Although his mind was somewhat cluttered, when Qiao Yu sat at the desk and opened that "Introduction to Riemannian Geometry," his thoughts immediately calmed down, and he immersed himself fully in this mathematics book that he previously couldn't understand.
When it came to self-learning, Qiao Yu actually had his own method, especially for foreign languages.
For the former, Qiao Yu listened a lot, memorized a lot, and spoke a lot.
He bought bilingual dictionaries online, sat in front of the computer, following along with the movie dialogues, listening and reading them repeatedly, looking up unfamiliar words in the dictionary on the spot, and memorizing them. During breaks, he would look at grammar content.
Initially, it took one or two weeks to finish watching a movie.
Then the pace gradually increased, and by the time he could watch a new foreign language film in three hours, he had basically mastered listening, reading, and writing skills in a foreign language.
Mathematics was a bit different.
In fact, Qiao Yu had known for a long time that the reason he found it increasingly difficult was because mathematics is a subject that requires prior knowledge. So reopening the "Introduction to Riemannian Geometry" this time wasn't an attempt to directly learn the content, but to find out what prior knowledge he needed.
So Qiao Yu casually opened the old computer at home, checked unfamiliar concepts online, and made notes.
Half an hour later, the book was filled with dense records.
Calculus, Linear Algebra, Differential Geometry, Topology, and Differential Equations, especially Differential Equations on Manifolds.
Of course, more detailed topics included Multivariable Calculus, particularly integrals and derivatives on curves and surfaces; Linear Algebra's vector spaces, matrices, linear mappings, eigenvectors, and all that messy stuff.
The good news was, Calculus and Linear Algebra were subjects Qiao Yu had dabbled in recently, and they didn't feel particularly difficult.
The bad news was, he hadn't specifically studied Differential Geometry, Topology, or any Ordinary Differential Equations and Partial Differential Equations. Even if he didn't need to learn so much now, he would definitely have to learn them later if he wanted to secure a university admission through a math competition.
The worse news was that after roughly understanding these subjects online, Qiao Yu found that they all seemed quite challenging.
If he could pass the mathematics Olympic Competition and earn the school some money, it would be nice to get a recommendation to Yanbei University to study foreign languages, after all, he only wanted that graduation certificate from Yanbei University…
As inappropriate thoughts ran through Qiao Yu's mind, there was a sudden knock on the door, which was then directly pushed open. The next moment, Xia Keke's little head peeked in.
"Brother Qiao, my grandpa's calling me to go home."
"Oh, then you should hurry home!"
"I came to see how your studying is going?"
"Advanced mathematics is hard, you know? It's only been half an hour, and you think I can master it?" Qiao Yu turned his head and said seriously, planning to find an excuse later for his reluctance to study.
"Is that so?" Xia Keke replied, thought for a moment, and then slipped into the room, casually closing the door.
"What are you up to?" Qiao Yu watched nervously as the little girl approached, quickly standing up in a defensive posture.
No one understood this little girl better than he did; underneath her innocuously innocent face was a heart reveling in chaos. Although he had indeed been a bit mischievous as a child, it was often her bad ideas that adults accused him of being the main culprit for.
The room wasn't that big, and in the next moment, Keke was already standing by his side.
Qiao Yu stood at a height of 1.75 meters, but the little girl in front of him was only a forehead shorter. Before Qiao Yu could react, the little girl suddenly stood on her tiptoes…
First, there was a pleasant scent from the tip of the nose, followed by a soft sensation on the lips, a bit cool, maybe even a bit sweet.
Shit, too sudden…
Didn't get a chance to use Flash…
When Qiao Yu snapped back to reality, he saw the little girl's bright eyes, with a teasing expression, staring right at him.
He—a vigorous, fifteen-year-old, model student in a mother's womb — had just been taken advantage of like this?
He felt aggrieved! Suddenly, he wanted revenge!
"I know you're angry, but if you dare fight back, I'll scream for help!" The little girl boldly whispered.
"Shameful!" Qiao Yu felt a surge of indignation, but he didn't voice it out.
He was known in the family compound as a rebellious teenager, while she was the invincible beautiful girl with excellent grades and a promising future. With such biases, the public opinion leans heavily on her side.
"But, if you can win a prize in the National Math Olympiad, I'll allow you to get back at me," the little girl teasingly said.
"Keke, it's getting late, time to go home and sleep. We have class tomorrow," came an elder's call from outside the door.
"Okay, okay, I know!" The little girl shouted back, then made a face at Qiao Yu, quickly turned around, and dashed out.
As she left the room, he could hear the elder's voice nagging outside the just-closed door: "Young girls shouldn't be running into boys' rooms."
"I know, I was just politely saying goodbye, grandpa, you always teach me to be polite too!"
Today he lost, completely and utterly.
"Huh, why is your face suddenly so red?" Qiao Xi leaned against the sofa with a scrutinizing gaze, making Qiao Yu feel slightly exposed.
"My face is red?"
"You should look in the mirror, you look just like a monkey's butt on Emei Mountain."
"Maybe it's just too hot. I'll go brush my teeth," Qiao Yu replied with forced calmness, then dashed into the bathroom, stood before the sink mirror, glimpsing at himself, indeed his face was quite reddened and embarrassingly wimpy-looking.
Qiao Yu took a deep breath and then picked up his toothbrush.
"What just happened in the room?"
Qiao Yu turned his head to find Qiao Xi leaning crookedly against the bathroom door with a nosy expression.
"Just said goodbye, what else could happen. What were you talking about outside just now?" Qiao Yu felt a little guilty.
"Qiao Yu, something's off with you!" Qiao Xi suddenly remarked.
"Hmm?" Qiao Yu was startled.
"You never cared about what I talked with Keke about before!" Qiao Xi said, with a tone that reminded Qiao Yu of that classic line from Detective Conan: "There is only one truth."
Qiao Yu composed himself and responded calmly: "What does that prove?"
Then, he went about brushing his teeth in an orderly manner, the blush on his face slowly fading away.
"Hmm, you're right."
Qiao Xi muttered to herself and then continued muttering: "Actually, we didn't talk much, Keke just kept asking about Teacher Lan's home visit. I told her, then I said, who knows if you'll forget about your family once you have a girlfriend.
Keke said she believes you definitely wouldn't, and even if you really lost conscience in the future, she'd take care of me when she grows up. Just look how sweet she is, unlike you! Always giving me a hard time. By the way, the little girl didn't pull that little girl's confession trick on you, did she?"
Qiao Yu, who was brushing his teeth, paused for a moment, then turned expressionlessly to gaze at his laughing mother, turned around, grabbed the door handle, and shut the bathroom door directly, then locked it…
"Bang!"
"Click!"
At last, the world was peaceful.