Hogwarts School Auditorium.

In the open hall, surrounded by magic torches and the magic candles in the sky above the auditorium, the freshmen gathered in the middle of the auditorium through the double doors.

The four long tables in the auditorium were now filled with witches and wizards in black robes.

The senior students looked at the group of new students who looked like little chickens, talking and laughing in whispers, completely oblivious to their nervousness, and the countless whispering voices gathered together, sounding like a noisy market.

"Is this Hogwarts? Legendary ...... The top university of human civilization?"

Danilova looked at her surroundings a little nervously, her cute little face crumbling tightly.

Even though I've read about Hogwarts countless times in the books before, the descriptions in the books are completely different from seeing the Magic Castle with my own eyes - not to mention, most of the content recorded in the books is still an abbreviated version.

In "Hogwarts, a History of the School", the tradition of crossing the lake for new students is only a brief introduction of less than two lines.

But for Danilova, the past few minutes can be said to be the most wonderful, dreamy, and exciting "magical journey" in her life: they light their wands, drive away the darkness, and help each other forward on the rugged path, just like the four founders of Hogwarts thousands of years ago, take a small boat, cross the waves, and arrive at the quaint and majestic magic castle.

As for the previous pride in the girl's heart, it had long since disappeared with the glimmer of light when crossing the lake.

As a "Muggle wizard" living in the non-magical world, she was too slow to learn magic, not to mention the girl named Luna Lovegood, and even Irina, who was also from Russia, far surpassed her.

Almost the next moment Elena waved her wand, the two of them raised it at the same time to cast the perfect light charm.

In addition to Luna and Irina, the other red-haired little witch only cast the perfect light spell with the same smooth flow after a few seconds of slow speed—needless to say, for these children from wizarding families, this basic magic may be as easy for them as understanding Cauchy's inequality.

Let alone......

Danilova stole a glance at the little silver-haired witch standing next to Professor McGonagall.

If Irina, Luna, and Ginny are to her the equivalent of torches to matches, then Elena Kaslana, who is only one year above her, can be said to be the difference between the moon and fireflies.

"Huh, this kid...... Oh, yes, that genius girl from Mr. Alexey's house......"

Elena's gaze happened to be at Danilova, and while Professor McGonagall was not looking, she quietly squeezed her eyes at Danilova and grimaced rather mischievously - she had learned Fourier series at the age of eleven, and this was also a little monster.

"Don't be too nervous, Danilova, I was a lot more nervous than you were this time last year......"

Immediately after, a voice like a mosquito sounded in the girl's ears.

Danilova looked around in confusion, saw that there was no change in the friends around her, and turned her head to look at Elena.

- Hmm, the perception is not bad -

A flash of satisfaction flashed in Elena's eyes, and she gave Danilova a look, her lips moving up and down almost invisibly.

"As I said before, the sorting ceremony is simple, the wise and knowledgeable Sorting Hat will put you in the most suitable place, if you're still a little nervous, why not recall the Laplace transformation in your mind......"

Laplace transform?

Danilova was slightly stunned at first, and then reacted quickly.

That's right, it's the content behind the Fourier series, just this summer, Dad gave her some exercises on this aspect, and the endless formulas in it are really fascinating.

Hearing the familiar words again, the tension in Danilova's heart unconsciously dissipated a lot.

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

In between Elena's and Danilova's "private chat", the Sorting Hat's singing was over, and Professor McGonagall took out a roll of parchment that was at least twice as long as before, looked at it carefully, and began to read the names in order.

At the sound of Professor McGonagall, the freshman ranks began to stir.

One by one, the freshmen stepped forward in order, sat on the four-legged stool and put on their hats and waited for the sorting house.

It's just that, compared to previous editions, this time the sorting process is a little more cumbersome - according to Elena's suggestion, some young wizards will try to actively "fill in" a volunteer before putting on their hats, and then wait for the sorting hats to adjust.

Undoubtedly, as Elena said before.

If a young wizard thinks where the house is going is very important to him/herself, the Sorting Hat will also take into account (his/her) feelings and will not assign them exactly as it thinks - provided you want to express this before putting on the hat and putting it on, of course, otherwise you can only hope that the Sorting Hat won't speak too quickly.

Not...... Wait, hats full of wisdom?

Danilova looked up at the worn-out peaked wizard hat, a flash of curiosity in her eyes.

Speaking of which......

Maybe...... Can the Sorting Hat help you answer a few questions that you haven't figured out before?

"Danilova Alexey!"

Before the girl could finish the thought in her head, Professor McGonagall's voice could be heard on the steps not far away.

As a surname starting with A, she is naturally at the top of the list - all the names on the Hogwarts admission list are transliterated into English, so there is no situation where the names of foreign students cannot be sorted.

"Whew...... Calm, calm...... Think about math ......"

Danilova exhaled nervously, and walked out of the queue to sit down in front of Professor McGonagall, muttering words to her lips.

"Hmm...... For all t>0, f(t)= mathcal^left=frac int_^ F(s)' e'ds......"

As the hat was about to be buttoned up to her head to cover her vision, Danilova saw the crowd in the auditorium, and everyone looked at each other, as if waiting for the result of her sorting house, and then the dark world and waiting in the hat.

"Well," she heard a whisper in her ear, "a wizard from a foreign country, you're welcome......

Hearing the voice in her ears, Danilova instantly became nervous, and subconsciously continued to recite the familiar formula in her mind.

“...... c' is the abscissa value of the convergence interval, which is a real constant and greater than the real value of all F(s)' at individual points, and for the continuous time function x(t) where the value of the t>=0 function is not zero, the value is ...... by the relation."

“...... Excuse me, but could you please pause. ”

The Sorting Hat was silent for a moment, then whispered with some hesitation.

“”