I Just Want to Be a Quiet Top Student

　　 Time is not affectionate, it passes very slowly while waiting for the salary, and it passes very quickly during the exam.

　　 Shen Qi didn't make any effective actions within an hour, and there was not much time left for him.

　　 Is it over? Is it all over.

　　 Is this my limit.

　　 No, this should not be the fate of Xueba.

　　 I have passed many subjects.

　　 also played games all night.

　　 I used to have a king rank.

　　 became a scumbag in a blink of an eye.

　　 I was disappointed and lost all directions.

　　 Until I saw mathematics, it was the only answer.

　　 During this hour, Shen Qi thought a lot, and when he was thinking about reminiscing about the past, it showed that he really had nothing to do.

　　 What is the source of this digital array? It looks like a group in terms of form, but I have never seen such a weird group, full of magic. It may be a fake group, right? Is it not a group at all?

　　 I tried my best to search in the brain knowledge base, and the only response to Shen Qi... The knowledge point you called is not in the service area.

　　 There is no way, no matter how strong the brain is, if there is a knowledge blind zone, it will give up treatment.

　　 Unless you create a new theory yourself, this is the only way.

　　 But Shen Qi currently does not possess this kind of self-contained master level.

　　 "Perhaps the previous time I took the exam with full scores, I went too smoothly along the way. How do you say that, the sky will be relegated to the people of Sri Lanka, and I must first suffer from his will and win his sister."

　　Shen Qi in the predicament was thinking wildly, thinking that he laughed himself, I am so talented, is this level 1 Chinese?

　　 "Teacher Tian, ​​you won't be able to save me this time. The six-decimal system is useless here."

　　 "Guerlain Liu, the algebraic knowledge you talked about is too exaggerated. This time I didn't use anything at all in IMO. I can get to this point by my own exploration."

　　 "Teacher Zhang, I haven't seen you for a long time. When I was in math grade 4, you stopped giving me a small stove and said there was nothing to teach me."

　　 The past scenes are played in Shen Qi's mind in fragmented ways. The experience of the past few months is like a dream. If you can get the IMO number one in the world, it will be the most beautiful dream.

　　 "Teacher Zhang, I went to your office a few months ago, and you asked me where I have learned by myself."

　　 "I said, I learned the Cayley transition matrix and the Weilstrass quadratic form. At that time, it was a bit pretending. At that time, I also had a little knowledge."

　　 "Then you were stunned in an instant."

　　 "I can't forget this scene. From then on I started the road of learning dominance."

　　 "Hehe, time flies, it's a third year in a blink of an eye."

　　 "Hehe... Fuck!"

　　 Shen Qi was a rousing spirit, he suddenly caught a trace of inspiration, which was fleeting and detached.

This kind of feeling seems to be familiar. At the beginning of this month, the domestic mathematics of the United Nations finale problem, it is this kind of electrical inspiration that saved Shen Qi. Teacher Tian rescued Shen Qi, and he showed off a cuneiform six-decimal system to prove that the root number 2 is Irrational number, show to the national championship champion.

　　 "Go back, go back."

　　 Shen Qi played back the random thoughts just now in his mind.

　　 "Teacher Zhang, I went to your office a few months ago, and you asked me where I have learned by myself."

　　 "I said, I learned the Cayley transition matrix and the Weilstrass quadratic."

　　……

　　 "Although mathematics is just a language or tool on the surface, most of its vivid concepts can provide the key to new areas of thought."

　　 "The determinants and matrices are completely reforms in the language of mathematics. Shen Qi, you must be deeply aware of this in order to make a difference in algebra."

　　……

　　 Shen Qi smiled, very happy, there is no way out of the sky.

　　 Teacher Tian rescued him last time, but this time Teacher Zhang rescued him.

　　 Actually, what Shen Qi should be most grateful for is himself. He never chose to give up in a difficult situation. Mathematics often requires persistence or even madness. He and his last stubbornness saved him.

　　 The Gloria Transition Matrix and Matrix Theory, which were pretended to be used in those years, finally came into play at the most critical moment.

　　 Regardless of what monsters or monsters this digital array is, whether it’s a group or not, they can’t escape the magic mirror in Shen Qi's hands, the matrix.

　　 The tool that can comprehend or translate group theory is the matrix.

　　According to the number array of the title:

　　1=1

　　196884=196883+1

　　21493760=21296876+196883+1

　　864299970=842609326+21296876+2*196883+2*1

　　……

　　Shen Qi wrote a matrix homomorphism:

　　A(gi*gj)=A(gi)*A(gj)

　　 expand it into a matrix expression:

　　|Ag-0|

　　|Ai-0|

　　|0-Aj|

　　……

　　 This matrix language looks very complicated, but its meaning is very simple and direct, that is, the matrix representation of a group G is a homomorphic mapping from the element g of G to a set of fixed-order non-singular square matrix A(g).

　　 To put it simpler, a group is a complex set of passwords that is very difficult to understand, and a matrix is ​​one of the mothers of decrypting a password.

　　The only requirement is that you must be proficient in various decoding methods, the more the better.

　　 If you can use a matrix to describe this digital array, it means it is a certain group, otherwise it is not.

　　 When Shen Qi expressed this number array in a regular replacement method, he was very surprised: "MMP...Monster-Group...It is actually a monster, a monster!"

　　What is the magic group?

　　 is the largest scattered single group.

　　 Compared with other groups, the age of the magic group is very young, only about forty years.

　　 This group is quite scary, so it was named Monster-Group by mathematicians.

　　 It is difficult for ordinary people to play with the demons. When they play, they drive themselves crazy and break the game.

　　 British mathematician Bocherz made a significant contribution to the theory of the magic group. He proved that the "money group moonlight conjecture" is a magical and awesome existence by looking at its name. Bocherz won the Fields Medal for his great achievement.

　　Mathematics, if you want to play it, you need a PhD in mathematics at least for the entry level.

　　 Why does this kind of question appear on the IMO test paper?

　　 There are middle school students in the world who can handle it?

of course not.

　　 don’t need to fix it either.

　　 Shen Qi's understanding is that for this magic group, it is OK to give two different mathematical explanations.

　　 Deciphering the magic group and describing the magic group are two different things.

　　 No one can crack Goldbach’s conjecture, but many people can describe Goldbach’s conjecture: any even number greater than 2 can be written as the sum of two prime numbers.

　　Similarly, what Shen Qi wants to do is the latter, but he cannot use words to describe it in pure mathematical language.

　　 He used two matrix languages ​​to translate

　　1=1

　　196884=196883+1

　　21493760=21296876+196883+1

　　864299970=842609326+21296876+2*196883+2*1

　　……

　　 It is enough to express clearly what it is, no need to decipher it.

　　 This question is about knowledge and the proficient use of matrices.

　　 We all know that there are many kinds of matrix representations for a group, because the order of the matrix can be changed.

　　 "First, let's send the Gloria Transition Matrix." Shen Qi sacrificed Gloria, the founder of matrix theory, and used the Gloria Transition Matrix to express the first magic group interpretation.

　　 "I will send another Jordang Standard Matrix."

　　 Soon, Shen Qi wrote two different matrix expressions.

　　 See if there is still time, he has another shot, and the third shot is the Hermitian matrix.

　　 "If three shots are not enough, then three more shots!"

　　 Shen Qi kills the character, Ka Ka Ka, he successively wrote the Klein abstract group matrix, the Weber prime field matrix, and the Henzel invertible element matrix.

　　 Six shots!

　　 Six shots in over an hour!

　　 "My body is not hollowed out~www.novelmtl.com~ If six shots are not enough, then six more shots!"

　　Shen Qi has never been so cool before, a kind of cool and crooked aftermath.

Jingle Bell.

　　 Then the bell rang.

　　 4.5 hours of competition time has come.

　　 "Six rounds, only six rounds...it's a pity." Shen Qi ran out of time. He only wrote six matrix languages, a little annoyed.

　　 After handing in the paper, Shen Qi saw the Russian players and the Indian-American players chatting and laughing together, and seemed full of confidence.

　　 "There are many masters in the world, and I am not the only one who can do this question." Shen Qi devoted all his life to this IMO. What kind of results can he achieve? Let fate.

　　 scoring work started in the afternoon of the same day and continued until the early morning of the next day.

　　 Professor Wiles, the leader of the judges group, is a 60-year-old man, and still insists on working.

　　 Can't remember how many cups of coffee I have refilled, and Professor Wiles has no sleep.

　　 There are four test papers in front of him, all of which have a full score of 42. They come from four different countries, Russia, the United States, South Korea, and China.

　　 After hesitating for a long time, Professor Wiles finally made up his mind. He gave a "+1" after 42 in one of the full score exam papers.

　　 For the last question, the other three perfect score contestants all used two methods to give mathematical explanations.

　　 The "42+1" player used six types, which is exactly equal to the sum of the other three players.

　　 The "42+1" player is from China, and the English name is Shen-Qi.

　　 The first 43-point player in IMO history was born. His name is Shen Qi.

　　……

　　……

　　This chapter says:

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