Crazy 48 Hours
Shen Qi quickly flipped through the Advanced Algebra exam paper in his hand, which was actually more like an Advanced Algebra problem set.
Based on preliminary assessment, these 36 questions are definitely not exercises from Advanced Algebra textbooks, or exercises of comparable difficulty.
If it were exercises from Advanced Algebra textbook, Shen Qi could finish 36 questions in 3 hours.
However, the current situation is not optimistic.
With time running out and the task heavy, Shen Qi bid farewell to Director Long and Sun Erxiong, and then strode away.
"It's good for Shen Qi to complete his credits as soon as possible. Mathematics is a subject that relies heavily on talent. If he can't achieve results before the age of 30, then he'll have a hard time in his life," Director Long said earnestly. "Let Shen Qi finish his credits as soon as possible and decide on his direction."
"I know Shen Qi pretty well; I led him in last year's Golden Autumn Camp, and I think he'll do well," Sun Erxiong agreed, then added, "However, our Mathematics Department's credits aren't given away for free. Getting them early requires real ability."
"These 36 questions are difficult. Is this the level of our math department's postgraduate entrance exam?" Director Long said with a pang of sympathy, "It must have been tough on this young man."
Sun Erxiong replied, "The postgraduate entrance exam is closed-book, Shen Qi's is open-book."
"Is there a difference between open-book and closed-book reading?" Director Long smiled.
"Actually, there's not much difference." Sun Erxiong laughed as well.
Director Long suddenly thought of a question, "Xiao Sun, maybe I'm overthinking it. Do you really think Shen Qi can solve all 36 questions on his own?"
Sun Erxiong understood what Director Long meant; Shen Qi might have hired a ghostwriter.
According to the test rules formulated by Director Long and Sun Erxiong, Shen Qi can access any materials within 48 hours and is not restricted to any location where he takes the test. In any case, Shen Qi just needs to hand in the test paper at this time the day after tomorrow.
This means that Shen Qi can ask anyone for help, or even find someone to help him complete the test paper.
The freshmen certainly couldn't help Shen Qi, but there were experts among the sophomores, juniors, and seniors in the School of Mathematics, as well as graduate students and doctoral students.
"I'm sure Shen Qi won't ask anyone for help; he will complete this test on his own," Sun Erxiong said.
"Oh, he's honest, he's an honest child." Director Long nodded, expressing his satisfaction.
"Honesty is one aspect, but most importantly, he has to perform this show all by himself. He can't afford to lose face by asking for help."
"Oh, you're concerned about saving face."
Shen Qi rushed to the library without stopping, determined to finish the problems he had set for himself, even if it brought tears to his eyes.
He didn't get any rest for the next two days of the weekend.
Whether useful or not, Shen Qi borrowed a bunch of books, including "Matrix Theory," "Linear Expansion Theory," and "Analysis of Euclidean Space," among others.
If these references were laid out, they could circle the Earth... Of course, they wouldn't circle the Earth once, but if stacked up, they would be nearly as tall as a person. Shen Qi divided the materials into several piles and placed them on the table in the library's study area to reserve a spot.
Before the battle begins, Shen Qi has one important thing to do: get a full stomach.
Half a pound of beef and a pot of boiled water, done.
Shen Qi returned to the library and began solving the problem.
In simple terms, Advanced Algebra is the general term for the advanced stage of algebra. The low-order equation systems we learn in middle school belong to elementary algebra, which is the most basic introductory chapter of algebra.
Modern university Advanced Algebra at the undergraduate level typically include two main branches: Linear Algebra and polynomial algebra.
Linear Algebra and polynomials can be simple or difficult, depending on the examiner's judgment.
It was obvious that the test paper in front of Shen Qi was quite difficult.
The first question involves Grassmann's expansion calculus.
Grassmann was an extraordinary man. He studied theology at the University of Berlin and became a mathematician through self-study.
In fact, Grassmann's theory of extensions was completed earlier than Hamilton's quaternions.
However, because Grassmann had a theological background, he Sun Yat-sen University emphasized the doctrines he advocated in his mathematical works, giving mathematics a mystical aura, which aroused the disgust of his peers and readers.
Look, the book "Linear Expansion Theory" that Shen Qi borrowed is actually a Chinese adaptation of Grassmann's expansion theory. The religious elements in this book have been removed, and new theories from the 20th and 21st centuries have been added.
"This product is a second-order hypercomplex number, and it is expressed in terms of second-order independent units, then..." Shen Qi flipped through the book for help, and the literature he consulted was the Linear Expansion Theory.
The USTC version of the Advanced Algebra textbook was of little use to Shen Qi. He pinned his hopes on "Linear Expansion Theory," but this reference book was also of little use. It was fine to read it as a novel to kill time, but it was useless for solving problems.
"Open-book exams are no use relying on anyone else; you can only rely on yourself." Fine, Shen Qi will do it himself and deduce it himself.
Thinking differently, if we take the outer product of a hypercomplex number γ and two hypercomplex numbers α and β as the inner product, then the three-dimensional expression of this product is... Shen Qi suddenly had a flash of inspiration, haha, I've got it!
Shen Qi wrote furiously:
Q=[αβ]γ
=(α2β3-α3β2)γ1+(α3β1-α1β3)γ2+...
Next, we will perform a series of determinant operations:
Q=▏α1β1γ1▏
▏α2β2γ2▏
Algebra cannot exist without geometry, and geometry gives new life to algebra.
Shen Qi used Q-geometry to explain the volume of a parallelepiped formed by line vectors α, β, and γ.
"So this volume can be positive or negative... That's it, let's do it this way!" Shen Qi obtained a planar quantity, and the first problem was solved.
I got so engrossed in doing the problems that I lost track of time.
Shen Qi glanced at the time on his phone and felt nervous. Time was running out.
43 hours and 27 minutes to go, progress 1/36.
At this rate of progress, even if I didn't eat, drink, or sleep, I still wouldn't be able to finish the remaining 35 questions!
Shen Qi subconsciously wanted to master all 36 questions, not just the passing grade of 28.
"Then I won't eat, drink, or sleep!" Shen Qi steeled his heart, still holding the same belief: he had to finish the act, even if it was a boast.
Shen Qi stopped looking up any information and sped up his answering.
Another three hours passed, and two more problems were solved.
40 hours and 27 minutes to go, progress 3/36.
Despair— Shen Qi hadn't experienced despair in a long time.
Professor Sun, Director Long, you guys are crazy! Is this homework for undergraduates? Is it for freshmen?
38 hours to go, progress 4/36.
Shen Qi worked continuously for nearly 10 hours and completed four questions.
He encountered trouble with the derivation and calculation for question 5.
The answer sheet for question 5 on the test paper was full, but Shen Qi still hadn't found the core solution.
It was already 10 p. m., but thankfully the library was open all night.
Exhausted, Shen Qi texted Professor Sun: "There's too little blank space on the exam paper, can I attach a page?"
Professor Sun replied instantly with a single word, "Okay."
It seems Professor Sun is keeping a close eye on Shen Qi.
Shen Qi is taking an academic credit test. He has a lot of freedom; he can go anywhere, access all kinds of information, and is even allowed to text the professor who set the questions.
However, this exam format often means that it is extremely difficult.