Hearing Professor Yang's roll call, all the freshmen's attention followed Yang Wuzhi's gaze and fell on the seventh person in the classroom. Yu Hua, who suddenly became the focus of the crowd, held a pen in his right hand and was writing mathematical characters one after another on the draft paper. An expression of extreme concentration.
"For the rest of my life." Seeing Yu Hua's focused look, Yang Wuzhi was not angry and just shouted again.
Seeing this, the student sitting closest to Yu Hua quickly knocked on Yu Hua's desk.
"Uh...Professor Yang, did you call me?" Yu Hua asked with a little embarrassment as he stepped back from his engrossed and efficient study state. Feeling the attention of everyone, he asked.
Yang Wuzhi nodded: "Tell me the definition of Lebesgue integral."
Hearing this question, feeling the atmosphere in the classroom and the gazes of the classmates, Yu Hua still didn't know the situation. As the first author of the paper on reconstructing Lebesgue integrals, he was very familiar with Lebesgue integrals. Then he started to talk: "The definition of Lebesgue integral is..."
From the definition of Lebesgue integral to examples and applications, Yu Hua ended with the difference between Lebesgue integral and Riemann integral.
"The Lebesgue integral sums by dividing the value domain, and the Riemann integral sums by dividing the definition domain. As a result, the Lebesgue integral is based on the Lebesgue measure theory, and it is an expansion of the Riemann integral. , and the important significance of Lebesgue integral itself is to reconstruct the basic theorem of calculus and lay the foundation for the birth of the subject of real variable function theory. I have finished speaking, thank you." After Yu Hua finished speaking eloquently, he sat down again.
There was silence in the classroom.
The six seniors who entered the Department of Mathematics 1.8 semesters earlier than Yu Hua still looked confused. If they were confused just now because Yang Wuzhi asked everyone to explain the definition of Lebesgue integral, then they are confused now. The pressure mainly comes from the crushing and inequality of academic level.
To be honest, every word Yu Hua said could be read by everyone present, whether in Chinese or English, if separated and listed separately. However, when they are put together, they don't know what they are.
God, what is the origin of this little boy?
"Mathematics is a subject that requires hard work and talent. Obviously, you don't work hard enough and you don't have the talent. After more than ten years of improvement, the learning difficulty of Lebesgue points has dropped a lot. Now there is only one month left before the end of the semester. You guys Think about it carefully. If you want to learn, study seriously. Don't spend three days fishing and two days drying nets. I also found that some students have a bad attitude and often go to the Bada Hutong. I want to ask him, are you going to study mathematics with those kiln sisters? ?”
Yang Wuzhi glanced at the other students who were still confused, shook his head, and instead of continuing the lecture, he severely criticized: "Finally, if it is really difficult to learn, or you feel that you are not suitable for mathematics, then transfer to other majors as soon as possible , don’t delay your studies and fail to graduate.”
The atmosphere is not good.
This is the problem faced by these students.
From the perspective of a patriot, every Tsinghua student is a first-rate patriot.
But from a student's perspective, more than half of the seven first-year mathematics students here are unqualified, either because they smoke, drink, or engage in prostitution and gambling.
To ask is to regret and blame oneself, to persuade is to imitate Hu Shi.
This back-and-forth gave Yang Wuzhi a headache when he saw these students. Tsinghua University is already very strict with students. If they don't complete enough credits, they will not be able to graduate. Among the more than ten departments in the school, this one is the most difficult to study.
Judging from the current situation of this group of students, not to mention graduation, it is a good thing not to be persuaded to quit.
"I realize my mistake, sir." The words echoed in the classroom, and the six students below each showed different expressions and reactions, and finally gathered together to stand up and bow.
You are so wrong. ——Looking at the familiar scene in front of him, Yang Wuzhi sighed in his heart. He didn’t know when Chinese mathematics would flourish. He looked at Yu Hua, who was delving into mathematical problems, and felt a little relieved and hopeful in his heart.
Yu Hua's talent in the field of mathematics is obvious to all, and has long been spread among the professors of the Department of Mathematics. In terms of seniority, Yang Wuzhi is a well-deserved master. Although he and Hua Luogeng have ideological differences, this is a matter between him and Hua Luogeng. , it has nothing to do with Yu Hua.
Yang Wuzhi is still looking forward to this mathematical genius who is famous at Tsinghua University and other major universities.
"Sit down, let's continue the class." Yang Wuzhi motioned for everyone to sit down, without disturbing Yu Hua, and continued to explain Lebesgue points.
Yang Wuzhi believed that Yu Hua was already familiar with Lebesgue integral, which was a knowledge content in the second semester of his freshman year, so he did not want to disturb him too much.
In the subject of mathematics, improvement in academic level mainly comes from self-understanding.
The master leads me in. Cultivation is personal.
The class continued, but from time to time, the attention of everyone in the audience turned to Yu Hua, who was sitting alone, and they were very curious about the identity and origin of this junior student.
Yu Hua didn't pay attention to everyone's gaze. He held the pen in his right hand and quickly immersed himself in the study of discrete logarithms again.
Discrete logarithms are a very interesting integer problem. To understand discrete logarithms, we must first clarify the definition of logarithms. Logarithms are the inverse operation of exponentiation, just like division is the inverse operation of multiplication, which means that for a given a and b, there is a number x such that bx=a. Similarly, a power bk can be defined for all integers k in any group g.
The discrete logarithm refers to the integer k such that bk=a, a logarithmic operation based on congruence operations and primitive roots.
Discrete logarithms can be calculated quickly under special circumstances. However, most cases do not have high-efficiency calculation methods. Modern cryptography is based on discrete logarithms, looking for solutions to discrete logarithms to establish encryption algorithms.
This is one of the three basic theories of modern cryptography.
After careful study, Yu Hua found that it is indeed very interesting. The properties and characteristics of discrete logarithms make it more compatible with other mathematical theories in the field of cryptography. It feels like discrete logarithms should be naturally used in cryptography. The field shines.
On the draft paper, a series of complex numbers and English letters formed the main body of the content. As the study of discrete logarithms deepened, Yu Hua already had an idea in his mind about the first set of encryption algorithms in the asymmetric era. These things on the paper It is the framework and structure of the first encryption algorithm.
The foundation is already solid. Once the framework and structure are established, Yu Hua will be able to formally establish a set of asymmetric cryptography encryption algorithms, bringing the world into the era of asymmetric cryptography.
"Ding!" Time passed slowly, and suddenly, the bell rang outside the classroom.
Hearing the bell, Yu Hua, who was concentrating on his research, once again exited the efficient learning state. He felt that his temples were a little bulging, and there was a faint feeling of dizziness in his brain. Most of his energy had been consumed. He shook his head gently: "In one more week, we can get it done. Well, doing such serious math problems really takes a lot of brainpower... Let’s eat first, low blood sugar can’t keep me in the best condition.”
In the mind, golden mathematical symbols continuously release a cold meaning, easing the discomfort under high-load operation.
Engaging in mathematical research is undoubtedly painful for the human brain. It is a process of finding analytical problems. To obtain the information entropy, the consumption is far greater than learning.
A little dizzy and with low blood sugar, Yu Hua needs to eat and rest to replenish himself.
