only takes one class a month. He is really popular." Zhou Yu'an could only sit on the ground. His main research direction is differential geometry + partial differential equations. He mainly came for Shen Qi, the credit for functional analysis He got it last semester.

"Who says it's not? Brother Xiao Qi is a new winner of the Philippine Award, and he is in full swing." Yu Lei, who was also sitting on the ground, was proud. A strong tutor means a strong student.

At this time, a boy with curly hair in the seat next to him gave up his seat and said to Zhou Yu'an, "Zhou, you sit here."

"Thank you, Rahil, I can just sit on the floor." Zhou Yu'an politely declined the curly-haired boy's offer to give up his seat. He is well-known among the graduate students in the Department of Mathematics. He is Shen Qi's undergraduate classmate, and he is doing research with Professor Figali , about to enter the doctoral stage.

This is Zhou Yu'an's third semester in the graduate department of the Mathematics Department of Pudong University. He has proved himself with his grades and has been recognized by his classmates. Some classmates offered to give up his seat to him.

"Brother Xiao Yu, you are amazing. You have already made a name for yourself. You are the next Brother Xiao Qi." Yu Lei saw it, and his pursuit target was right in front of him, Zhou Yu'an.

At this time, a girl with a mixed-race face came in, she hurried all the way, holding a math book in her hand.

"One second is not bad, just right." The girl stepped on the spot more accurately, she smiled at Shen Qi.

Shen Qi made a gesture to invite you to sit down. He knew this girl, the number one beauty in the Department of Mathematics of Pudong University. She, Yu Lei and Ralph were enrolled in the Graduate School of Mathematics Department of Pudu University at the same time in January this year.

You can only sit on the ground, and the seats with chairs are full.

But beauties are treated differently. Some boys give up their seats to this mixed-race girl.

The mixed-race girl refused several boys to give up her seat. She sat on the ground next to Yu Lei: "Hey, Yu, do you have any extra pens?"

"Yes, Heidi, I am happy to help you." Yu Lei handed the mixed-race girl a pen and three blank papers. He is used to using a laptop to record the key points of the teacher's lectures, and he also brings a pen and paper for emergencies.

"Thank you." The mixed-race girl said with a smile, she has a good impression of the good-looking Yu Lei.

Shen Qi, who was secretly observing, saw every move in the classroom. He focused on Zhou Yu'an, Yu Lei, and Ralph.

Zhou Yu'an won the respect of his classmates with the highest academic level among his contemporaries.

Yu Lei, who has just entered school, has a handsome face. He is very attractive to girls and is good at dealing with all types of girls.

Ralph, a native American, is a bit introverted. He is very hardworking and has few friends.

Shen Qi began to give lectures. In this edition of the functional analysis textbook, the Muller-Shen theorem about Banach spaces and Shen's proximity theorem were added.

Counting Walsh's theorem and Riemann's theorem, Shen Qi's name appeared in two Princeton mathematics textbooks, functional analysis and number theory.

The atmosphere in the classroom was active, and the students asked some questions, some of which were unconstrained and strange.

It would also be a special kind of psychological satisfaction if you can let the Philippine award boss hang the blackboard.

"Hanging the blackboard" means that the teacher cannot answer the students' questions, and cannot provide effective answers or proofs.

Shen Qi hung up on the blackboard once. When he was just a doctoral student, he took a tutorial class. An Arab undergraduate student asked Shen Qi how to prove the Riemann Hypothesis. Shen Qi at that time was speechless.

Riemann's conjecture was finally proved by Shen Qi, and he has never hung up a blackboard since then.

"So, are you satisfied with my answer about Banach space, Yu Lei?" Shen Qi asked in English.

Yu Lei spoke actively in class and showed himself. He just raised a question about the Banach space.

Shen Qi answered Yu Lei's question perfectly, and Yu Lei was very satisfied and benefited a lot.

"Yu Lei, your question is very routine, and the technical content is not high, so I can answer you." Zhou Yu'an whispered in Chinese.

"Brother Xiaoyu, don't hit me like this, my glass heart can't bear it." Yu Lei didn't look like he was hit at all. After all, he just came to Puda for a few months and was still in the stage of learning and growing.

Shen Qi looked around the audience and asked, "Do you have any questions? If not, let's go to the next study."

The mixed-race girl raised her hand: "Professor Shen, I have a question?"

"Tell me your doubts, Heidi." Shen Qi performed his duties, preaching, teaching, and solving doubts.

Heidi has exquisite facial features, fair skin but fine pores, and she should be of Asian descent. She said: "We all know that if one of the linear or orthogonal dimensions of the Hilbert space H is infinite, then the Hilbert space H The Bert space H must be a finite n-dimensional Euclidean space Rn. Then, conversely, in a finite n-dimensional Euclidean space, the maximum linearly independent vector group and the maximum orthogonal basis can be the same, how to explain the Greek The linear dimension and the orthogonal dimension of the Halbert space are equal, and both are finite n-dimensional? Professor Shen, can you answer my doubts?"

Heidi's tongue-twister-like question aroused the curiosity of the male students in the classroom. They entered the same thinking channel as Heidi and waited for Shen Qi's answer.

Yu Lei was startled, this girl who looks like a goddess is so powerful! Princeton is really talented!

On the stage, Shen Qi slapped his hands three times in a row, and he said loudly, "Heidi, our Heidi, Princeton's Heidi! Hey, Heidi, you should go to Hollywood to audition, I can guarantee, Heidi Lamarr is definitely not as good as you in math."

Heidi smiled sweetly, "Why not?"

Wow.

The boys in the classroom were screaming excitedly. Most of them had heard of the legend of Heidi Rama, and even Heidi Rama was the dream goddess of some of them.

Heidi Lamarr was once a first-line female star in Hollywood. She is beautiful and charming, and she is as famous as Vivien Leigh and Ingrid Bergman at the same time.

Long beauty alone cannot become the fantasy object of Princeton boys.

Heidi Lamarr is a super academic. When she was in college, her main job was applied mathematics and communication engineering. She is an inventor. She invented frequency hopping technology, which is considered to be the origin of CDMA.

"Mother of CDMA" and "Mother of Spread Spectrum" Heidi Lamarr's side job is to act in movies, but she accidentally became a popular actress in Hollywood.

In Shen Qi's functional analysis class, a mixed-race girl who is the same as Heidi-Lama First-Name, she raised a question about Hilbert space, which was very in-depth.

Facing female students who value both good looks and intelligence, Shen Qi of course can't hang the blackboard. He smiled and began to explain his doubts.

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