Super God-Level Top Student
Chapter 926 - 350: Twilight of the Empire (Part 2)_3

However, the foundational content of Qiao's Algebraic Geometry will only appear in the next volume, which is formally introduced in the third semester. The textbooks haven't been distributed to the students yet.

The Qiao Class has already been in session for two weeks. This course is scheduled for four classes per week, with a very high intensity.

But Xu Changshu has noticed that these little fellows, who don't know the bounds of the sky and earth, have recently been showing some signs of restlessness.

This is evident from their daily homework assignments.

Some students are getting quite playful. For instance, they've started leaving thought-provoking questions for the professor in their assignments...

So today, Xu Changshu has decided to teach these so-called little geniuses a lesson...

Honestly, at this age, who wasn't considered a genius by their teachers?

When the music signaling the start of class stopped, Xu Changshu didn't open his teaching plan as he usually did. Instead, he directly began writing on the blackboard.

Very quickly, several terms were written on the blackboard.

Virtual Boundary Number ξ: In Qiao Algebra, it represents high-dimensional transformations.

Rotation Element ω: The fundamental rotation in Qiao Space, which can be viewed as a core element guiding the transformation of superspiral structures.

Transition Number τ: In Qiao Algebra, τ represents the jump from one dimension to another, used to describe the interaction and connection between different dimensions.

Manifold Factor μ: A parameter in Qiao Space used to measure and regulate morphological complexity, influencing the shape and extension of the space.

After writing down these four fundamental concepts, Xu Changshu turned around and looked at the bewildered faces of the students below the podium.

"Some of you feel that our current course pace is too slow, a complete waste of time, and wish to explore something new. So I've decided to grant your wish. Today, we'll get an early introduction to the content of Qiao's Algebraic Geometry. The four special numbers written on the board are the most fundamental concepts in Qiao Algebra.

This afternoon's classes will proceed as follows: In the first class, I'll explain a few example problems to help you grasp these concepts, their mathematical properties, and applications. In the second class, I'll assign two problems from Qiao Algebra related to these four concepts, and you'll have one class period to solve them.

If you're able to solve them successfully, I'll revise the teaching plan to introduce new content earlier. Of course, if no one solves them, I suggest you obediently stick to my planned curriculum. Any questions?"

"No questions!" Ten voices responded loudly and energetically.

Out of the twelve students in the class, only ten answered. The main reason was that two of them didn't dare to make a sound...

Yes, at this moment, both Gu Zhengliang and Zhang Zhou were utterly stunned.

The normal pace of the class was already difficult enough, having to stay up late every night to finish homework, and now you want to jump dimensions? Who on earth does that! Couldn't this class have two more normal people?

Unfortunately, Xu Changshu completely ignored their reaction.

This seasoned professor at Yanbei, who had once mastered calculus by sixth grade, smiled slightly before starting to write the example problems.

Suppose in a multidimensional superspiral space, a point P undergoes a fundamental rotational transformation impacted by the Virtual Boundary Number ξ via the Rotation Element ω. Now consider using the Transition Number τ to move point P from its original position to a new position Q.

Given that the Manifold Factor μ represents the spatial curvature and topological changes from P to Q:

1. With the initial coordinates of P as (x, y, z), and after ξ acts on P, the coordinates become (−y, x, z). Given ω = eiθ (where θ is the specified rotation angle), calculate the new coordinates of P.

2. If τ describes the transition mapping from P to Q, and μ represents the rate of spatial changes under this transformation, describe how μ affects the path of τ from P to Q.

The classroom was unprecedentedly quiet. After finishing the example problems, Xu Changshu turned around, looked at the focused faces of the students, smiled, and began his explanation: "First, let's look at the first question. This is a basic calculation problem, but to solve it, we must first understand the statement of the question.

Referencing the fundamental concepts I just wrote, P undergoes a fundamental rotational transformation via ω under the influence of ξ. What comes to mind first?"

The classroom remained quiet until someone responded after a moment: "The rotation matrix?"

"Correct, the rotation matrix, but not entirely correct, because you've only considered the rotation and overlooked the dimensional changes. Since ξ itself also represents high-dimensional transformations, you need to understand it like this..."