Steady

"Why? Shen Qi, please state your specific point of view," Teacher Ma questioned.

Shen Qi answered firmly, "In this problem, no matter how the quadratic model of the objective function locally linearizes at the point xk, I can regard it as an augmented quadratic function of the potential function!"

Teacher Ma remained noncommittal and then asked, "Could you explain the definition of the potential function Φ(x)?"

With Teacher Ma no longer dwelling on the algorithmic logic, Shen Qi Sun Yat-sen University, realizing he had successfully navigated this difficult situation.

Therefore, momentum is very important. Shen Qi became more and more courageous as the battle progressed. "Φ(x) is continuously differentiable on X. I have a proof in my paper, which I will not go into detail here. The conclusion of this proof is on page 6. A(x) and B(x) satisfy the diagonal matrix of Equation 7. Then each stationary point of Φ satisfies H(x)=0."

Teacher Ma asked three questions in a row, "Does this contradict the fact that ▽G(x)▽F(x) is a P0-matrix defined in Linear Algebra?"

"No, it's not contradictory." Shen Qi answered immediately, firmly and decisively. "When Gi(x) = Fi(x) = 0, Aii(x) and Bii(x) do not have specific values ε1 and ξ1. In practice, calculating this matrix will not cause any problems."

After a few seconds of silence, Teacher Ma stopped asking questions and said to Director Long, "Director Long, I've finished asking my follow-up questions."

"Okay." Director Long nodded and asked Teacher Xiong, "And you, Teacher Xiong, do you have any additional questions?"

"I only have one question." Teacher Xiong looked at Shen Qi and said, "Shen Qi, I received your paper twenty days ago. Overall, it's well-written and meets the academic standards of a Mathematics Department undergraduate. Of course, this is just my personal opinion; the final decision rests with the main defense professor and the college/university's approval."

"My question is, Shen Qi, what is the value and prospect of your paper? Yes, that's right, you wrote it in the paper, and you also dictated it yourself, that you proposed a new algorithm based on the classic generalized complementarity problem. So, where does the value of the new algorithm lie?" Teacher Xiong spoke slowly and deliberately.

"This..." Shen Qi's morale, which had just risen, immediately plummeted by three points.

That's a brilliant question, Teacher Xiong.

Yes, what is the true value of my mathematical paper? Or rather, what is its practical application?

This problem had actually troubled Shen Qi for a long time.

Papers focusing on applied disciplines will specify what practical problems the research topic solved, what practical benefits it brought, and what technological welfare it created for the country and its people.

Whether it's curing diseases and saving lives, inventing a new material, or improving the production efficiency of a certain process, these are all tangible results with significant achievements and practical applications.

What is the real-world value of mathematical papers, especially those focusing on fundamental theories, and how can their practical applications be promoted?

Shen Qi couldn't quite explain it either.

He believed that when pure theoretical Mathematical Research is pushed to its limits, it will inevitably have immense power, far-reaching influence, and even change the course of human civilization.

However, before reaching the pinnacle of research, Shen Qi has been pondering the value and significance of purely theoretical basic mathematics in the general public.

"That's how mathematics is—refined but not very practical." Shen Qi didn't know how to specifically answer Teacher Xiong's question about its value, so he could only speak the truth.

"However, we remain hopelessly addicted," Shen Qi added, his tone a mix of helplessness and unwavering conviction.

"That's the thing about mathematics: it's sophisticated but not very practical."

Director Long, Teacher Ma, Teacher Xiong repeated Shen Qi's words, all three saying in unison, "Brilliant!"

These three teachers dedicated their lives to Mathematical Research and became experts in the field. As they progressed through their studies, they found themselves increasingly lonely, with fewer and fewer like-minded individuals to have heart-to-heart talks with.

That's how mathematics is; the more advanced and refined it is, the harder it is to understand and appreciate.

"But we remain completely engrossed in it and cannot extricate ourselves," Director Long said with great feeling. "The Q&A session is now over; we will now proceed with the summary."

After asking all the real, hard questions, the summary was just a perfunctory formality.

Finally, Shen Qi bowed in thanks and left the defense session.

Now all that's left is to wait.

For Shen Qi's dissertation defense, the defense panel will issue a scoring opinion. If the panel does not approve Shen Qi's dissertation, then there is no need to report it to higher authorities.

If the defense panel recommends Shen Qi for a bachelor's degree in the Mathematics Department, the recommendation form will be submitted to the next higher level department. After the higher level department reviews and approves the recommendation, Yenching University will issue a bachelor's degree certificate in mathematics.

Shen Qi naturally wanted to get it done in one go, but he couldn't get involved in the subsequent review process.

So Shen Qi went to Sun Erxiong every day. "Professor Sun, which department has my dissertation defense review form been sent to?"

"How would I know? I wasn't even on the defense panel."

"Professor Sun, could you please help me find out?"

"It hasn't left the institute yet; it's still under review within the institute."

"Oh, thank you."

Shen Qi was preoccupied with something, unable to eat or sleep, and even too weak to run. Waiting was agonizing.

Half of the second semester of my freshman year has passed, and the number of courses in the Mathematics Department has increased compared to my freshman year.

Advanced Algebra and mathematical analysis are still being taught, while analytic geometry Analytic Geometry out, and Probability Theory has taken center stage.

College English takes several semesters, as well as some general education courses.

University Physics has also been introduced, and Mathematics Department students are required to take this course.

Shen Qi didn't know if he would pass the thesis defense. If he failed, he would have to continue attending classes, taking final exams, and going through the usual process.

You also need to pass the CET-4) as a formality. Undergraduate graduates will receive two certificates: a degree certificate and a graduation certificate.

The conventional way to obtain a degree certificate is to complete all credits in four years of university. The fast track is like Shen Qi's, which involves participating in the thesis defense early, obtaining the graduation certificate, and passing the CET-4).

It was late April before they knew it. After an Advanced Algebra, Sun Erxiong said to Shen Qi, "Go to the photo studio now and take your registration photo. Blue background, small two-inch."

Upon hearing this, Shen Qi jumped up excitedly. "I've been waiting for so long, this day has finally come!"

"Registration photos, I have them." Shen Qi took a small plastic bag from his pocket and handed it to Sun Erxiong: "These are my two-inch registration photos with a blue background, six of them. That should be enough for the degree certificate."

"You always carry your registration photo with you, buddy," Sun Erxiong said, taking Shen Qi's registration photo.

"Professor Sun, when will I receive my certificate?" Shen Qi asked expectantly, feeling one step closer to his goal.

"It'll be before May Day at the earliest, or within May at the latest. Anyway, it'll definitely be given to you before the end of this semester. Just wait, what's the rush?" Sun Erxiong turned and left, but after taking a few steps, he turned back and said, "Shen Qi, your bachelor's degree certificate should be secure. It's just a matter of time before it's in your hands. Next, you need to plan your future development. In the field of mathematics, you need to have a main focus. You need to choose a specialization when you pursue a master's or doctoral degree."