Research starts with PhD students

Chapter 27 Progress 100, research completed!
Zhang Shuo is still very concerned about whether research can make progress without using scientific research coins.

Research coins can be used to directly purchase task progress. Improved progress brings inspiration and understanding of the next direction. The effect is so good that it is impossible to refuse.

After using it several times, he felt that the scientific research coins were a bit like scientific research drugs.

I use one, and I want to use the second one...

Then the third, the fourth.

Never ending!

Keep spending coins and have fun!

There are no side effects to Krypton coins, but the number of scientific research coins is limited. There is only one guaranteed daily, and the rest are rewards for completed results.

With a clear direction, using scientific research coins to improve concentration and creativity can increase task progress even more.

"So, you can't always spend your coins. Research coins should be used at critical times. You still have to rely on yourself to do research normally."

"For C-level research, if you invest more than 20 research coins, you will lose money."

"Scientific research coins are like money. We should save some and use them at critical moments in the future..."

Zhang Shuo checked the number of scientific research coins——
【Scientific research currency: 22. 】

In the past few days, not only have I used up the guaranteed amount every day, but sometimes I can't help but use one more.

This is also one of the reasons why the task progress is growing so fast.

Zhang Shuo secretly made up his mind that unless he was doing critical research, he must restrain his desire to spend money.

Eat, sleep, go to class...

The life of a PhD in mathematics is still very leisurely.

There are only Academic English classes in the morning.

After class, Huang Kai took Zhang Shuo to the library, mumbling non-stop, "I didn't sleep well last night. I was thinking about the direction the whole time. The most important thing for us as first-year PhD students is to find the direction."

"I decided to listen to my advisor and focus on studying nonlinear wave equations."

"From today on, I will fall in love with the wave equation—"

"For the thesis! For the diploma!"

Zhang Shuo complained helplessly, "Your slogans are as loud as your snoring last night."

"Haha~~~"

Huang Kai smiled awkwardly and pointed to a corner, "Go over there and save a seat for me."

After saying that, he went to look for a book.

Zhang Shuo was holding several thesis materials in his hands, all downloaded from academic websites. The library, study room or dormitory were all the same to him.

In short, just look at the paper information.

Several papers are studies on second-order partial differential equations, including proofs of smoothness and regularity of some characteristic types of equations, as well as several special solution methods.

This information is helpful for research.

Sometimes, seeing some content in a paper and connecting it to your own research can help speed up the progress of your task.

After waiting for a while, Huang Kai came over with a book on wave equations.

"That's it!"

He sat down and began to read attentively, but after only ten minutes or so his mind began to wander, looking around and not knowing what he was doing.

The two girls sat opposite each other.

There was a girl with braids who was very beautiful, with big eyes, fair cheeks, and a moderate figure. She was dressed in a short shirt and jeans, which made people unable to help but take a few glances at her.

The other one is short, with a round face, untied hair, and big-framed glasses. He looks a bit silly and cute.

They seemed to be discussing math problems in a low voice, using words like "Hilbert," "countable," and "inner product."

Huang Kai stared at it for a few seconds and suddenly became alert. He whispered to Zhang Shuo, "I have seen those two girls. They are graduate students in the Department of Mathematics."

"Look at me!"

"I'll show you the correct way to approach a junior girl in math!"

He said and stood up.

"You don't want to read anymore?" Zhang Shuo's mouth curled up when he heard it. He could only give an encouraging look and raised his thumbs, "Keep it up!"

Then, continue reading the information.

It’s interesting to chat up pretty girls, but the paper in your hand is more attractive.

If you can make a few more points, you can complete the research task, have results, write papers, and get scientific research coins as rewards.

Isn’t this much more interesting than chatting up schoolgirls?
After reading an example of combining the finite difference method with the calculus of variations to more accurately solve the second-order partial differential equation, Zhang Shuo immediately connected it to his own research.

“If you want to narrow the range of solutions and reduce the complexity of the algorithm, you can use multiple methods to conduct joint analysis.”

"Some processes of conventional solution methods can also be embedded in the algorithm to help make numerical substitution more accurate..." He thought about it and checked the system task progress.
【Progress: 93.183%.】

Sure enough, it went up again!
Zhang Shuo showed a relieved smile, and when he came to his senses, he noticed Huang Kai standing next to him, followed by the two girls who had just faced each other.

"Better ask him."

Huang Kai introduced the two girls, "Zhang Shuo, my roommate. This kind of question is a piece of cake for him."

"Zhong Yijing, Deng Xiao."

He pointed at the two girls and introduced them separately. The girl with braids was Zhong Yijing, and the short and cute one was named Deng Xiao.

Huang Kai handed over the draft book in his hand and explained with a smile, "Please help me look at this. It's a functional analysis question for graduate students."

"Hey, I can't remember it for a moment..."

Zhong Yijing and Deng Xiao also looked at Zhang Shuo.

There was some doubt in the eyes of the two men. Huang Kai had just said confidently that he would help take a look, but after looking for a long time he still had no clue.

Can this really work together?

"Let me see."

Zhang Shuo took a curious look at the question, "Given a separable Hilbert space H, prove that there are countable orthogonal canonical sets..."

"This is easy!"

He took the pen and explained while writing, "We can first assume that the countable density in H is {u_n}, that is, for any x∈H and ε>0, there exists some n such that..."

"Next, define a new set {v_n}..."

"Now let's prove that {v_n} is an orthonormal set. First, we prove that {v_n} is an orthogonal set."

"For different m and n, u_m and u_n correspond to different vectors in H..."

"..."

"..."

“For any n, we have //v_n//=//u_n///u_n////=1.”

"Hence, {vn} is a canonical set."

Zhang Shuo nodded with satisfaction after finishing his speech. The functional analysis questions at the graduate level were still very simple for him. He could almost know the ideas and methods by just taking a look at the questions.

He turned to look at the two school girls and asked, "Do you understand what I just said?"

Zhong Yijing and Deng Xiao were both stunned on the spot.

They had been discussing the topic for the entire morning, and it was solved in just a few seconds?
The other party just took a look and wrote down the answer without even having time to think. It felt like he was doing an elementary school math problem.

The PhD students in the mathematics department are so scary!
Zhong Yijing glanced at Huang Kai again and her mood immediately improved a little.

She nodded towards Zhang Shuo and said, "Senior, it's still a little confusing, but you've already written the answer, let's take it and try to understand it, it's almost there."

She picked up the draft book and said thank you, then walked to the opposite table and picked up her phone, a sweet smile appeared on her lips, and she asked, "Senior, can you add my contact information?"

"If I have any questions, I'll ask you again."

Deng Xiao reacted and quickly went to get his phone, "Yes, I'll add a contact number too."

She added, "Is it okay to bother you?"

Zhang Shuo hesitated for a moment, but still nodded and said, "Okay, but I rarely chat on my phone. Sometimes, it may take several hours for me to see new messages. Don't mind if I reply late."

Zhong Yijing smiled sweetly, "If there is an urgent problem, I will make a video call."

The two girls asked for the contact information and walked away.

Zhang Shuo continued reading the paper.

Huang Kai also sat back in his seat and sighed with a blank expression, "I take back what I said. Using math to chat up girls is something only geniuses like you can do."

"A poor student like me can only be a matchmaker at best..."

In the next few days, Zhang Shuo spent all his time in the library and read all the papers he had found.

Some papers may not be helpful to research, but they can enrich his knowledge, expand his thinking, and make him feel that he has gained a lot.

Even if you are not focusing on improving your research progress, if you see knowledge that is useful for your research and think about it, it will also improve your task progress.

97.543%.

98.311%.

99.144%...

After reading a research paper on Lie symmetry analysis, Darboux transform and non-local symmetry of partial differential equations, and then thinking about the problem of general algorithms, the last obstacle to my research instantly fell apart.

From the transformation of the second-order elliptic partial differential equation to the substitution of numerical values ​​in multi-parameter analysis, to the determination of boundary values ​​and the substitution to prove the asymptotic solution...

Everything is smooth now.

(End of this chapter)