Li Miaomiao was speechless: "You look at the computer here every day, and you can pass the final exam over 90?
" The courses in the department require a lot of calculation and practice."
She was a little disappointed, disappointed by the other party's arrogance.
Zheng Li spread his hands: "Let's wait and see."
Li Miaomiao nodded: "You don't need to wait and see. Now I need your help to answer some questions here."
"No problem, but there will be a fee." A single came to the door.
Li Miaomiao didn't worry too much about the charging issue, "Please help me answer it first, and I'll forward it to you on WeChat immediately after you solve it."
After she finished speaking, she took out the draft paper she had prepared in her schoolbag: "Here!"
"Set V It is a finite-dimensional Euclidean space, V1, V2 are non-trivial subspaces of V and V="
The most troublesome thing for him in the mathematics of the earth is to remember nouns, finite-dimensional and Euclidean spaces, these concepts and corresponding nouns and Zheng The education he received was quite different.
Zheng Li scanned the question at a glance and said directly:
"This is a very typical question to be solved by using matrix expansion thinking. First, set dimV1=m, dimV2=n, let m, n>0. Take V1 and V2 respectively. Each set of orthonormal bases of V, together they are a set of bases of V."
Zheng Li said while writing on the draft paper, and just finished writing when he finished the solution.
"The essence of this question is to test your understanding of the application of the matrix concept in Euclidean space."
Li Miaomiao snatched the draft paper from Zheng Li's hand. Her first reaction was "the words are a bit ugly."
Li Miaomiao took the paper After carefully reading the answers above, he stared at the other party with his good-looking eyes, as if he wanted to get to know Zheng Li again.
Although she couldn't understand whether Zheng Li's answer was right or not, combined with Zheng Li's explanation, Li Miaomiao's intuition told her: This should be right.
Li Miaomiao came prepared today. Although the couple was over for a week, 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 from the Internet to embarrass Zheng Li, in order to make him realize his mistake and get back on track.
For most college students, the most important thing in student career is grade point.
The problem she was looking for was a problem in the finals of the college mathematics competition: "Have you done it before?"
Zheng Li shook his head: "No, do you need to do such a simple problem to 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 question, if he just came here, he might not be able to understand the question, but fortunately he passed the test these days When a computer searches for information on the Internet, it almost always browses English pages.
English in mathematics is very simple, and the grammatical structure cannot be simpler, as long as you know the meaning of nouns, you can understand it.
"The first question says that f(x) is a continuous function on R, and its domain and value range are both R, and then the condition is given that when n tends to infinity, dividing f(n) by n will is equal to n. Then let you prove sup|f(x)-2014x|<∞, let sup|f(x)-2014x|=M, M is limited."
"For x∈R, there is always such a The fact is established, there is n, so 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 of t ranges from 0 to 1, which is a closed set."
At this time, if Li Miaomiao listens carefully to Zheng Li's speech, he will find that his speech rhythm is very stable, and his tone is also calm. Variety.
But now her mind is full of: who am I, where am I, what is he talking about.
Just like the first question, Zheng Li wrote while talking, filling the front and back of the two draft papers. After Zheng Li finished writing, he pushed 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. Do you not understand any step by step
?"
Blushing, she was embarrassed to say that she didn't understand.
There are basically classes every afternoon in the Numerical Academy, and the study room is usually empty except for the exam week. So no one else bothered the two of them.
Li Miaomiao shook her head, and cleared up what she had just heard from Zheng Li: As a person who learns advanced mathematics, you don't need to know so much.
"Wait for me for a while, I'll take it to my friend to show me whether what you said is right or not."
Zheng Li nodded and said it doesn't matter. He has full confidence in himself. As a mage who has lived for a long time, this kind of The very elementary content of the analysis is not difficult for him at all, and it is not as difficult as eating dessert after a meal.
He was surprised by the primitive way of transmitting knowledge on the earth, the efficiency of listening, speaking, reading and writing is too low.
The way of knowledge transmission does not match the level of technological development.
When Zheng Li was in the Mage Academy, everyone paid through the magic net and downloaded the purchased knowledge into their brains. A flash of nostalgia flashed in his eyes. Countless years have passed since he lived in the academy.
In his opinion, the acquisition of 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 to see if these questions are written correctly, please After that, I will ask my dad to treat you to dinner."
Liu Gui is a professor in the Mathematics Department of Jiangcheng University, and he and Li Miaomiao's parents have been colleagues for many years, and they have watched her grow up since she was a child.
Liu Gui was in the office of his Mathematics Academy at this time, and shook his head helplessly after receiving the call: I need to trouble him for the advanced mathematics of the freshman.
He glanced at his phone and his expression became serious.
Liu Gui thought it was just a freshman's advanced math, but he found out that what the other party took 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 he was deeply impressed by the topics of this year's Qiu competition.
Liu Gui turned on the computer, read it carefully on the computer screen, and then dialed the phone immediately:
"The writing is very good, but it must not be done by you, not to mention that the handwriting is completely different from yours, and the topic alone is not the same. You can do it."
Li Miaomiao refused: "You look down on people, don't you? Why are you so sure."
Liu Gui: "I don't know where you found that geometry problem. The difficulty is at least the end of the first year of the mathematics college The final question of the exam, given that you can only score 120 points in high school mathematics, you will definitely not be able to do it."
"The other two analysis questions are the content of this year's Qiu competition, if you can do it, you won't be able to learn it Liberal arts and mathematics."
Liu Gui said mercilessly: "Tell me, who did you ask to do it?"
Li Miaomiao didn't take it seriously after being teased, but smiled and said: "Hey, can you tell me that you did it right first?"
Liu Gui nodded and said: "There is nothing wrong with doing all three questions. The thinking is very clear, and the solution is also the most concise solution.
" Who did you ask to do it?"
"I took the junior students this year, and when I took the selection exam, I didn't find anyone who could get these two analysis questions right."
Over the years, Qiu Sai has been reinstated by Qingbei, and at most one extra All the people from the University of Science and Technology of China took over. Even if the mathematics department of Jiangcheng University can be ranked among the top ten in China, the students of Jiangcheng University will have to depend on luck if they want to win the bronze medal in the Qiu competition.
Li Miaomiao smiled and said, "It's a freshman in your college, his name is Zheng Li."
Liu Gui looked shocked on the other side of the phone: "It's the Zheng Li who claims to be able to answer freshman math analysis and advanced algebra problems for a fee. " ?