The words "In the Dream" in the lower left corner have disappeared.

He has returned to reality.

In fact, 10 minutes have passed in reality, which corresponds to half an hour in the dream.

But his mind was still stuck in the exercise.

This question was given to him by Teacher Ran, so there is no answer.

At least she wouldn't tell herself the answer until he went to ask Ran Bingqing for help.

And she won't give him too much time at all, otherwise he wouldn't be worthy of being called Teacher Ran's protégé at all.

The questions given before were all done on the same day, and they were given to Mr. Ran the next day.

So far he hasn't missed.

I didn't want to miss this time, since Mr. Ran gave him the question, it proved that she believed that she had the ability to answer.

In this way, the scope of problem-solving knowledge will not exceed that of high school.

He was also preparing to study university courses on his own, but unfortunately he was held back by Chinese and English.

Thinking of this, Yi Cheng fell asleep.

Real-life time cannot be wasted.

Thirty minutes passed.

Yi Cheng sat up from the bed.

Finished.

The two-minute sleep method didn't work anymore. (This is a sleep method invented by the U.S. military in World War II in order to allow pilots to fall asleep quickly and fight quickly, so I won't write it here, so as not to be suspected of the number of words.) ）

No matter how much you relax and meditate, the question in your brain still turns and turns.

The brain is so excited that it can't sleep, and it's really hard.

As a last resort, Yi Cheng had no choice but to get up and use the time in reality to solve the problem.

He carefully pulled out his chair and glanced at the goddess surrounded by a cloth, trying to move as lightly as he could so as not to disturb her.

Then he turned on his phone's flashlight and hung it above his head, dimming the light as low as he could.

I don't know how long it has been, but Yi Cheng still hasn't caught the damn beast, and thus falls into anxiety.

Yi Cheng's first thought was the method of comparison of differences.

However, this is a lot of computation, and two variables appear in this equation at the same time.

You'll have to find a way to make the connection......

"Huh? Gaussian function. ”

A voice sounded, causing Yi Cheng to almost jump out of his chair in fright.

The pencil in his hand flew out.

He took a picture of his phone—

I don't know when, Lan Bing appeared next to him.

She was clasping her hands and staring at the scrap of paper he had placed on the table.

"You actually know the Gaussian function?" Yi Cheng bent down to pick up the pen and looked at her with an incredulous look.

Sure enough, a goddess who can't do math isn't a good goddess, is she?

By the way, she's now the goddess of lv2, so it's normal to know some math.

"Of course. Gauss is known as one of the world's three great mathematicians. ”

The three major mathematicians in the field of mathematics -

Archimedes, Newton and Gauss.

The other two will be talked about later, how awesome is Gauss?

Here's a simple example:

At the age of 10, Gauss had already surpassed his math teacher.

At that time, the math teacher Butener came up with a very classic problem: 1+2+3...... Add all the way to 100 and sum.

Gauss quickly figured out that the answer was 5050.

He calculates it like this, 1 + 100 = 101, 2 + 99 = 101...... There are 50 sets of these numbers.

50X101=5050。

This algorithm is now called Gaussian algorithm in primary school textbooks.

At the age of 19, he discovered the seventeen-sided ruler and diagram method, which solved a problem that had been unsolved since Euclid.

In the same year, he published and proved the law of quadratic reciprocity.

……

It is not an exaggeration to say that Gauss was one of the first three great things we came into contact with.

"Isn't that easy?"

Lan Bing said, holding his chin in his hand.

"Isn't it okay to prove that this function increases monotonically in the interval?"

Hey?

Yi Cheng tilted his head in confusion.

This guy actually hit the nail on the head.

It seems that the goddess is a bit level.

"But it's easy to say, it's hard to prove this formula." Yi Cheng slammed his lips.

He's just stuck here.

"It's not difficult, it's easy."

Lan Bing said, looking at Yi Cheng with his hands folded.

"If you know Gauss, you must also know the other two who are listed as the top three mathematicians with him, right?"

"Of course, Archimedes, Newton." Yi Cheng is like a treasure, "Archimedes has two very famous stories, the principle of leverage and the principle of buoyancy, and he has a saying, just give me a fulcrum......"

"Stop, focus on the latter one."

"Newton?" A fog formed in Yi Cheng's eyes, recalling Newton's great achievements.

Newton's Three Laws?

Universal gravitation?

"Optics"?

Gold standard?

Calculus?

"Oh, calculus?!" Yi Cheng suddenly looked at Lan Bing with a sudden realization.

"yes, that's right." Lan Bing laughed happily, "Calculus." To be precise, the twins of the integral -

It originated from the difference proposed by another famous person, Fermat.

Later, it was developed and matured, and now we call it micro-business. ”

This micro-business is not the micro-business that you do business in the circle of friends.

It has another more well-known name -

Derivation.

After Lan Bing's reminder, when Yi Cheng looked back again, he found that there was a fierce beast hiding in the grass, obviously a kitten.

Proving that a function increases monotonically in a certain interval is actually the easiest way to find a derivative, except for the stupid differential comparison method.

It's a lot easier that way.

Yi Cheng lifted the pen, all the way like a bamboo.

f(n)=n^3+2mn^2+m^n-m

Derivation:

……

The function then has only one real root within a continuous positive integer interval.

The proposition is proven.

Yi Cheng finally breathed a sigh of relief and leaned back in his chair.

I can give Mr. Ran an errand tomorrow.

The goddess still has two brushes, and it seems that this system is not in vain.

"By the way, usually this kind of question will be followed by a second question, and the second question will be more difficult. Isn't there a question for this? ”

Lan Bing said strangely.

Yi Cheng flipped the card over, and sure enough, there was a line of beautiful small words at the back-

[2. Prove that none of the positive real number solutions of the equation are rational numbers.] 】

Awesome.

Yi Cheng suddenly felt that his whole body was filled with electricity again.