As a mage, I just want to pursue the truth

Chapter 5 The Shocked Professor

Li Miaomiao was speechless: "You look at the computer here every day, how can you get more than 90 points in the final exam?"

"If you were a literature major, I would think you were reading literature and memorizing it on the computer, but the problem is that math majors require a lot of calculations and practice."

She was a little disappointed, disappointed in the other party's arrogance.

Zheng Li spread his hands: "Let's wait and see."

Li Miaomiao nodded: "No need to wait and see, I have some questions here that I need your help to answer."

"No problem, but there will be a fee." Zheng Li thought that the first order had finally come.

Li Miaomiao didn't bother about the fee issue. "Please help me solve it first. I will transfer it to you on WeChat as soon as you solve it."

After saying that, she took out the draft paper she had prepared in her schoolbag and said, "Here!"

"Let V be a finite-dimensional Euclidean space, V1 and V2 be nontrivial subspaces of V and V = "

The most difficult part of Earth mathematics for him was remembering terms, such as finite dimensions and Euclidean space. These concepts and the corresponding terms were completely different from the education Zheng Li had received.

Zheng Li scanned the questions and said directly:

"This is a typical problem that uses matrix expansion thinking to solve. First, set dimV1=m, dimV2=n, and let m, n>0. Take a set of standard orthogonal bases for V1 and V2 respectively, and they together form a set of bases for V."

Zheng Li wrote on the draft paper as he spoke, and finished writing when he finished explaining the solution.

"The essence of this question is to test your understanding of the application of matrix concepts in Euclidean space."

Li Miaomiao snatched the draft paper from Zheng Li, and her first reaction was "The handwriting is a bit ugly."

After Li Miaomiao carefully read the answer on the paper, she stared at the other person with her beautiful eyes, as if she wanted to get to know Zheng Li all over again.

Although she didn't understand whether Zheng Li's answer was correct or not, combined with Zheng Li's explanation, Li Miaomiao's intuition told her: this should be correct.

Li Miaomiao came prepared today. Although the one-week couple relationship was over, Li Miaomiao still regarded Zheng Li as her friend, and she had an inexplicable sense of loyalty to her friends.

She deliberately found difficult problems on the Internet to embarrass Zheng Li, in order to make him realize his mistakes and get back on track.

For most college students, the most important thing in their student life is GPA.

The question she found was from the finals of a college mathematics competition: "Have you done this before?"

Zheng Li shook his head: "No, do you need to do such a simple question before you can solve it?"

Li Miaomiao nodded: "Okay, it's only five minutes now, I still have two questions here, please help me solve them."

"Let f：R->R be a continuous function which satisfies
Sup|f(x+y)-f(x)-f(y)|<∞(x,y∈R)
Prove sup|f(x)-2014x|<∞(x∈R)”

"Let f1, f2, f3,., fn are analytic functions on D={z||z|<1} and continuous on "

Zheng Li glanced at the questions. If he had just arrived, he might not be able to understand them. Fortunately, when he was searching for information on the Internet through the computer these days, he mostly browsed English pages.

Mathematical English is very simple, and the grammatical structure cannot be simpler. You can understand it as long as you know the meaning of the nouns.

"The first question says that f(x) is a continuous function on R, and its domain and range are both R. Then it gives the condition that when n tends to infinity, f(n) divided by n will equal n. Then it asks you to prove that sup|f(x)-2014x|<∞, so let's assume sup|f(x)-2014x|=M, where M is finite."

“For x∈R, there is always the fact that there exists n such that x is between n and n+1. Therefore, |f(x)-f(n)-f(xn)|+|f(xn)-2014| is less than or equal to 2M+sup|f(t)-2014t|, where t ranges from 0 to 1 and is a closed set.”

If Li Miaomiao listened carefully to Zheng Li's speech at this time, she would find that his speaking rhythm was very stable and his tone did not change.

But all she could think about now was: who am I, where am I, and what is he talking about.

Just like the first question, Zheng Li wrote while talking, filling up both sides of two draft papers. After he finished writing, Zheng Li pushed it towards her and said, "If you don't understand anything, you can ask me. If you don't understand, you can read my answer first. Is there any step from which you don't understand?"

Li Miaomiao's face flushed, and she was embarrassed to say that she didn't understand anything.

The School of Mathematics has classes almost every afternoon, and the study room is usually empty at this time except during exam weeks, so no one else comes to disturb the two of them.

Li Miaomiao shook her head and cleared up what she had just heard from Zheng Li: As a person studying advanced mathematics, you don’t need to understand so much.

"Wait for me for a moment. I'll take it to my friend to see if what you said is true or not."

Zheng Li nodded to indicate that it didn't matter. He had full confidence in himself. As a wizard who had lived for a long time, this kind of elementary analysis was not difficult for him at all. It was not as difficult as eating dessert after a meal.

He was surprised by the primitive way of transmitting knowledge on Earth. He heard that the efficiency of reading and writing was too low.

The way knowledge is transmitted does not match the level of technological development.

When Zheng Li was in the Mage Academy, everyone paid through the Magic Network and downloaded the purchased knowledge into their brains. A trace of nostalgia flashed in his eyes. Countless years had passed since he was away from the academy.

In his opinion, knowledge on earth is too cheap to acquire, and the Internet allows everyone to access massive amounts of information.

After Li Miaomiao took a photo of Zheng Li's answer and sent it to Professor Liu, she stood up and walked outside the study room and called him directly to ask:

"Uncle Liu, please help me check whether these questions are written correctly. Thank you for your help. I will ask my dad to treat you to a meal later."

Liu Gui is a professor in the Department of Mathematics at Jiangcheng University. He and Li Miaomiao's parents have been colleagues for many years and he has watched her grow up since she was a child.

Liu Gui was in his office in the School of Mathematics at that time. After receiving the call, he shook his head helplessly: I would have to trouble him with the advanced mathematics for the first year.

He glanced at his phone and his expression turned serious.

Liu Gui originally thought it was just freshman advanced mathematics, but he found out that what the other party handed over was actually the test papers of Qiu Sai in the first half of this year.

He guided his junior students to participate in the Qiu competition this year and was deeply impressed by the topic of this year's competition.

Liu Gui turned on the computer, looked carefully at the screen, and then immediately made a phone call:

"It's well written, but it's definitely not yours. Not to mention that the handwriting is completely different from yours, the title alone is not something you can do."

Li Miaomiao refused: "You look down on me, don't you? Why are you so sure?"

Liu Gui: "I don't know where you got that geometry question, but it's at least as difficult as the last question in the freshman final exam of the School of Mathematics. With your high school math level of only 120 points, you definitely can't solve it."

"The other two analysis questions are all from this year's Qiu competition. If you can solve them, you don't have to study liberal arts mathematics."

Liu Gui showed no mercy: "Tell me, who did it?"

Li Miaomiao didn't take it seriously after being scolded, but laughed and said: "Hey, tell me first if I did it right?"

Liu Gui nodded and said, "There is no problem with all three questions. The ideas are very clear and the solutions are the simplest ones."

"The Qiu competition was only held in the first half of this year. The official answer cannot be found outside. Tell me, who did you ask to do it?"

"I'm teaching juniors this year, and during the selection exam, I didn't find anyone who could answer these two analysis questions correctly."

Over the years, the Qiumei Mathematics Competition has been dominated by students from Tsinghua University, Peking University, Fudan University, Jiaotong University, and at most the University of Science and Technology of China. Even though Jiangcheng University's Department of Mathematics is ranked among the top ten in China, students from Jiangcheng University have to rely on luck to win a bronze medal in the Qiumei Mathematics Competition.

Li Miaomiao smiled and said, "He is a freshman in your college. His name is Zheng Li."

Liu Gui was shocked on the other end of the phone: "Is it Zheng Li who claims to be able to answer freshman math analysis and advanced algebra questions for a fee?"

(End of this chapter)