Chapter 292

Cheng Nuo's winter vacation officially began in the noisy quarrel with Mu Leng.

After a busy semester at the university, Cheng Nuo finally had time to take a break.

After lying at home like a salted fish for several days, after being comfortable enough, Cheng Nuo had to get up again to start his study process.

"Complex Variable Functions" and "Ordinary Differential Equations", two courses that are needed in college students' mathematical competitions, also need to be completed by Cheng Nuo by himself before the Chinese New Year.

After taking a taxi, Cheng Nuo went straight to the largest bookstore in Qingcheng.

Originally, I thought of only buying the two books of complex variable functions and ordinary differential equations, but I thought that I would simply come, so it was better to buy more at one time, so Cheng Nuo took more than a dozen books from the bookshelf and checked out the bill one by one.

"Real Variable Functions and Functional Analysis", "Abstract Algebra", "Probability Theory and Mathematical Statistics", "Topology", "Partial Differential Equations", ......

These are all courses that the Department of Mathematics will learn during the four years of college.

Holding a stack of books weighing more than a dozen pounds, he returned to his bedroom.

The hundreds of high school review books on the bookshelf in the bedroom have been cleaned up by Jiang Lan, and they are a little empty at the moment. Cheng Nuo neatly placed more than a dozen books on the bookshelf and smiled lightly.

With his learning speed, it is estimated that this bookshelf will soon be filled again!

Learn, Sao Nian!

After making a cup of coffee, Cheng Nuo sat at his desk and opened the title page of the book "Complex Variable Functions".

In terms of difficulty, the complex variable function is naturally a notch higher than the high algebra and number fraction of the freshman year. This course is gradually developed with derivatives and integrals as the starting point.

As a branch of function theory, compared with real variable functions, complex variable functions use complex number fields as independent variables to perform various function operations.

This textbook mainly explains the content of complex variable functions through three aspects.

Analytic Functions, Commonality Reflection, Riemann Surfaces.

Cheng Nuo had scratch paper in his hand, reading the book and calculating the theorems in the book.

For example, the Cauchy-Goursat theorem refers to the theorem that a function f(z) has a theorem in the region U, and g(z) is called the analytic original function of f(z) on the region U, if g(z) is parsed on U and g'(z)=f(z) is true everywhere on U.

After reading this theorem, Cheng Nuo did not directly look at the following proof process of the theorem, but directly proved it himself on scratch paper.

[Let γ: [a,b]→C be a segment-by-segment smooth curve, the parametric equation γ(t),a≤t≤b, if f(x) is continuous on the γ, then ∫f(z)dz=∫(a,b)f(γ(t)γ'(t)dt,......]

After the certificate, Cheng Nuo opened the textbook and compared. The idea is exactly the same.

Sure enough, the great mathematician Cauchy and I have the same idea!

Holding a beautiful mood, Cheng Nuo continued to look down.

............

It took almost two days for Cheng Nuo to finally finish reading the more than 200-page book "Complex Variable Functions". The contents of the book have been fully comprehended. Although it is still a long way from becoming a great leader in the field of complex variable functions, it is enough to cope with the mathematical competition.

Cheng Nuo was in no hurry to learn another book of ordinary differential equations on his own. The agreed time to hold a lecture with Qingcheng No. 2 Middle School is three days later, and today, Cheng Nuo plans to visit the head teacher of the high school, Lao Tang, at No. 2 Middle School first.

Walking into the campus of No. 2 Middle School, which had been absent for half a year, Cheng Nuo felt like he was returning home.

A year ago today, he was still an ordinary high school student, numbly accepting the 6-to-9 study life, confused and at a loss for the future, not knowing what to do in the future. But now, he's different!

His clenched fingers turned a little white, and the goal of becoming the king in his heart became more and more determined.

According to memory, Cheng Nuo came to the office of the mathematics group.

Push the door in, and the office is still in a familiar layout. It's just that after Cheng Nuo glanced around, he didn't find Old Tang's figure.

"Cheng Nuo, you're back!" Suddenly, a surprised voice attracted the attention of the other math teachers in the office.

Especially when I heard the name that was known as a legend, my eyes swept around the office one by one, and finally stopped at the boy.

The group of teachers in the mathematics group is half of the people who have watched Cheng Nuo grow up step by step, and they are naturally overjoyed to see Cheng Nuo.

"Cheng Nuo, did you kid take the college entrance examination and forget about our group of old guys. It's been more than half a year, and I haven't seen you come back to see us once. Teacher Zhang, who had eyes and often asked Cheng Nuo to help with the questions, turned his chair and joked with a smile.

"No, no, how dare I. Cheng Nuo smiled bitterly and waved his hand repeatedly, "You also know that the study at Tsinghua University is not much more relaxed than that in high school, it's not that I don't want to visit, but I really can't spare time." ”

"It's okay, it's okay. Another math teacher spoke, "Lao Zhang, this guy just saw that you, the top student in the college entrance examination, were not taught by him, and he had a lot of resentment." You're here to find Old Tang, right, he's now tutoring students in your original Class 18 classroom. ”

"Then teachers, I ......"

"Go, go, I don't know what blessings that old Tang guy has cultivated in his life to teach you such a good student. In the laughter and scolding of Teacher Zhang, Cheng Nuo closed the door and walked out of the office of the mathematics group.

Since there are only 16 classes in the third year of high school, that is, the second year of Cheng Nuo's senior year, the original classroom of the 38th class of high school has become a mathematics competition tutoring classroom. And because Lao Tang cultivated Cheng Nuo as the top student in the college entrance examination, and his own mathematics level is really enough, he became the tutor of this year's competition.

After coming to the classroom door, Cheng Nuo looked inside through the glass window of the back door.

There were more than 30 students sitting in the classroom, mostly boys, with only a few girls, looking up at the blackboard and concentrating.

If nothing else, these 30 or so students will participate in the unified high school math league next year. Then the first prize winner will have the opportunity to sign up for the IMO to be held in March next year to win glory for the country.

Before, Cheng Nuo had not participated in IMO, not even a competition coaching like this. This is a big regret for Cheng Nuo. It's just that I don't know if anyone in my group of juniors can replace him to win the gold medal in the IMO finals.

Cheng Nuo gently pushed open the back door of the classroom, quietly touched, crept in, and found an empty seat in the back row to sit down.

Old Tang on the podium was giving a serious lecture and did not notice that there was an extra "student" in the classroom.

Old Tang held a competition coaching book and talked eloquently.

"Next, let's look at the last question. This is the penultimate question in the second test of last year's math league, I took a look at your test papers, only Chen Gong did it alone, and I will tell you about this question......"