After being woken up by Zhou Shuang's roar and his vague 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 has developed before.

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

Qiao Yu developed a strong interest in algebra and number theory. While reading at night, 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 class videos of top professors from top Chinese universities on the Internet, you can even find complete videos of top foreign universities.

Yanbei University, Huaqing University, Shuangdan University, Xi'an Jiaotong University, MIT abroad, Princeton Institute for Advanced Study, Harvard... you can find it all! If you were more patient, Qiao Yu even found Fields Medal winners on the Internet. Published popular science lecture videos on number theory.

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

In addition, Qiao Yu's English is very strong, and what he lacks is just some mathematical terms. After encountering them a few times, he can understand them, so that he does not have to be troubled by poor subtitle translations and can directly absorb the most complete knowledge of those big guys. Explained, so progress is rapid.

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

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

It was a bit troublesome to use my phone to watch videos directly in class during the day, so I just used it to answer questions.

Qiao Yu copied many questions about algebra and number theory from the Internet in his exercise book. Fortunately, the final track of the Little Libaba World Mathematics Competition also included algebra and number theory. Moreover, the questions were very clever, so Qiao Yu naturally copied them. Come down.

Study and prepare for the competition at the same time.

Finding out the distribution patterns of prime numbers and solving the problem of factoring large prime numbers are mid- and long-term plans for the dream of getting rich. Getting rewards from the school and the prize money from the Little Libaba competition are short-term plans.

People have to live first before thinking about the future. If possible, it is best to live more comfortably.

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

On one side, Qiao Yu took out his exercise book. On the other side, Zhou Shuang, who was silently comprehending what Qiao Yu just said, stretched his head over before entering the study mode.

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

What he saw then seemed to be a math problem, and the question seemed to be written because he didn't quite understand what Qiao Yu had copied. The most terrible thing was that the question stem was taken apart, and except for a few weird letters, he couldn't understand each of the questions. He knew every word, but when combined together, it made him feel like he was reading the exercises 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 this question seems too abstract. What is an ideal I? What is a closed ideal? Didn’t the primary school Chinese teacher say that ideals are individual human beings’ plans and aspirations for the future? How can it still be closed?

"Yes, a math question. This ideal is not an ideal in Chinese, but a concept in ring theory. You can understand that ideal is a special subset of a ring."

"What is ring theory?"

"You've never heard of it, right?"

"Um."

"Have you ever heard of linear algebra? An ideal is similar to a subspace of a vector space in linear algebra. When you go to college, you will definitely come into contact with this stuff."

"The big universe is within the small universe?" Zhou Shuang had never heard of linear algebra, but he understood subspace consciously.

There are often settings like this in fantasy novels. After the protagonist ascends from the original world, he discovers that the universe he is in is just a branch of a larger universe. If you want to make progress, you must continue to fight monsters and upgrade, and do what you did in the small world before. Things, do it again.

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

"So how come this math problem looks like 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 analysis after analyzing the original question. There must be a solution. The conditions are very clear. The ideal I is closed, which means that for When the variables x and y are scaled, the degree of the polynomial remains unchanged.

Given that the dimension of the quotient ring is 6, it means that there are 6 independent quotient ring primitives. Combining other conditions, it can be seen that these ideals have specific algebraic geometric structures. Combining the conditions of conditional one-dimensional number and scaling invariance, we can It can be deduced that the number of ideal I's is limited. See, once you think about it, this question is actually not difficult, right?"

Qiao Yu explained to Zhou Shuang casually, in a standard chicken-to-duck manner.

He knew that Zhou Shuang would definitely not understand, so he was actually trying to persuade this guy to quit despite the difficulties.

Junior high school teachers have never taught such things as ring theory and group theory.

He has an understanding of ring theory because when he was studying statistics, he came into contact with homology statistics and needed to use algebraic topology to analyze data structures. Data structures include ring structures, homology groups, etc.

Moreover, many results in algebraic topology are based on ring theory. In the same way, it is precisely because it involves algebraic topology that Qiao Yu also has some research on group theory. After all, one of the most classic concepts in algebraic topology is the fundamental group, which Describing the surrounding properties of space through paths is actually a group.

Yes, just to find a way to solve the lottery problem, Qiao Yu spent more than two years on the Internet to learn all kinds of mathematical knowledge, trying to find loopholes in the mathematical design of the lottery through various mathematical principles, so as to proceed. The principles of making a fortune.

It turned out that the Chinese lottery had no loopholes for mathematicians. You can imagine how big a blow it was to Qiao Yu.

Of course, it is not without its benefits. This confirms that Qiao Yu will never touch anything that is too risky, such as betting or stock trading...

The point is that it is best not to be too ambitious.

Qiao Yu felt that the backlash caused by people trying their best but not being able to reach the goals they set for themselves can sometimes be cruel, especially when Star City clearly stipulates that junior high school students are not allowed to repeat a grade.

After all, with the learning ability and knowledge reserve shown by Zhou Shuang, it is really too difficult to just pass the line after working hard for the last month. If you can get into the general high school in this way, it is indeed a good idea for those who study hard every day and never
Chapter completed!