Chapter 107 Determine the direction of graduation thesis [Please subscribe]

"He is the best among this year's freshmen. Not only did he win the Olympic gold medal, he also topped the college entrance examination. Last year, he proved a difficult mathematical problem, the infinite number of Carmichael number intervals, right after he entered school."

"There is another thing you probably don't know. In addition to being a student at the School of Mathematics, he also studied engineering mechanics."

At this moment, Chen Yuran was like sharing her favorite treasure, listing all of Xu Yuan's excellent qualities.

His face was filled with joy and happiness as he spoke.

But as he was speaking he realized something was wrong and suddenly stopped talking.

Facing Chen Jianfang's half-smile, he was stunned for a moment and quickly changed the subject.

"Dad, you haven't told me yet."

"Why did your hospital mention Xu Yuan?"

"It shouldn't be."

"Maybe I saw it by chance in the newspaper." Chen Jianfang still kept his smile and asked, "It seems that you know him very well. Do you know each other?"

"No...I don't know..."

Chen Yuran was touched by her father's heart, and she denied it with a stammer: "We are far away from each other."

"Besides, he is still my junior."

It is obvious that her relationship with Xu Yuan has not reached the stage of meeting his parents. If Chen Jianfang knew about this, he would definitely tell her to find a chance to bring him back for dinner.

And according to their family tradition, not only parents will come, but also uncles, aunts, uncles, aunts, and second aunts will come. After all, she is the youngest in the whole family. She is really worried that Xu Yuan will not be able to withstand this Shura situation.

Therefore, it is better to keep it a secret from your family until you are mentally prepared.

Chen Jianfang was obviously a little regretful when he heard this.

After thinking about it for a while, I finally said a few more words.

"I need a chance to get to know someone. I'm almost a junior and I don't even have a close male classmate."

"Your mother wants you to get married right after graduation."

"Come on."

As he spoke, he even made funny gestures and didn't look like a strict father at all.

Chen Yuran looked at her father's back and couldn't help but mutter, "He doesn't look like a professor at all."

She didn't know how her father treated his colleagues and students in the hospital. At home, he was always in a casual and frivolous manner and no one would think he was a great professor.

However, this sentence also reminded her that if she forgot Xu Yuan, she would still have to deal with her mother-in-law in the future.

Her mother's biggest request for her was to find a boyfriend she liked and was suitable for in college, then get married and have children right after graduation, saying that when you are young, you will be in better health and recover faster after childbirth.

In addition, she has so many relatives in her family who can help her screen people at every level, so the probability of meeting an unsuitable boy is very low.

Thinking of this, I couldn't help but worry for Xu Yuan.

I was thinking whether I should give him a reminder after school starts.

The next second, her face suddenly turned red with shame: "Chen Yuran, isn't it too early to think about this now?"

He muttered to himself, then turned his attention back to the computer screen and continued browsing the news.

……

Xu Yuan was not familiar with the domestic news reports. After the closing banquet of the International Cryptography Conference, he and Wang Xiaoyun, Ding Jian and others took a plane back to Yanjing the next day, and then took another bus to the provincial capital Luyang City on the same day, hoping to go home before school started.

There were only a few days left before the start of the sophomore year at Qinghua University, and he planned to go there a few days earlier.

I can't stay at home for long.

The main reason was that he had promised Chen Yuran that he would look for her during the summer vacation, but the international cryptography conference had delayed it until now.

Although they would communicate over the phone during the summer vacation, it was still fundamentally different from meeting in person.

Besides, breaking one's promise is not his character.

When Xu Yuan came out of the exit of Luyang Station, he soon saw his sister Xu Ying waving at him.

Looking more closely, it seemed that her best friend Zhao Lingling was also beside her.

"My brother has made great progress again. He can actually give reports to so many gray-haired foreign professors."

"I would be terrified."

Xu Ying took brisk steps to meet Xu Yuan. When she got closer, she looked Xu Yuan up and down and walked around him in a circle. Then she patted Xu Yuan's shoulder and said with pride.

Xu Yuan was a little surprised when he heard this: "Does everyone in the family know about this?"

He did not tell his family that he was going to attend the international cryptography conference this time, he just said he was going to Yenching for academic exchanges.

Unexpectedly, by the time the conference was over, his family had already known about his presentation.

They don't have a computer at home, and the newspaper can't be published so quickly. There is almost no source of information, so there is obviously only one possibility.

Just as he thought of this, his sister's voice came to his ears again, interrupting his analysis directly.

"You went abroad to participate in such a big event without telling your family. If Lingling hadn't said she saw the news online, I wouldn't have believed that person was really my dearest brother."

"Xu Yuan."

"You also studied cryptography?" Zhao Lingling asked.

Xu Yuan nodded: "It was by chance that I came across the content of hash function cryptography."

"It seems that what everyone said on the forum is right. You are born to study science." Zhao Lingling said with admiration: "You studied mathematics and engineering mechanics at the same time, and accidentally came into contact with cryptography and participated in the world's top cryptographic algorithm cracking project. This talent is really terrifying. It is stronger than anyone I know."

As soon as he finished speaking, he turned his gaze to Xu Ying: "I really envy you for having such a great brother."

"Don't you see who his sister is?" Xu Ying showed her unique silly smile again: "How can my brother Xu Ying not be powerful?"

Xu Yuan was watching this scene and didn't know whether to laugh or cry. In order to prevent his sister from getting more and more excited, he had to take the initiative to interrupt the current topic.

"It's getting late, sister, let's go home first."

"Yes, go home."

Xu Ying came to her senses immediately after hearing the shout: "Mom deliberately didn't open the store today, waiting for you to come home."

As he said that, he grabbed Xu Yuan's arm and ran outside. Zhao Lingling standing next to him couldn't help laughing.

Just as my sister Xu Ying said, the tobacco and liquor store at home was not open today.

Ms. Liang Yanli and Xu Jianguo personally cooked a table full of delicious dishes and invited Zhao Lingling to have dinner with them in the evening.

At the dinner table, Ms. Liang Yanli naturally asked a lot about the conference, but Xu Yuan took into consideration that his parents did not understand cryptography, so he did not go into details and just briefly described what had happened.

For Liang Yanli and Xu Jianguo, their son's outstanding performance in such an international event is the greatest affirmation of them.

Especially during this period when customers come to buy things, they will ask them for parenting experience.

I want to know how to educate students to win gold medals in competitions and top scorers in college entrance examinations.

But after today.

It's time to change that.

The question should be how to train cryptographers.

As for their answers, they can be summed up in just a few words.

The child is too outstanding, there is nothing we can do.

At this time, Ms. Liang Yanli lovingly put a piece of pork ribs into Xu Yuan's bowl and asked him something.

"Xiao Yuan."

"Which newspaper reported the news of your attendance at this meeting?"

"Do you have a photo?"

Xu Yuan put the ribs into his mouth naturally, and his voice was a little unclear when he answered.

"I don't know this either."

After spitting out the bones, he asked again: "Mom, what do you want so many newspapers for?"

"I cut out all the content about you from the newspaper and made a booklet so that it would be convenient for acquaintances to read when they come over." Liang Yanli said with a somewhat boastful smile.

As soon as she finished speaking, Zhao Lingling agreed with her: "I think your method is very good, Auntie."

"If I see it, I'll leave it for you."

"Just let Yingying find it. I just have a collecting hobby." Liang Yanli smiled even more.

Although Xu Yuan didn't know when Ms. Liang Yanli developed this hobby, it was a good thing to make her parents happy.

I think I should cultivate the habit of reading newspapers more often in the future.

that's it.

After a warm and joyful dinner, Xu Yuan stayed at home for two days before setting off for Yanjing again.

After more than a month, I returned to the dormitory. I tidied up first before taking out my cell phone to call Chen Yuran. I took advantage of the few days left before school started to visit the attractions in Yanjing.

It is worth mentioning that Li Zhenya and Wang Haitao also chose to return to school early.

And gave reasons that could not be refused.

They have to sign up as welcome volunteers and get in touch with the junior students in this year's Class 4 as soon as possible.

Of course, this also includes my junior classmates.

The three people in the dormitory were already in place, and Liu Yang, who was from Yanjing, naturally couldn't help but run over.

-

Friday, August 2004, 8, in the men’s dormitory of Bauhinia Apartment.

In the dormitory, Li Zhenya and Wang Haitao were lying on the bed, humming from time to time and too lazy to move.

After two days of welcoming new students, I am almost exhausted.

"My arms are so sore."

"My legs hurt too."

“I declare this to be the dumbest decision I have made this year and I will not attend orientation next year.”

"Who knew girls' luggage were so heavy." Wang Haitao echoed Li Zhenya's words.

Listening to the two people's whining, Xu Yuan shook his head and couldn't help but smile: "Who are you who picked up the school girl's luggage? Your skin has at least become two shades darker in two days." As he spoke, he stood up from the desk and picked up the things on the table.

"Fortunately, I didn't sign up. It would be too sunny there." Liu Yang curled his lips and continued.

When Li Zhenya and Wang Haitao heard the two people stabbing each other, their humming sounds couldn't help but increase by several decibels.

After pondering for more than ten seconds, I heard Li Zhenya say a truth with great emotion.

"It seems that senior is still the best. She is gentle, considerate and caring."

Then he sat up in shock from his dying illness, as if he had been revived, and skillfully got out of bed and turned on the computer on the table.

I went on the Penguin account to chat with my senior schoolmate.

According to school regulations, sophomores are allowed to buy computers. Li Zhenya and Liu Yang have already paired up with one, but Wang Haitao has not considered buying a computer yet.

Xu Yuan thought that he could use the computer in the discussion room freely, so he did not bring one in the dormitory.

Mainly, when writing papers, he prefers to write the manuscript first, and then produce both Chinese and English electronic versions. In this case, even a laptop is not of much use to him.

At this time, Li Zhenya noticed what Xu Yuan was holding and casually asked a question.

"Xu Yuan, are you going to the library again?"

"Do you want to go together?" Xu Yuan nodded and asked back.

Upon hearing this, Wang Haitao sat up from the bed, lowered his eyes and looked at Xu Yuan with a resentful expression on his face.

"Brother Yuan."

"You make us look like idle fish."

Even Liu Yang shook his head: "I haven't adjusted to the new semester yet, and I don't want to go to the library."

Xu Yuan listened to what they said and sighed:
"You think I do."

"This is not a graduation thesis, and the direction has not been determined yet."

As soon as these words were spoken, they immediately caused the same shock to the other people in the dormitory, and they were almost crying with envy.

"Go quickly, or I won't be able to eat dinner."

"You haven't decided on the direction of the paper yet, and we don't even know how to write the paper format."

Li Zhenya was quite surprised and replied: "I thought you would focus on cryptography next."

"That's indeed possible. After all, Brother Yuan shocked all the cryptography experts at the International Cryptography Conference." Wang Haitao couldn't help but interrupt when he heard something that interested him.

Several days had passed since the International Cryptography Conference, so they naturally knew the situation at the scene.

Based on Xu Yuan's achievements in the field of cryptography, he should continue his studies.

But the reality is that Xu Yuan did not intend to make cryptography his main career.

Xu Yuan understood their ideas, but he had his own plans.

How could it change because of some accidental event?

He organized his words in his mind and explained, "In my opinion, mathematics is more like a tool. Only when you have a solid enough grasp of mathematical knowledge can you be more comfortable with other majors." As he spoke, his eyes were filled with yearning for the highest temple of mathematics.

Having said that, naturally, no one else would say anything more.

Then Xu Yuan didn't waste any more time. He took his things, pushed the door open, left the dormitory and went to the library.

Compared with the discussion room arranged for him by the department, the textbooks and literature in the library are undoubtedly more abundant.

This helped him determine the direction of his graduate thesis.

……

Zhang Jundong has become a junior and has deliberately withdrawn from the student union to concentrate on reviewing.

After considering many factors during this summer vacation, he finally made up his mind to strive for a place in the department's graduate school, so he found time to go to the library to review his major courses as soon as school started.

I thought that even if I didn’t get the qualification for admission to graduate school in the end, I would still be admitted to the graduate school of my own school.

I went up to the study area on the third floor with my books and was just about to find a seat to sit down when a familiar figure appeared in my sight.

"Xu Shen is here too."

He muttered something to himself in surprise, then after a slight hesitation, walked towards him.

Choose to sit next to Xu Yuan.

Although he is Xu Yuan's senior as a junior, everyone in the entire mathematics department knows Xu Yuan's ability. He can ask for help when he encounters something he doesn't understand while studying with the academic genius.

Speaking of which, he has met Xu Yuan several times and is relatively familiar with him compared to other people in the department.

Out of politeness, he quietly greeted Xu Yuan: "Xu Shen, are you here to review as well?"

Xu Yuan had just sat down and was still considering the direction of his thesis, so he had not yet entered the deep learning state. He turned his head when he heard a familiar voice, and recognized that it was Zhang Jundong, a senior from the second class, and responded humbly.

"Hello, senior."

As these three words floated into Zhang Jundong's ears, he suddenly felt extremely comfortable.

After all, who can resist being called senior by a genius in the mathematics department?

But before he could enjoy it for long, he heard Xu Yuan continue: "I'm writing my graduation thesis."

"It's a pity that we haven't decided on the direction yet."

"Write a graduation thesis?" Zhang Jundong repeated this sentence, and he could no longer hear what was said afterwards.

I never expected that Xu Yuan, who was just in his sophomore year, was already writing his graduation thesis.

You know, we don’t even know where his graduation thesis is.

The key point is that in this way, he will become his junior in the future, after all, the other person is about to graduate.

Maybe the sentence senior just said is the last one you will be lucky enough to hear.

However, he has rarely seen anyone who can write a graduation thesis at the beginning of the sophomore year.

This means that all credits have been earned.

I mastered all the professional courses in four years of university plus university physics and English in just one year.

It's really amazing.

Besides, Xu Yuan was different from ordinary students in the department. He was studying both mathematics and engineering mechanics. In particular, he had just seen the news a few days ago announcing that the MD5 encryption algorithm was successfully cracked by their team.

So many different things were done so well that one could not help but wonder if he had thirty-six hours in a day.

"I really admire you, Senior."

The thought stayed here, and Zhang Jundong immediately changed his words and directly called Xu Yuan "senior".

The next second he thought of something and continued to ask, "Senior, with your ability, you will definitely be admitted to graduate school, right?"

"The department asked me to directly pursue a Ph.D. in science." Xu Yuantou said casually without replying.

And these words were like a steel knife, stabbing into his heart and making him feel extremely uncomfortable.

I wanted to slap myself twice: "I shouldn't have asked that question."

Thinking that I was still worrying about the entrance examination for postgraduate study, Xu Yuan was already studying for a doctorate.

I feel more and more the disparity in life.

However, this blow made him serious and he began to focus all his attention on the books, preparing to have a math review competition with Xu Yuan.

Although his talent and level cannot be compared with Xu Yuan, he believes that he is not inferior to anyone in his serious review state.

Especially with the bonus from Xu Yuan.

However, this confidence only lasted for a few minutes before it collapsed like a high-rise building exploding.

He admitted that he was wrong.

And it is extremely wrong.

I have no idea where I got the courage to challenge Xu Yuan's seriousness.

During the review process just now, he found that he was easily disturbed by external factors. Whether it was the allowed whispers of others or the simple sound of coughing or moving chairs, he could not help but raise his eyes and cast a curious look towards the source of the sound.

It's so hard to immerse yourself in the state and concentrate.

On the other hand, Xu Yuan is completely different.

After his secret observation, he found that Xu Yuan was like an old monk in meditation, not disturbed by the outside world. No matter what happened in the study room, he didn't even move his eyelids.

It was like being in different latitudes. Although they could see each other, the surrounding environment could not affect them. At this time, he finally understood why Xu Yuan could learn so much knowledge at the same time.

This state of concentration alone is unmatched by anyone else.

It can be said that fragmented time is used to the extreme.

"There is a reason why a genius is called a genius."

"This kind of talent is really enviable!"

Zhang Jundong sighed silently in his heart, and then buried himself in reviewing his mathematics major again.

-

As time passed, the mathematics content he had mastered kept flashing through Xu Yuan's mind.

From algebra to complex functions to functional analysis of partial differential equations, and even to number theory, which I was good at, I still couldn't decide on the research direction and content that was suitable for my graduation thesis.

Of course, if he just wanted to write a paper casually, he could write a few in a month.

However, this kind of paper is no different from spamming.

Apart from wasting his time, he didn't think it would improve his math skills in any way.

Anyway, there are still a few months before the graduation defense after the new year as Tang Shihong requested, so there is no need to be too anxious.

At this time, compared to Xu Yuan who had his own plans, Zhang Jundong who was sitting next to him had a frown on his face.

"This question is too weird. I have no idea what to do."

He rested his left arm on the table, holding his forehead with one hand while checking calculations in a draft book with a pen in the other.

Unfortunately, after thinking for several minutes, I still had no idea how to solve the problem, and the determination I had made with great difficulty was gradually worn out.

He sat in the library to review for two hours, and then wanted to try to do the question set he had just bought to consolidate his knowledge. However, he encountered an obstacle and could not move forward before he had solved two questions.

Faced with this situation, he has many choices. He can either skip this question and do the next one, or give up doing the question and continue reviewing to consolidate his knowledge.

But either way, this question will be like a fishbone stuck in the throat, making today's review incomplete.

So after some psychological preparation, he slowly turned his head and glanced at Xu Yuan on his right.

"This kind of question shouldn't be difficult for Master Xu, right?"

I want to ask the other party for advice on how to solve the problem, so as not to waste such a good opportunity to meet Xu Yuan today.

However, he was also afraid of disturbing Xu Yuan's current state. After all, it is not easy to concentrate on studying. If he is interrupted, it will take a long time to recover to his previous state.

Just as he was hesitating, he suddenly noticed that Xu Yuan stopped writing, stretched, and took the initiative to change his concentration.

He had waited so long for this opportunity that he dared not waste it, so he immediately handed over the question set.

"Xu Shen..."

"Can I ask you a question?"

Hearing this, Xu Yuan turned his eyes and said casually, "Let me see it."

I agreed very readily.

Mainly, he thought that instead of thinking about the direction of his graduation thesis, it would be better to solve a problem to change his mind.

Maybe your thoughts will become clear all of a sudden.

Besides, Zhang Jundong was just a junior, so he thought that the questions he was doing would not be difficult at all.

"To God Xu." Zhang Jundong was extremely surprised and handed the question set directly to Xu Yuan.

Xu Yuan took the question book and lowered his eyes to look at it. The questions on it immediately appeared in his field of vision.

"Assume that the second-order partial derivative of u(x, y) is continuous."

"A sufficient condition to prove that u(x, y) = f(x)g(y) is u = m/x
y=u/x..."

“u≠0”

……

After reading it silently in my mind, the corresponding solution ideas will automatically emerge in my mind.

"This problem is not very difficult. It can be solved."

He said this in a deep voice to Zhang Jundong, then focused his attention on the problem and started to check the calculations with a pen. At the same time, he did not forget to unravel the problem for Zhang Jundong and simplify it.

"Comprehensive questions like these involving partial derivatives and partial differential equations require the use of abstract thinking to analyze."

“Try to find the key points of the question as much as possible.”

“Then you can use methods of order reduction and separation of variables.”

"But you should pay special attention to the fact that any constants must be converted into corresponding functions. Now it is much clearer."

At this point, there are more steps to solve the problem on the draft paper, and the large number of formulas does not appear messy at all.

“Let u/x = v(x, y)”

"uv/y=vu/y, (uv)'=u'v=uv'=0＜=＞c"

……

"It's solved."

After Xu Yuan finished writing the last mathematical symbol, he handed the draft paper to Zhang Jundong.

It can be seen that Zhang Jundong is still immersed in this problem. He carefully looks at the verification steps and recalls what Xu Yuan just said. Seeing this, Xu Yuan did not disturb Zhang Jundong's train of thought.

After a pause of nearly a minute, Zhang Jundong finally came to his senses, his face full of joy.

"Xu Shen, you are so amazing."

"I just couldn't figure out the solution to the partial differential equation problem, but after you finished explaining it, I suddenly felt like everything was clear."

"No wonder everyone liked to listen to your lectures before."

Zhang Jundong was very sure that he had not been able to solve this problem before. He didn't even know where to start. He sat there for a long time without any idea at all.

But after Xu Yuan's analysis and explanation, my originally confused thoughts suddenly became clear.

It seemed as if Xu Yuan's explanation had some kind of magic that helped him open the door to the correct answer in an instant.

He even had a feeling that even if he encountered a similar question in the future, he would be confident that he could try to do it and there would not be another embarrassing situation like the one just now.

Without wasting any time, he immediately turned his attention to another question of the same type.

I want to do a few more questions while my thoughts are clear so that I can master them thoroughly.

But it is worth mentioning that while Zhang Jundong continued to solve the same type of partial differential equation problems, Xu Yuan's attention was also on partial differential equations and he came up with some ideas.

"Partial differential equations may be a good research direction and can be used as the content of a graduation thesis."

At this moment, I was muttering thoughtfully. The more I thought about it, the more I felt that this was indeed a very suitable topic for my graduation thesis.

A partial differential equation is an equation that involves partial differentials of an unknown function.

The highest order of partial derivatives of an unknown function appearing in an equation is called the order of the equation.

It is the most widely used second-order partial differential equation in mathematics, physics and engineering technology.

Therefore it is also called mathematical physics equation.

Partial differential equations can also be used in computational fluid dynamics.

Although he did not include physics in his major, he still studied university physics courses.

As the saying goes, mathematics and physics are inseparable. Further research on partial differential equations will help him to combine physics and mathematics to generate new inspiration.

The thought stayed here, and Xu Yuan basically made a decision. He then stood up and walked towards the science area of ​​the library, preparing to borrow some textbooks and literature on partial differential equations so that he could choose specifically which part of the partial differential equations to study.

In order to thank Zhang Jundong for providing him with inspiration, he did not forget to thank him before getting up and leaving.

"Thank you this time."

Zhang Jundong was solving the problem with full confidence when he suddenly heard Xu Yuan's words and was a little confused.

He thought that he was clearly the one asking Xu Yuan for help, so no matter how you look at it, he should be the one expressing his gratitude to Xu Yuan, but why was he suddenly the one being thanked?

He really couldn't understand this.

However, just when I was about to ask Xu Yuan for clarification, I stood up and found that Xu Yuan had already gone downstairs.

I had no choice but to give up.

"Why is God Xu thanking me? It's so strange..."

Leaving this question in my mind, I finally sat down again and continued to solve the remaining partial differential equation problems.

……

After Xu Yuan decided to use partial differential equations as his thesis, he felt much more relaxed than the previous two days.

After all, we have a clear direction, and the next step is to find an entry point and concentrate on research to draw conclusions.

He believed that he would be able to complete the paper before the end of the year.

As for the fact that he had determined the direction of his graduation thesis, he had no intention of hiding anything.

The next day, I came to Tang Shihong's office.

After all, Tang Shihong is his graduation thesis advisor, and he might need to ask him some questions later, so he must first let Tang Shihong know the direction and general content of his thesis.

After entering the new semester, Lu Chunming was about to graduate. In addition, he was not planning to continue to pursue a doctorate, so he recently began to busy himself with his graduate thesis.

As a result, he went to Tang Shihong's office more frequently, wanting to make his thesis as perfect as possible.

This is not.

They happened to meet each other again in the morning.

"Junior brother is also looking for a mentor, so why don't we go together?"

Downstairs in the complex building where Tang Shihong's office is located, Lu Chunming saw Xu Yuan from afar and stopped to wait for a while. When he came closer, he still greeted him enthusiastically as usual.

Xu Yuan nodded and replied, "I'm going to discuss my graduation thesis with Professor Tang."

Lu Chunming naturally knew that Xu Yuan graduated early. Although he was envious of him for having spent four years in undergraduate studies, he felt relieved when he learned that Xu Yuan was also worried about his graduation thesis.

The two of them chatted about common topics as they went upstairs.

"I have been writing this paper for a long time, but unfortunately my supervisor is still not satisfied and has not approved it."

"It was a mistake to choose differential geometry as the thesis topic."

"Junior brother."

"You'll find out when you study differential geometry as a graduate student."

Lu Chunming counted the pitfalls he had encountered and sincerely hoped that Xu Yuan would not follow in his footsteps.

Otherwise, revising the paper would be a very painful thing.

Xu Yuan certainly knew that Lu Chunming's paper involved differential geometry. After all, Tang Shihong's main research area was in the field of differential geometry.

In the field where he is good at, he will naturally set higher standards for Lu Chunming.

He also suspected that he was partly responsible for this.

It was because he performed so well during his undergraduate studies that the department's definition of an excellent student was raised.

The requirements for a graduation thesis like this are definitely slightly higher than before.

What's more, Lu Chunming is a graduate student.

But he certainly wouldn't say this to someone's face, otherwise he would just bring hatred upon himself.

Soon the two of them arrived at the floor where Tang Shihong's office was located, and heard Lu Chunming ask again:

"That's right, junior brother."

“Have you decided on the direction of your graduation thesis?”

"It has been officially confirmed." Xu Yuan nodded and answered truthfully: "I plan to study partial differential equations."

"Partial differential equations?" Lu Chunming frowned slightly when he heard that.

After a slight hesitation, he could not help but remind her: "Partial differential equations are mathematical physics equations. Are you sure you want to choose this as your graduation thesis?"

"Yes." Xu Yuan's face was full of affirmation.

Perhaps knowing that he could not persuade Xu Yuan, Lu Chunming stopped talking about this matter.

Although partial differential equations involve mathematics and physics, and studying this field requires knowledge of both mathematics and physics, Xu Yuan is only going to write an undergraduate thesis after all, and it is not for publication in an SCI journal, so naturally he does not need to choose something too in-depth to study.

In short, as long as he can pass the graduation defense smoothly, he believes that Xu Yuan can handle it with his ability.

When the two stood in front of the office door, almost the moment Lu Chunming knocked on the door, they immediately heard a familiar voice coming from inside.

"Come in."

The next second, Lu Chunming pushed the door open and Xu Yuan followed behind him.

"tutor."

Tang Shihong still looked at Xu Yuan first as usual, immediately put on a smile on his face and warmly invited Xu Yuan to sit down.

"Sit down quickly."

Then he turned his head to look at Lu Chunming and shouted: "What do you want to see me today?"

"Teacher, I would like you to help me look at my thesis again." Lu Chunming said embarrassedly when he heard this.

Although Tang Shihong is strict with his graduate students, he hopes that they can learn knowledge and contribute to the development of domestic mathematics, rather than just get a diploma.

So after hearing what Lu Chunming said, his attitude softened and he took the initiative to ask him for the paper.

"Bring the stuff over here."

"Thank you, tutor." Lu Chunming's face immediately brightened up and he quickly handed over the paper he had prepared long ago.

Xu Yuan did not disturb Tang Shihong at this time. He sat alone beside him and waited patiently.

As time passed, it was obvious that Tang Shihong's brows gradually became furrowed, and it was obvious that he was still not satisfied with the content of the paper.

More than ten minutes later, he raised his eyes and spoke to Lu Chunming, explaining the problems in the paper in detail.

"It's still the same problem as last time. The proof is partially insufficient."

"Blind citation of literature."

"There are also some problems with the formatting in some places, and it is not even as good as Xu Yuan's first paper."

Lu Chunming listened to all these words, and naturally did not dare to refute a word.

Although he really wanted to say that Xu Yuan's first paper was published in the Annals of Mathematics, his graduation thesis naturally could not be compared.

But when the words came to my lips, they turned into: "Then I'll go back and revise it."

After dealing with Lu Chunming's thesis, Tang Shihong finally turned his attention to Xu Yuan.

With the corners of his mouth raised and a smile on his face, he said tentatively: "You came to me right after the end of summer vacation and just as the school started. Let me guess if you have an idea for your graduation thesis." But his tone seemed very confident.

When Xu Yuan heard this, he no longer hesitated and nodded in agreement.

"I knew I couldn't hide it from Professor Tang."

"I do have a direction for my graduation thesis, and I will officially start writing it during this period."

"Great."

When Tang Shihong heard the answer he wanted, he couldn't help but shout out.

Then he quickly asked, "What is it about?" His eyes were full of anticipation and curiosity.

During the year that Xu Yuan studied at Qinghua University, he published a paper on ticket sales in the Annals of Mathematics and also made a name for himself in the field of cryptography by successfully cracking the world's top password MD5. It can be said that he had a higher starting point than other undergraduates and even graduate students.

With the blessing of these halos, Xu Yuan's graduation thesis seems to be expected.

In addition, the direction of the thesis has not been determined yet, so I should be happy now that I can finally start writing it.

In response to Tang Shihong's question, Xu Yuan did not give a direct answer. Instead, he took out a piece of draft paper from his pocket and handed it to him.

“This is the abstract of the paper I wrote, but it doesn’t have any specific content yet.”

Tang Shihong took it quickly and immediately lowered his eyes to focus on the contents on the draft paper.

As the information came into his eyes, his brows soon became even more furrowed than before.

"Partial Differential Equations……"

"Theory of the Monge-Ampere equation?"

He muttered these two key pieces of information, and the next second he looked up at Xu Yuan and asked in disbelief, "You plan to study the Monge-Ampere equation, which is not an easy task."

That's right.

After weighing the pros and cons last night, he finally decided to focus on the Monge-Ampere equation.

The so-called Monge-Ampere equation is a nonlinear partial differential equation proposed by French mathematician Monge when he studied the problem of optimal transmission. It was named after further in-depth research by Ampere. Among them, the proof of the Calabi conjecture for which mathematician Shing-Tung Yau won the Fields Medal was related to this equation.

As an inevitable equation for optimal transmission, it is used in machine learning.

The general form of the equation is detDu=f(x,u,Du)

Although as Tang Shihong said, this content is not an easy bone to chew and it is easy to tire your teeth.

But the more challenging it is, the easier it is to generate inspiration during the research process and improve your mathematical thinking and level.

In addition, the Monge-Ampere equation is widely used in machine learning, and studying this equation will help the development of computer technology.

"I became interested in partial differential equations by chance, and after some analysis, I chose the Monge-Ampere equation as the starting point of my thesis." Xu Yuan answered Tang Shihong's question truthfully.

Tang Shihong still frowned, and after a slight hesitation, he gave his real advice.

"Mathematicians' existing knowledge of partial differential equations has not been broken for many years. It is almost impossible to develop a new theorem of Monge-Ampere equation theory in just a few months."

"So I suggest you change your direction and study partial differential equations later."

Tang Shihong said this because he naturally didn't want to see Xu Yuan delay his graduation. His choice of partial differential equations was too difficult.

As for Lu Chunming next to him, he was extremely dumbfounded. He thought Xu Yuan was just studying some small things in partial differential equations, but he didn't expect that he would throw out the ultimate bomb in the field of partial differential equations right away.

This seemed to make him suddenly feel a little disgusted with his graduate thesis.

Xu Yuan naturally knew that Tang Shihong was thinking about him, but he also had some confidence.

After hearing what he said, he still insisted on his choice: "I still want to try studying the Monge-Ampere equation."

……

(End of this chapter)