This sudden attack made Lin Chaoxi make two decisions.
First, continue to study hard.
Second, the "study hard" work must be more confidential so that Lao Lin cannot find any more signs.
After dinner, Lao Lin took her to stand in front of the two tall bookshelves. Five minutes later, he asked her, "How do you feel?"
“It’s a difficult feeling.”
"Based on your meager knowledge, what do you think is the difficulty of advanced mathematics?"
"It looks like a heavenly book." Lin Zhaoxi said honestly.
Lao Lin looked at her with some disappointment.
But what Lin Chaoxi said was true. She even thought that many people were like her and felt that advanced mathematics was difficult, the kind of difficulty that they could tell was difficult at first glance.
"Are all the things your father has taught you about the beauty of mathematics useless now?"
“But that doesn’t mean these things can become simple.”
“That makes sense.”
Lin Zhaoxi: “…”
Lao Lin turned to look at Pei Zhi: "What do you think?"
"It's okay." Pei Zhi said.
I mean, it looks okay...
Lin Chaoxi stood side by side with the two in front of the bookshelf. The air suddenly became quiet for a while. She finally understood: "Dad, do you know how to teach me?"
Lao Lin smacked his lips and said, "No."
Lin Zhaoxi: “…”
"What's that look?"
"Why not?"
“I didn’t get good results teaching adults before.”
Lin Chaoxi thought, it turns out that he had failed teaching practice experience, but: "Have you also taught adults?"
"I lied to you."
After Lao Lin finished speaking, even Pei Zhi showed a thoughtful expression.
But Lao Lin himself refused to continue the topic. He took a book from the bookshelf, found a quiet corner, and took them to sit down. The warm sunlight of the winter afternoon was shining down, and the air was filled with the old smell of paper, but it was also very comfortable.
"How did you teach Pei Zhi before?" Lin Zhaoxi asked, looking at his father sitting opposite him.
“No,” Lao Lin said honestly. “He can basically understand it by reading the book and doing the exercises.”
This is the difference between ordinary people and geniuses. Lin Chaoxi said sadly: "Dad, you can tell me anything. I can bear it."
"'Difficult' is a degree that cannot be precisely defined." Lao Lin said seriously, "And in mathematics, imprecision is fatal."
Lin Chaoxi nodded. Old Lin's conversion speed was really fast, and she sat up straight in an instant.
“So the foundation of advanced mathematics is not calculus or those complicated formula definitions and their proofs. What you need to be familiar with first is a more precise language.”
Lin Chaoxi somewhat understood what Lao Lin meant: "We find it difficult because we are not familiar with the language of mathematics, just like children who cannot understand what adults say, so we cannot understand many problems."
"Ruzi is teachable. Personally, I think this is where the problem may first arise."
"Dad, you are so sharp." Lin Chaoxi hurriedly flattered him.
"Your flattery is a bit unnatural," Lao Lin commented.
Lin Zhaoxi: “…”
“The word ‘precision’ may sound difficult, but every important statement in mathematics can be expressed in four different languages, either affirmatively or negatively…”
"What?"
"Object a has property p. Every object of type t has property p. There is an object of type t that has property p. If you state a, then you state b." Lao Lin finished speaking in one breath, looking like he had accomplished something, and asked, "Do you understand?"
“I don’t understand…” Lin Chaoxi was confused.
"Congratulations, you now understand a little bit about the difficulty of understanding mathematical language."
"……Thank you."
"You are welcome."
"You can't understand these four sentences right away, which tells us the importance of practice in understanding problems in advanced mathematics." Lao Lin said as he pushed the book he had just taken from the bookshelf over to me. "It's different from elementary mathematics, where the exercises are done to improve your proficiency. The exercises in advanced mathematics are there to help you understand the problems better. Not doing exercises or doing too little practice will definitely not work."
Lin Chaoxi opened it in a daze, and then found that it was a book about formal logic. It did not contain much content, but there were a lot of exercises at the back.
The first part is about the accurate expression of language.
Lao Lin said with some regret: "Of course this book is not very good. Just do it casually and ask me if you have any questions."
He was about to leave after he finished speaking, but Lin Chaoxi quickly stopped him.
"dad!"
"Any questions?"
"Then how can I learn?"
"This question is quite valuable." Lao Lin looked back at her and smiled. "Personally, I think that the way to learn advanced mathematics and even most subjects in college should be self-study. Under the guidance, you should find a path that you can understand, build your own knowledge system and keep climbing up. Then answer a question: Among the countless explanations of 'what is mathematics', there is a sentence that goes like this: mathematics makes the invisible visible. How do you understand this sentence?"
At this point, Lao Lin pretended to be casual and said, "Anyway, you will go to Yongchuan in a few days to take the Mathematical Union exam, and you can also attend the intensive training. If nothing unexpected happens, you will attend the intensive training at Sanwei University. The books there are good. I will make a list of books for you and you can study them yourself. You can do this book casually first. If you have any questions, summarize them and ask me when the time comes." After Lao Lin finished speaking, he said very straightforwardly, "Then the class is over."
Lin Chaoxi finally understood why Old Lin said that his teaching effect on college students was not very good...but she immediately found the most critical issue from that sentence: "Wait...are we going to Sanwei University for intensive training?" She asked in disbelief.
"Didn't I say that before?"
"No." Pei Zhi said without giving any face.
"Well, now you know."
"Why?"
"Lao Zhang called to inform me. If you don't want to go, I'll tell him."
Old Lin's level unexpectedly became higher and higher. Lin Chaoxi and Pei Zhi looked at each other for a while, unable to slow down at all.
Lao Lin patiently explained: "Have you done the test paper in Yongchuan?"
Lin Zhaoxi subconsciously wanted to say "no", but suddenly remembered that they didn't "do it", but often did the test papers sent by Yongchuan in the Internet cafe...
"It's said that it was some kind of selection test. Did you fall for it?" Lao Lin said, "Lao Zhang is really too ambitious. But you guys can go to Sanwei University and see what a higher education institution is like."
Lao Lin spoke quickly and tried his best to appear nonchalant, but Lin Chaoxi could still sense a hint of unnaturalness and indescribable frustration in his tone.
She even felt that Lao Lin didn't actually want her to go there, so he chose the most understated way in his subconscious mind to inform them.
——
Two days later, Lin Chaoxi and Pei Zhi received a training notice from the Provincial Education Commission. It was not sent through the school but was sent to their home alone.
She opened the letter and read it through, only to find that it was not a short-term training program, but a training program that lasted for a whole year and utilized almost all of their vacations.
The first phase started on January 15, one day after the mathematics league exam, which meant that they could just pack their bags and live in Sanwei University without having to go home until the Spring Festival.
January 9th to January 12th - Final exams
January 13-14——National Middle School Mathematics Competition
January 15th - The first training session begins
From February 16th to February 22nd, the Spring Festival holiday,
February 23~March 1——Second training session
May 1st ~ May 7th - The third training session
June 10th - Anning City High School Entrance Examination
Lin Chaoxi carefully arranged her schedule and found that her time was more tight than she thought. In the past six months, she not only had to deal with the high school entrance examination, but also had to deal with intensive training. More importantly, she had to teach herself advanced mathematics and find a way to solve the problem of Lao Lin's car accident.
She thought she was well aware of the urgency of time, but she discovered that plans never keep up with changes in this world.
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