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Chapter 41 Good intentions
After being woken up by Zhou Shuang's shout and implicit suggestions, Qiao Yu wanted to continue sleeping on his stomach but found that he couldn't fall asleep.

This is probably due to the good living habits that Qiao Yu had developed before.

Unable to sleep, Qiao Yu took out his exercise book and began to work on the questions.

Qiao Yu developed a strong interest in algebra and number theory. At night, while reading books, he used the Internet to find various teaching videos to deepen his understanding of modern algebra and number theory systems.

Qiao Yu is truly grateful to the almighty Internet.

Not only can you easily find complete lecture videos of top professors from top universities in China on the Internet, you can even find complete videos of top universities abroad.

Yanbei, Huaqing, Shuangdan, Xi'an Jiaotong, MIT, Princeton Institute for Advanced Studies, Harvard... it's really everything! If he was more patient, Qiao Yu even found a popular science lecture video on number theory posted by a Fields Medal winner on the Internet.

Although many of them are not in the form of a blackboard, such as the Fields Medal winner, Richard E. BORCHERDS, who directly started his lecture with a piece of paper and a pen, the effect is similar for Qiao Yu.

In addition, Qiao Yu's English is very strong. What he lacks are just some mathematical terms. After encountering them a few times, he is able to master them. He does not need to be bothered by the poor subtitle translation. He can directly absorb the most complete explanations from those big guys, so he makes rapid progress.

This is also the reason why he enters the learning state at night and unknowingly studies until three or four in the morning. The extremely high difficulty makes him experience the joy of learning again.

Can't sleep, can't sleep at all.

It was a bit troublesome to watch videos on my phone during class, so I just used it to practice questions.

Qiao Yu copied many algebra and number theory questions from the Internet in his workbook. Fortunately, the finals of the Xiaolibaba World Mathematics Competition also included algebra and number theory. The questions were very clever, so Qiao Yu naturally copied them down.

Study and prepare for competitions at the same time.

Figuring out the distribution of prime numbers and solving the problem of factoring large prime numbers are mid- and long-term plans for the dream of getting rich, while getting awards from school and prize money from small competitions are short-term plans.

People have to survive first before they can think about the future. If possible, it would be best if they could live more comfortably.

Money can provide adequate nutrition and maintain a good mood, so it is very important.

Qiao Yu took out the exercise book, while Zhou Shuang, who had not yet entered the learning state and was silently trying to understand what Qiao Yu had just said, leaned his head over again.

There was no way. He was now extremely curious about everything Qiao Yu did.

Then he saw something that seemed to be a math problem, and the question stem was written by Qiao Yu because he couldn't understand it. The worst thing was that when the stem was separated, he knew every word except a few strange letters, but when they were put together, he felt like he was reading a martial arts method in a fantasy novel.

"Is this a math problem? What does ideal mean?" Zhou Shuang couldn't help but ask.

The main reason is that the question is too abstract. What is an ideal? What is an ideal closure? Didn’t the elementary school Chinese teacher say that an ideal is a human individual’s plan and vision for the future? How can it be closed?
"Yes, it's a math problem. This ideal is not the ideal in Chinese, but a concept in ring theory. You can think of it as an ideal being a special subset of a ring."

"What is ring theory?" "You haven't heard of it, right?"

"Ah."

"Have you heard of linear algebra? An ideal is similar to a subspace of a vector space in linear algebra. You will definitely come across this when you go to college."

"A big universe within a small universe?" Zhou Shuang had never heard of linear algebra, but he felt he understood subspace.

There is often such a setting in fantasy novels. After the protagonist ascends from his original world, he finds that the universe he is in is just a branch of a larger universe. If he wants to make progress, he must continue to fight monsters and level up, and do everything he did in the small world again.

Qiao Yu glanced at Zhou Shuang sideways, then nodded affirmatively, indicating that this understanding was really great!

"So how come this math problem is like something from a fantasy novel? Can this thing really be solved?" Zhou Shuang asked again like a curious baby.

"You didn't see the original question. The original question was not stated like this, it was more abstract. This is my solution after analyzing the original question. There must be a solution. The conditions are very clear. Ideal I is closed, which means that the degree of the polynomial does not change when the variables x and y are scaled.

The dimension of the given quotient ring is 6, which means there are 6 independent quotient ring primitives. Combining other conditions, we can know that these ideals have a specific algebraic geometric structure. Combining the conditions of one dimension and scaling invariance, we can deduce that the number of ideals is finite. See, once you think about it, this problem is not difficult, right? "

Qiao Yu explained to Zhou Shuang casually, which was a typical case of talking at cross purposes.

He knew that Zhou Shuang would definitely not understand, so he was actually trying to persuade this guy to give up.

Things like ring theory and group theory were not taught by our junior high school teachers.

He has some knowledge of ring theory because he came across homology statistics when studying statistics. He needed to use algebraic topology to analyze data structures, which include ring structures and homology groups.

Moreover, many results in algebraic topology are based on ring theory. Similarly, because of algebraic topology, Qiao Yu also did some research on group theory. After all, one of the most classic concepts in algebraic topology is the fundamental group, which describes the surrounding properties of space through paths, which is actually a group.

Yes, just to find a way to solve the lottery problem, Qiao Yu spent more than two years desperately absorbing various mathematical knowledge on the Internet, trying to find loopholes in the mathematical design of the lottery through various mathematical principles, so as to embark on the path to becoming rich.

It turned out that the China Lottery had no loopholes at all for mathematicians. You can imagine how big of a blow this was to Qiao Yu.

Of course, it is not without benefits. This has made Qiao Yu determined that he will never touch anything that involves gambling, such as gambling, or stock speculation...

The key point is that people should not aim too high.

Qiao Yu felt that when people tried their best but failed to reach the goals they set for themselves, the backlash could sometimes be cruel, especially since Xingcheng had a clear rule that junior high school students were not allowed to repeat a grade.

After all, with Zhou Shuang's learning ability and knowledge reserves, it would be too difficult for him to pass the entrance exam directly after working hard for the last month. If he could get into a regular high school like this, it would be disrespectful to those children who study hard every day and never dare to slack off.

(End of this chapter)