Li Miaomiao was speechless: "How can you get over 90 in the final exam if you look at the computer here every day?"
"If you are from the literature department, I can also think that you are looking at the computer to read the literature endorsement. The problem is that the courses in the mathematics department require a lot of calculations and exercises."
She was a little disappointed, disappointed with the other party's arrogance.
Zheng Li spread his hands and said, "Let's wait and see."
Li Miaomiao nodded: "No need to wait and see, now I have some questions that I need your help to answer."
"No problem, but you have to pay." Zheng Li thought to himself that the first order finally came to his door.
Li Miaomiao didn't dwell too much on the charging issue, "You can help me answer it first. Once you figure it out, I'll forward it to you on WeChat immediately."
After saying that, she took out the draft paper prepared in her schoolbag: "Here!"
"Suppose V is a finite-dimensional Euclidean space, V1 and V2 are non-trivial subspaces of V and V=..."
The most troublesome thing about earth mathematics for him is remembering nouns, finite dimensions, and Euclidean space. These concepts and corresponding nouns are completely different from the education Zheng Li received.
Zheng Li scanned the questions at a glance and said directly:
"This is a very typical question that uses matrix expansion thinking to solve. First, let dimV1=m, dimV2=n, let m, n>0. Take a set of orthonormal bases of V1 and V2 respectively. Together, they is a set of basis of V..."
Zheng Li was writing on the scratch paper as he spoke, and he just 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's hand. Her first reaction was, "The writing is a bit ugly."
After Li Miaomiao carefully read the answers on the paper, he stared at the other party with his beautiful eyes, as if he wanted to get to know Zheng Li again.
Although she couldn't understand whether Zheng Li's answer was correct or not, based on Zheng Li's explanation, Li Miaomiao's intuition told her: This should be correct.
Li Miaomiao came well-prepared today. Although their one-week relationship ended, Li Miaomiao still regarded Zheng Li as her friend. 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 career is their grades.
The question she was looking for was a question in the finals of a college student mathematics competition: "Have you done this before?"
Zheng Li shook his head: "No, do you still need to do such a simple question before you can solve it?"
Li Miaomiao nodded: "Okay, it's only five minutes now. I have two more 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 read the questions. Fortunately, when he looked for information on the Internet through his computer these days, he almost always browsed English pages.
English in mathematics is very simple, and the grammatical structure couldn't be simpler. As long as you know the meaning of the nouns, you can understand it.
"The first question says that f(x) is a continuous function on R. Its domain and range are both R. Then it gives the condition that when n tends to infinity, dividing f(n) by n will Equal to n. Then let you prove that sup|f(x)-2014x|<∞, you might as well assume sup|f(x)-2014x|=M, M is finite."
"For x∈R, it is always true that there is n such that x is between n and n+1. Therefore, |f(x)-f(n)-f(xn)|+|f( xn)-2014| will be less than or equal to 2M+sup|f(t)-2014t|, where the value range of t is 0 to 1, taking a closed set."
At this time, if Li Miaomiao listened carefully to Zheng Li's speech, he would find that his speech rhythm was very stable and his tone did not change.
But now all she could think about was: who am I, where am I, and what is he talking about.
Just like the first question, Zheng Li wrote as he spoke, filling both sides of the two draft papers.
After Zheng Li finished writing, he pushed it to her, "If you don't understand something, you can ask me. If you don't understand, you can read the answer I wrote first. Is there any step you don't understand?"
Li Miaomiao's face flushed, and she was embarrassed to say that she didn't understand anything.
The Mathematics Institute basically has classes every afternoon, and the study room is usually empty except during exam weeks. So no one else came to disturb the two of them.
Li Miaomiao shook his head and cleared up what he had just heard from Zheng Li: As a high-level math student, you don't need to know so much.
"Wait for me for a moment, and I'll take it to my friend to see if what you said is correct."
Zheng Li nodded and said it didn't matter. He had full confidence in himself. As a mage who had lived for a long time, this very basic analysis content was not difficult for him at all. It was not as difficult as eating dessert after a meal.
The primitive way in which the earth transmits knowledge surprised him. The efficiency of listening, speaking, 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, as countless years had passed since he lived in the academy.
In his opinion, access to knowledge on earth is too cheap, and the Internet allows everyone to have access to massive amounts of information.
After Li Miaomiao took a photo of Zheng Li's answer and sent it to Professor Liu, he got up and walked outside the study room, called directly and asked:
"Uncle Liu, please help me see if these questions are written correctly. Please forgive me. I will ask my dad to treat you to dinner later."
Liu Gui is a professor in the Mathematics Department of Jiangcheng University. He and Li Miaomiao's parents have been colleagues for many years, and they have watched her grow up since childhood.
Liu Gui was in his office in the Department of Mathematics at this time. After receiving the call, he shook his head helplessly: The freshman high school math student needs to trouble him.
He glanced at his phone and his expression became serious.
Liu Gui thought it was just high math for his freshman year, but he found that what the other party brought over was actually the test questions from the Qiu Competition in the first half of this year.
He guided junior students to participate in the Qiu Competition this year and was deeply impressed by the topics of this year's Qiu Competition.
Liu Gui turned on the computer, looked at the computer screen carefully, and then immediately dialed the number:
"The writing is quite good, but it is definitely not done by you. Not to mention that the handwriting is completely different from yours. Even this question alone is not something you can do."
Li Miaomiao refused: "Isn't it okay to look down on people? Why are you so sure?"
Liu Gui: "I don't know where you found that geometry question. It's at least as difficult as the final question in the final exam for freshmen in the Department of Mathematics. You can't do it with a score of only 120 in high school mathematics. "
"The other two analytical questions are all part of this year's Qiu competition. If you can do them, you won'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 criticized, but smiled and said: "Hey, tell me first, are you doing the right thing?"
Liu Gui nodded and said: "I did all three questions without any problems. The thinking was very clear and the solution was the simplest solution."
"Qiu Sai only completed the competition in the first half of this year. The official answer can't be found outside. Tell me, who did you ask for it?"
"I took care of junior students this year. During the selection exam, I didn't find anyone who could answer these two analysis questions correctly."
Qiu Sai has been restored to the Qing Dynasty in the past years, with at most one person from the University of Science and Technology of China taking over. Even if the mathematics department of Jiangcheng University ranks among the top ten in the country, students from Jiang University have to rely on luck to win the bronze medal in Qiu Sai.
Li Miaomiao smiled and said, "He is a freshman in your college. His name is Zheng Li."
Liu Gui looked shocked on the other side of the phone: "Is it Zheng Li, who claims to be able to answer freshman mathematical analysis and advanced algebra problems for free?"
