Although his mind was a little messy, when Qiao Yu sat down at the table and opened the "Introduction to Riemannian Geometry", his mind immediately calmed down and he devoted himself to this mathematics book that he could not understand before.
Regarding self-study, Qiao Yu actually has his own method, especially for foreign languages.
The former is a metaphor for listening more, memorizing more, and speaking more.
Buy foreign language comparison dictionaries online, sit in front of the computer, listen and read the lines in the movie over and over again, look up new words in the dictionary on the spot, and then memorize them. Read the grammar content during the break.
Initially it might take one or two weeks to finish watching a movie.
Then the progress gradually accelerated. By the time a new foreign language movie could be watched in three hours, he had basically mastered the listening, reading and writing skills of a foreign language.
Mathematics is different.
In fact, Qiao Yu knew very early on that the reason why he found it more and more difficult to learn is that mathematics is a subject that requires prerequisite knowledge. Therefore, when he reopened "Introduction to Riemannian Geometry" this time, he did not want to directly learn the content in it, but It needs to be clarified what prerequisite knowledge he needs.
So Qiao Yu turned on the old computer at home. When he encountered a concept he didn't understand, he looked it up online and marked it.
Half an hour later, there were dense records in the book.
Calculus, linear algebra, differential geometry, topology, and differential equations, especially differential equations on manifolds.
Of course, more details include multivariable calculus, especially curves, integrals on surfaces, derivatives; linear algebra’s vector spaces, matrices, linear maps, eigenvectors, and other messy things.
The good news is that Qiao Yu has learned some bits and pieces of calculus and linear algebra some time ago, and they don't feel particularly difficult.
The bad news is that Qiao Yu has not studied differential geometry, topology, or ordinary differential equations and partial differential equations. Even if you don't need to learn so much now, you will definitely have to learn it in the future if you really want to rely on mathematics competitions to get admitted to university. .
The worse news is that after roughly understanding it online, Qiao Yu found that none of these subjects seemed easy to deal with.
It would be great if he could pass the Mathematics Olympiad and earn a lot of money from the school, and be recommended to Yanbei University to study foreign languages. Anyway, he just wants the diploma from Yanbei University...
Qiao Yu was having unbearable thoughts in his mind when the door was suddenly knocked twice and then pushed open. The next moment, Xia Keke's little head poked in.
"Brother Qiao, I'm here to tell you to go home."
"Oh, then you should go home quickly!"
"Let me see how you're doing with your studies?"
"Is it difficult to know high-end mathematics? How can you learn a flower in just half an hour?" Qiao Yu turned his head and said seriously, planning to go back and make excuses for his fear of difficulty.
"Is that so?" Xia Keke replied, thought for a while, then got into the room and closed the door behind her.
"What are you going to do?" Qiao Yu watched the little girl rushing over with vigilance, and quickly stood up and put on a defensive posture.
No one understands this little girl better than him. Underneath her innocent face, which is harmless to humans and animals, she has a heart that fears the world will be in chaos. Although he was indeed naughty when he was a child, many of his bad ideas came from this little girl. But in the eyes of adults, he is the main culprit.
The room was just that big, and the next moment, Coco was standing next to him.
Qiao Yu was already 1.75 meters tall, but the little girl in front of him was only one forehead shorter than him. Then before Qiao Yu could react, the little girl suddenly stood up on her tiptoes...
First, a burst of fragrance came from the tip of the nose, and then there was a soft touch on the lips, with a hint of coolness, and it seemed a little sweet.
Fuck, it’s too sudden...
Didn't have time to use flash...
When Qiao Yu came to his senses, he saw Xiao Nizi's bright eyes opposite him, staring at him with a half-smiling expression.
He, a young man who was just fifteen years old, single and full of energy, was actually taken advantage of like this?
What a big loss! He suddenly wanted to take revenge!
"I know you are angry, but if you dare to talk back, I will call for help!" Xiao Nizi whispered confidently.
"Shame!" Qiao Yu felt trembling with anger, but did not say anything.
He is a recognized delinquent in his family's courtyard, while his opponent is an invincible beautiful girl with both good character and academic performance and a bright future. With the support of stereotypes, his opponent's public opinion advantage is too great.
"But, if you can really win the prize in the National Mathematical Olympiad, I will allow you to come back with revenge." Xiao Nizi said softly with pride.
"Keke, it's very late. I have to go home and go to bed. I have to go to class tomorrow." The old man's voice came from outside the door.
"Okay, okay, I know!" Xiao Nizi responded loudly, then made a face at Qiao Yu, turned around quickly and rushed out.
As I walked out of the room, I could still hear the old man muttering outside the door that had just been closed: "Little girls, please don't run into the boy's room."
"I know, I just said goodbye politely, Nao, you often teach me to be polite!"
Today he lost, a complete defeat.
"Hey, why is your face so red all of a sudden?" The probing gaze of Qiao Xi, who was leaning on the sofa, made Qiao Yu slightly off guard.
"I'm blushing?"
"Go and look in the mirror. It's no different from a monkey's butt on Mount Emei."
"Maybe it's because the weather is too hot. I'm going to brush my teeth first." Qiao Yu replied calmly, then rushed into the bathroom, stood in front of the sink mirror, and took a look. Sure enough, his face did look red. , very worthless.
Qiao Yu took a deep breath and picked up the toothbrush.
"What happened in the room just now?"
Qiao Yu turned his head and saw Qiao Xi leaning in front of the bathroom door with a gossipy look on her face.
"I just said goodbye, what else can I do? What did you talk about outside just now?" Qiao Yu felt a little guilty.
"Qiao Yu, something's wrong with you!" Qiao Xi suddenly said.
"Huh?" Qiao Yu was surprised.
"You never cared about what I talked about with Coco before!" The tone in which Qiao Xi said this reminded Qiao Yu of the classic line from the anime Detective Conan: "There is only one truth."
Qiao Yu calmed himself down and replied calmly: "Does this mean anything?"
Then I started brushing my teeth step by step, and the blush on my face began to slowly fade away.
"Yeah, that's right."
Qiao Xi muttered to herself next to her, and then started talking to herself: "Actually, I didn't talk about much with Coco just now. She just kept asking about Teacher Lan's home visit. I told her something, and then I
I just said that I don’t know if you will have a wife and forget about your mother when you become successful.
Coco said that she believed you would not do it. Even if you really have no conscience in the future, she would still take care of me when she grows up. Look, this girl is so considerate, unlike you! She loves me every day. By the way, I was little just now.
The girl won't go into your room and play the trick of a little girl confessing her love, right?"
Qiao Yu, who was brushing his teeth, paused for a moment, then turned his head expressionlessly, glanced at his mother who was smiling but not smiling, turned around, picked up the door handle, closed the bathroom door directly, and then locked it...
"Bang!"
"Crack!"
Chapter completed!