Li Miaomiao was speechless: "You spend all day on the computer, how can you expect to get over 90 on the final exam?"
"If you're a literature major, I can assume you're using your computer to read academic papers and memorize texts. The problem is that math courses require a lot of calculations and practice."
She was somewhat disappointed, disappointed by the other person's arrogance.
Zheng Li shrugged: "We'll see."
Li Miaomiao nodded: "No need to wait and see. I have some questions here that I need your help with."
"No problem, but there's a fee." Zheng Li thought to himself that he finally had his first order.
Li Miaomiao didn't dwell on the issue of payment. "You help me solve it first, and I'll transfer the money to you on WeChat as soon as you find the answer."
After saying that, she took out the draft paper she had prepared from her schoolbag: "Here!"
Let V be a finite-dimensional Euclidean space, and V1 and V2 be nontrivial subspaces of V such that V = ...
The most troublesome part of Earth's mathematics for him was memorizing terms like finite dimensions and Euclidean space. These concepts and their corresponding terms were completely different from the education Zheng Li had received.
Zheng Li glanced at the question and said directly:
"This is a typical problem that can be solved using matrix extension thinking. First, let dimV1=m, dimV2=n, and let m and n=0. Take an orthonormal basis for V1 and V2 respectively, and together they form a basis for V..."
As Zheng Li spoke, he wrote on a draft paper, finishing writing just as he finished explaining the solution.
"The essence of this question is to test your understanding of the application of the concept of matrices in Euclidean space."
Li Miaomiao snatched the draft paper from Zheng Li's hand. Her first reaction was, "The handwriting is a bit ugly."
After carefully reading the answers on the paper, Li Miaomiao stared at the other person with her beautiful eyes, as if she wanted to get to know Zheng Li again.
Although she couldn't understand whether Zheng Li's answer was right or wrong, based on Zheng Li's explanation, Li Miaomiao's intuition told her: it should be correct.
Li Miaomiao came prepared today. Although the one-week relationship had ended, Li Miaomiao still regarded Zheng Li as her friend. She had an inexplicable sense of loyalty to her friends.
She deliberately found difficult questions online to embarrass Zheng Li, hoping to make him realize his mistakes and get back on track.
For most college students, GPA is the most important thing in their student life.
The question she found was from the final round of the National Undergraduate Mathematics Competition: "Have you done this before?"
Zheng Li shook his head: "No, do you really need to do practice problems to solve such a simple one?"
Li Miaomiao nodded: "Okay, it's only been five minutes. I still have two more questions here. Please help me solve them too."
“Let f：RR 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 had just arrived, he probably wouldn't have been able to understand it. Fortunately, when he searched for information online these past few days, he had mostly browsed English pages.
Mathematical English is very simple; the grammatical structure is extremely simple, and you can understand it as long as you know the meaning of the nouns.
"The first question states that f(x) is a continuous function on R, with both its domain and range on R. It then gives the condition that when n approaches infinity, f(n) divided by n will equal n. The question then asks you to prove sup|f(x)-2014x|∞. Without loss of generality, assume sup|f(x)-2014x|=M, where M is finite."
"For x∈R, there always holds the fact that there exists an n such that x lies 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 t takes values from 0 to 1 and is a closed set."
If Li Miaomiao listened carefully to Zheng Li's speech at this moment, she would find that his speaking rhythm was very stable and his tone did not change.
But right now, all she can think about is: Who am I? Where am I? What is he saying?
Just like with the first question, Zheng Li wrote as he spoke, filling both sides of the two draft papers to the brim.
After Zheng Li finished writing, he pushed the paper towards her, saying, "If there's anything you don't understand, you can ask me. If you didn't understand, you can read through my answer first. Is there any step you don't understand?"
Li Miaomiao blushed; she was too embarrassed to admit that she hadn't understood any of the parts.
The math department has classes almost every afternoon, and the study rooms are usually empty at this time, except during exam weeks. So no one else bothers them.
Li Miaomiao shook her head, clearing away everything she had just heard from Zheng Li: As someone who studies advanced mathematics, you don't need to know so much.
"Wait a moment, I'll take it to my friend and have him check if what you said is correct."
Zheng Li nodded, indicating that he didn't care. He had full confidence in himself. As a monk who had lived for a long time, this kind of basic analysis was no challenge for him at all. It was not as difficult as eating dessert after a meal.
The way Earth transmits knowledge is so primitive that it surprises him; the efficiency of listening, speaking, reading, and writing is too low.
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