my scientific age

Chapter 107 Reconstructing the Lebesgue Integral!
Wu Xiaoyuan responded: "In the second bedroom, I think I'm reading a book, and it will take a quarter of an hour to eat. You go and see Xiaohua first."

"it is good."

Hua Luogeng nodded, suddenly stepped forward, hugged Wu Xiaoyuan and kissed his forehead lightly.

"Dong dong!"

Hua Luogeng stood in front of the second bedroom door and knocked gently on the door.

"Please come in." Yu Hua's voice came from inside.

Pushing open the door, Hua Luogeng stepped into the room and saw Yu Hua sitting in front of the desk with the textbook "Theory of Real Variable Functions" on the table, as if he had just finished studying.

"How is the real variable function theory?" 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 Master had just finished today's work, he spoke softly and did not mention Hua Luogeng's work: "The theory of real variables is very interesting, but it was a little difficult to understand at first. It got better after that and it wasn't difficult for me."

interesting?

Hearing Yu Hua's answer, Hua Luogeng laughed and shook his head, but he didn't think that Yu Hua was fooling him. The scene of the students of Tsinghua Garden's Department of Mathematics studying the theory of real variables appeared in his mind, and he couldn't help joking: "I'm afraid you are the only one who thinks real variables function. On the interesting side, those fourth-year students of the Department of Mathematics, faced with the theory of real variables, feel like they have fallen into a bottomless dark abyss. They either have a splitting headache, or they cry a lot, and even there is a reason why functions need to be learned. Consolidation remarks are never funny, only torture.”

Real variable function theory, this is the content of the fourth year of the National Tsinghua Department of Mathematics. Since the real variable function theory was formed in the late [-]th century to the early [-]th century, the entire branch of mathematics was established for a short time, which made it very difficult to learn. .

In the entire National Tsinghua University Park, there are not many arithmetic students who can truly understand the theory of functions of real variables.

"Students really find real variable function theory interesting. As long as they have learned calculus, they can understand the proof of real variable function theory and the integrability of functions. After all, real variable function theory 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 of time, students can also feel the fun of those mathematicians who are studying hard problems. They are not studying hard problems, they are studying hard problems. ……grasp knowledge."

There was really no pretence to his words.

Real variable function theory is difficult to return to. In later generations, it will even take ten times to learn it before you can move it. However, as long as you lay a good foundation, you will be able to learn quickly, and you will gradually feel the interest from real variable function theory. .

Studying the four properties of integrability, differentiability, continuity, and convergence of functions, you can gradually feel the charm of the mathematical world in the whole process, and gain the pleasure of mastering advanced logic knowledge only for the wise.

This sense of pleasure is beyond any mortal level of emotion, 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 felt why those mathematicians like to study advanced knowledge that ordinary people cannot understand, because they are mastering knowledge!
Their wisdom has surpassed all ordinary people of the same time,

Their figures are about to shine forever on the river of time,
Their knowledge hangs high in the universe like stars, leading countless descendants forward.

Who can compare this feeling of standing at the high level of the entire civilization?

The pleasure of nicotine?

The taste of alcohol?
Communication between men and women?
Everything is just a human feeling.

"You kid..."

Hearing Yu Hua's remarks, a unique and familiar atmosphere came towards him, Hua Luogeng smiled, but he didn't want to say anything, the conversation changed: "How about your article on reconstructing the definition of Lebesgue integral? already?"

Reconstructing the definition of Lebesgue integral, this is the study task that Hua Luogeng assigned to Yu Hua last weekend.

This study topic seems to be nothing, but in fact there is a hidden mystery.

Refactor!

This is the top priority of the entire study topic. It is not difficult to learn the Lebesgue integral. After all, standing on the shoulders of the predecessors, ordinary students only need to follow the gourd and draw the scoop, as long as they master this knowledge.

Reconstruction is different, not only to master this knowledge, but also to understand and construct this knowledge in a fundamental sense, to go back to the beginning, to strip the entire mathematical formula and definition, return to the most primitive state, feel the situation at that time, and then Restructure.

If you want to know what it is, and know why it is, it is inseparable from knowledge reconstruction.

Of course, ordinary students cannot reach the level of reconstruction, and only true geniuses can use knowledge to reconstruct.

The shoulders of the predecessors are not so easy to stand on.

"Master, it's already written, here it is." Yu Hua heard this, with a serious face, he immediately took out the latest mathematical paper from his schoolbag and handed it to Hua Luogeng.

The entire mathematical paper has more than [-] words. It took Yu Hua half a day to complete. Through reverse thinking and Riemann integral defects, he reconstructed the definition of Lebesgue integral.

"Do you know what I mean by asking you to reconstruct the Lebesgue integral?" Hua Luogeng took a look at the entire mathematical paper. The title of the paper was "Reconstructing the Lebesgue Integral". Below was a series of familiar mathematical formulas. He nodded lightly, Not in a hurry to take a closer look, his eyes turned to Yu Hua.

Yu Hua nodded: "I know, the Lebesgue integral has truly perfected calculus. To learn the theory of real variables, you need to fully understand the Lebesgue integral."

Master Hua Luogeng chose Lebesgue points as a study topic, not randomly, but with deep meaning.

Because, Lebesgue calculus is the basis of real variable function theory.

As a crucial link in calculus, Lebesgue integral is the knowledge crystallization of Henri Lebesgue. product of influence.

In 1854, Riemann's new work defined the field of calculus, Riemann integral, once Riemann integral was launched, it immediately filled many gaps in calculus, making calculus, a mathematical weapon, more and more sharp, but Riemann integral itself There are still deficiencies, such as the integration of discontinuous functions and non-differentiable functions, and so on.

In 1902, a man appeared in the mathematical world. The mathematical genius Lebesgue published his doctoral thesis "Integration, Length and Area", established the theory of measure and integration, and made some functions that are not integrable in the sense of Riemann integral become integrable. , and then reconstruct the fundamental theorem of calculus, forming a new subject - real variable function theory.

Lebesgue integral is the 'watershed' of mathematical analysis. Previous calculus was generally divided into classical analysis, and later analysis based on the development of real variable function theory is called modern analysis.

To learn the theory of functions of real variables, the Lebesgue integral is inseparable, and this is the reason why Master Hua Luogeng asked him to reconstruct the Lebesgue integral.

Compared with simply mastering, reconstructing knowledge can understand it thoroughly.

"As expected of a genius, it's all right. It's time to eat. Let's go out first. Otherwise, your wife will rush you. After dinner, you will go to the study. I have something to discuss with you." smile, praised.

Yu Hua asked curiously, "Master, what's the matter?"

"You'll find out later." Hua Luogeng sold out for a while and didn't say it bluntly.

(End of this chapter)