Chapter 41 Good Intentions
After being woken up by Zhou Shuang's roar and 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 started thinking about 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 really grateful to the almighty Internet.
Not only can you easily find complete class videos of top professors from top universities in China on the Internet, you can even find complete videos of top foreign universities.
Yanbei, Huaqing, Shuangdan, Xi'an Jiaotong University, foreign MIT, Princeton Institute for Advanced Study, Harvard... you really have it all! If he had been more patient, Qiao Yu had even found a popular science lecture video on number theory posted on the Internet by a Fields Medal winner.
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. What he lacks is just some mathematical terms. After encountering them a few times, he can understand them, so that he does not need to be troubled by poor subtitle translations and can learn them directly. Those big guys gave the most complete explanations, so I made rapid progress.
This is also the reason why he enters the study state at night and unknowingly learns 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 little troublesome to use my phone to watch videos during the day in class, 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, algebra and number theory were also included in the final track of the Little Libaba World Mathematics Competition. Moreover, the question was very clever, so Qiao Yu naturally copied it.
Study and prepare for competition at the same time.
Understanding 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 awards from the school and prize money from the Little Libaba Competition are the immediate plans.
People have to survive first before they can think about the future. If possible, it would be best to live more comfortably.
Money can provide sufficient nutrition and maintain a good mood, so it is very important.
On one side, Qiao Yu took out an exercise book. On the other side, Zhou Shuang, who was silently comprehending what Qiao Yu just said, stretched his head over before he entered the study mode.
No way, he is now extremely curious about everything Qiao Yu does.
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 when the question was taken apart, except for a few weird letters, he knew every word, but when put together, it made him feel like he was reading the exercises in a fantasy novel.
"Is this a math question? 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 ideal closure? 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 mathematical problem. This ideal is not an ideal in Chinese, but a concept in ring theory. You can understand that an ideal is a special subset of a ring."
"Ring "What is it?" "You haven't heard of it, right?"
“Hmm.”
“Have you ever heard of linear algebra? The ideal is similar to a subspace of a vector space in linear algebra. This thing, when you go to college, you will definitely You will get in touch with it.”
“The big universe is a small universe?” Zhou Shuang had never heard of linear algebra, but he understood subspace.
There is often a setting 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 again.
Qiao Yu glanced sideways at Zhou Shuang, and then nodded affirmatively, saying 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, and the ideal I is Closed, which means that the degree of the polynomial is unchanged when scaling the variables x and y.
The dimension of the given quotient ring is 6, which means that the degree of the polynomial is constant. 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 one-dimensional numbers and scaling invariance, it can be deduced that the number of ideal I is limited. , 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, but 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 knows about 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 and homology groups.
And 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 describes the surrounding properties of space through paths. It 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 the mathematical design of the lottery through various mathematical principles. loopholes, thus embarking on the path to making a fortune.
It turned out that the Chinese lottery had no loopholes for mathematicians. You can imagine the blow to Qiao Yu.
Of course it is not without its benefits. This confirms that Qiao Yu will never touch anything that is too game-like. For example, betting, or stock trading...
The point is that it is best not to be too ambitious.
Qiao Yu feels that the backlash caused by people trying their best but being unable 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 indeed 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, you really don't respect those children who study hard every day and never dare to slack off.
(End of this chapter)