Hogwarts School Great Hall.

In the spacious hall, magical torches and floating candles illuminated the surroundings as bright as day. Led by Professor McGonagall, the first-year students passed through the double doors and gathered in the center of the hall.

Four long tables within the hall were already filled with male and female wizards dressed in black robes.

The upper-year students watched the group of new students like a flock of chicks, whispering and laughing among themselves, completely oblivious to their nervousness. The countless murmurs merged into a sound resembling a bustling market.

"This is Hogwarts? The legendary... top institution of human civilization?"

Danilova nervously examined her surroundings, her cute face tightly set.

Even though she had read countless introductions about Hogwarts in books, the written descriptions were entirely different from seeing the magical castle in person—moreover, most of the information recorded in the books was a simplified version.

In "Hogwarts, A History," the tradition of the first-year students crossing the lake was described in fewer than two lines.

But for Danilova, the past few tens of minutes could be described as the most magical, dreamy, and anticipated "magical start" of her life: they lit their wands, dispelled the darkness, supported each other as they walked along the rugged path, and, like the four Hogwarts founders a thousand years ago, boarded small boats, crossed the waves, and arrived at the ancient and majestic magical castle.

As for the little bit of pride in the girl's heart, it had long since vanished with the faint light during the lake crossing.

As a "Muggle-born witch" living in the non-magical world, she was too slow in her magical learning. Not to mention the girl named Luna Lovegood, even Irina, who also came from Russia, far surpassed her.

The two of them raised their wands and cast the Lumos charm perfectly almost immediately after Aileenna waved her wand.

In addition to Luna and Irina, another red-haired little witch also cast the perfect Lumos charm smoothly only a few seconds later—undoubtedly, for these children from wizarding families, this basic magic was as simple as understanding the Cauchy inequality.

Not to mention...

Danilova secretly glanced at the silver-haired little witch standing next to Professor McGonagall.

If Irina, Luna, and Ginny were like a torch compared to a match for her, then Aileenna Kaslana, who was only one year above her, could be described as the difference between the moon and a firefly.

"Hmm? This child... Oh, right! The talented girl from Mr. Alexei's family..."

Aileenna's gaze happened to meet Danilova's. Taking advantage of Professor McGonagall's inattention, she winked at Danilova and made a playful face—finishing Fourier series before the age of eleven, she was also a little monster.

"Don't be too nervous, Danilova. I was much more nervous than you at this time last year..."

Then, a voice like a mosquito hum sounded in the girl's ear.

Danilova looked around in confusion, seeing that her surrounding companions hadn't changed at all, and turned to look at Aileenna.

--Hmm, not bad perception--

Aileenna's eyes flashed with satisfaction, and she gave Danilova a look, her lips moving almost imperceptibly.

"As I said before, the Sorting Ceremony is very simple. The wise and knowledgeable Sorting Hat will sort you into the most suitable house. If you are still a little nervous at that time, why not recall Laplace transforms or something in your mind..."

Laplace transforms?

Danilova was slightly stunned at first, then quickly reacted.

Oh, right, that's some of the content after the Fourier series. Her father had given her some practice problems on this during the summer vacation. The endless formulas were so fascinating.

Hearing familiar words again, the nervousness in Danilova's heart disappeared a lot without realizing it.

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

In the interval between Aileenna and Danilova's "private chat," the Sorting Hat's song had ended. Professor McGonagall took out a roll of parchment that was at least twice as long as usual, looked at it carefully, and began to read out the names in order.

The line of first-year students began to stir as Professor McGonagall called out the names.

One by one, the first-year students stepped forward in order, sat on the four-legged stool, put on the hat, and waited to be sorted.

However, compared to previous years, this year's sorting process was slightly more complicated—according to Aileenna's suggestion, some young wizards would try to actively "fill out" a preference before putting on the hat, and then wait for the Sorting Hat to adjust.

There was no doubt, as Aileenna had said before.

If a young wizard thought that the choice of house was very important to (him/her), the Sorting Hat would also consider (his/her) feelings and would not allocate entirely according to its own ideas—of course, the premise was that you needed to actively express this before putting on the hat, otherwise, you could only hope that the Sorting Hat's speaking speed wouldn't be too fast.

Hmm...wait, a hat full of wisdom?

Danilova looked up at the old, pointed wizard hat, a hint of curiosity flashing in her eyes.

Speaking of which...

Maybe...the Sorting Hat could also help her answer a few questions that she hadn't understood before?

"Danilova Alexei!"

Before the thoughts in the girl's mind were finished, Professor McGonagall's voice came from the steps not far away.

As a surname starting with A, she was naturally ranked at the front—the names on the Hogwarts admission list were all uniformly transliterated into English, so there was no situation where foreign students' names could not be sorted.

"Huff...calm down, calm down...think about math..."

Danilova took a slightly nervous breath, walked out of the queue, sat down in front of Professor McGonagall, and muttered to herself.

"Hmm...for all t0, f(t)=mathcal^left=fracint_^f(s)'e'ds..."

Just as the hat was about to be placed on her head and block her vision, Danilova saw the crowd of people in the hall, all craning their necks and looking, as if waiting for her sorting result. Then, it was the dark world inside the hat and the waiting.

"Hmm," she heard a faint voice say in her ear, "a wizard from abroad, welcome..."

Hearing the voice in her ear, Danilova instantly became nervous, her mind went blank, and she subconsciously recited the most familiar mathematical formula.

"...c' is the abscissa value of the convergence interval, which is a real constant and greater than the real part value of all individual points of f(s)'. For a continuous-time function x(t) whose function value is non-zero for t=0, through the relation..."

"...excuse me, miss, could you please pause for a moment. I don't quite understand..."

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

Although it could understand each word in this little witch's mind when they were separated.

But, when they were combined together...

And most importantly, apart from these puzzling "spells," the child's mind was blank at this moment, without any emotions or questions...

After another moment of pause—

"Oh, well, forget it—"

Accompanied by a long sigh, the Sorting Hat glanced at Aileenna, who was watching intently not far away, thought for a few seconds, and shouted loudly.

"Ravenclaw!"

At the same time, Aileenna nodded slightly.

As expected--

This broken hat doesn't understand math either!

That makes things much easier!

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