Wu Xiaoyuan responded: "I'm in the second bedroom. I'm probably reading a book. It's still a quarter of an hour before dinner. You go and see Xiaohua first."
"good."
Hua Luogeng nodded, suddenly took a step forward, hugged Wu Xiaoyuan and kissed his forehead gently. After getting a look from Wu Xiaoyuan, the smile on his face did not diminish, and he went to the second bedroom.
"Boom!"
Hua Luogeng stood in front of the second bedroom door and knocked gently.
"Please come in." Yu Hua's voice came from inside.
Pushing open the door, Hua Luogeng walked into the room and saw Yu Hua sitting in front of his desk. The textbook "Theory of Real Variable Functions" was placed on the table, looking like he had just finished studying.
"How are you studying the theory of real variable functions?" Hua Luogeng came to the desk, glanced at the textbooks on the table, and asked.
Yu Hua raised his head and saw the tiredness on Hua Luogeng's face. Knowing that the master had just finished today's work, he spoke softly and did not mention Hua Luogeng's work: "The theory of real variable functions is very interesting. It was a little difficult to understand at first.
It got much better later and it was not difficult for me."
interesting?
When Hua Luogeng heard Yu Hua's answer, he laughed and shook his head. He didn't think that Yu Hua was fooling him. The scene of students from the Department of Mathematics at Tsinghua University studying the theory of real variable functions came to mind. He couldn't help but joked: "I'm afraid you are the only one who thinks that real variable functions are
In terms of interestingness, those senior students in the Department of Mathematics feel as if they have fallen into a dark abyss with no bottom when faced with the theory of real variable functions. Either they have a splitting headache, or they wail incessantly, and even ask why functions should be
I never find the comments about real changes interesting, only torture."
The theory of real variable functions is a course content for the senior year of the Department of Mathematics at National Tsinghua University. Since the theory of real variable functions was formed from the end of the 19th century to the beginning of the 20th century, the entire branch of mathematics has only been established for a short period of time, making it very difficult to learn.
.
In the entire National Tsinghua University, there are only a handful of mathematics students who can truly understand the theory of real variable functions.
"Students really find the theory of real variable functions interesting. As long as they learn calculus, they can easily understand the proof of the theory of real variable functions and the integrability of functions. After all, the theory of real variable functions is an in-depth development theory of calculus.
.”
Yu Hua smiled, explained softly, and slowly talked about his feelings: "And after studying during this period, students can also feel the fun of those mathematicians delving into difficult problems. They are not delving into difficult problems; they are
……grasp knowledge."
There really was nothing pretentious about his words.
The theory of functions of real variables is difficult to master. In later generations, it has even reached the point where you have to learn it ten times before you can use it. However, as long as you lay a good foundation and learn it, you will get started quickly, and you will gradually feel the interest from the theory of functions of real variables.
.
By studying the four major properties of functions such as integrability, differentiability, continuity, and convergence, you can gradually feel the charm of the mathematical world during the entire process, and gain the pleasure that only a wise person can gain from mastering advanced logical knowledge.
This sense of pleasure is beyond any mortal level emotion and is comparable to the inner strength of cultivation in myths and legends.
The most important thing is that only a few people based on human civilization can truly experience this feeling.
After this period of study, Yu Hua, who has been studying advanced mathematics day and night, has gradually realized why mathematicians like to study advanced knowledge that ordinary people cannot understand, because they are mastering knowledge!
Their wisdom has surpassed that of all ordinary people of their time,
Their figures will shine forever in the long river of time,
Their knowledge hangs high in the universe like stars, leading countless future generations forward.
Who can compare to this feeling that stands at the highest level of the entire civilization?
The high of nicotine?
What does alcohol taste like?
Communication between men and women?
Everything is just a human feeling.
"You kid..."
Hearing Yu Hua's words, a unique and familiar atmosphere came to him. Hua Luogeng smiled and didn't want to say anything. He changed the topic: "How did you write the article about reconstructing the definition of Lebesgue integral?"
Already?"
Reconstructing the definition of Lebesgue integral is a learning topic assigned by Hua Luogeng to Yu Hua last weekend.
This learning topic may seem like nothing, but it actually has a hidden mystery.
Refactor!
This is the top priority of the entire study topic. It is not difficult to calculate Lebesgue integral. After all, standing on the shoulders of predecessors, ordinary students only need to follow the example and master this knowledge.
Reconstruction is different. It is not only necessary to master this knowledge, but also to understand and construct this knowledge in a fundamental sense. It is necessary to go back to the beginning, peel off the entire mathematical formulas and definitions, return to the most original state, feel the situation at that time, and then
Restructure.
If you want to know how it is and why it is so, you cannot do without knowledge reconstruction.
Of course, the average student cannot reach the level of reconstruction, and only true geniuses will use knowledge reconstruction.
The shoulders of the predecessors were not so easy to stand on.
"Master, it has been written, and it's here." After hearing this, Yu Hua looked serious and immediately took out his latest mathematics paper from his school bag and handed it to Hua Luogeng.
The entire mathematics paper is more than a thousand words, and it took Yu Hua half a day to complete it. He reconstructed the definition of Lebesgue integral through reverse thinking and the defects of Riemann integral.
"Do you know the significance of me asking you to reconstruct the Lebesgue integral?" Hua Luogeng took a look at the entire mathematics paper. The title of the paper was "Reconstructing the Lebesgue integral". Below it was a series of familiar mathematical formulas. He nodded slightly.
Not in a hurry to take a closer look, he turned his attention to Yu Hua.
Yu Hua nodded: "I know, Lebesgue integral has truly perfected calculus. To learn the theory of real variable functions, you need to fully understand Lebesgue integral."
Master Hua Luogeng chose Lebesgue integral as a study topic. He did not choose it randomly, but it contained profound meaning.
Because Lebesgue calculus is the basis of real variable function theory.
As a crucial link in calculus, Lebesgue integral is the crystallization of knowledge of Henri Lebesgue. It has produced another great influence on calculus after Cauchy and Riemann, the finalists of calculus.
the product of influence.
In 1854, Riemann's new work defined the field of calculus, the Riemann integral. Once the Riemann integral was launched, it immediately filled many gaps in calculus, making the mathematical weapon of calculus even sharper, but the Riemann integral itself
There are still deficiencies, such as integration problems of discontinuous functions and non-differentiable functions, etc.
In 1902, a man appeared in the world of mathematics. The mathematical genius Lebesgue published his doctoral thesis "Integral, Length and Area", established measure theory and integral theory, and made some functions that were not integrable in the sense of Riemann integral become integrable.
, and then reconstruct the basic theorem of calculus, forming a new discipline - the theory of real variable functions.
Lebesgue's integral was a 'watershed' in mathematical analysis. Previous calculus was generally divided into classical analysis, and later analysis based on the development of real variable function theory was called modern analysis.
To learn the theory of real variable functions, one cannot do without the Lebesgue integral, and this is exactly why his master Hua Luogeng asked him to reconstruct the Lebesgue integral.
Rather than simply mastering it, you need to reconstruct the knowledge to understand it thoroughly.
"You are indeed a genius. You can figure it out in just one click. It's time to eat. Let's go out first, otherwise your wife will rush you later. After dinner, go back to the study. I have something to discuss with you." After hearing this, Hua Luogeng showed satisfaction on his face.
smiled and praised.
Yu Hua asked curiously: "Master, what is it?"
"You'll find out later." Hua Luogeng kept it secret and didn't say it bluntly.