I failed a course, and the system became my study supervisor.

Chapter 7 Make-up Exam and System Assessment
Time is like a rigid and indifferent traveler, galloping along its own path without stopping. Even the prosperous Spring Festival atmosphere with family reunions cannot stop it.

……

"Make-up exam subject: Mathematical Analysis, exam duration: two hours. Please respect the exam rules and cherish the make-up exam opportunity!"

Xu Ling sat upright on a chair in the examination room. A teacher with a dignified look on his face was solemnly reading out the examination rules on the podium.

At this time, the honor task in the task bar has been automatically accepted by the system and cannot be abandoned. It requires Xu Ling's supplementary exam scores in all three subjects to reach 94 points or above.

The penalty for failure was unacceptable to Xu Ling: deprivation of the right to use the system.

Without the system, Xu Ling would be a complete academic failure.

The clearer Xu Ling's positioning was, the more nervous he became. Not only did his heart rate increase significantly, but even his palms began to sweat.

But Xu Ling had no way to retreat and could only fight with his back against the wall.

Thinking of the exercise book he had carefully completed before, Xu Ling's nervous mood was relieved, and he looked at the test paper in his hand seriously.

“题一：计算积分∫ 1/(1+x^2)(1+x^3)积分限为0到+∞”

……

“题十：假设：C^2∈[0，1]，f(1)=f(0)=1，证明：
|f(x)|≤1/4∫|h(t)|dt, the integration limit is 0 to 1, h(x) is the second-order derivative function of f(x).

……

The question was not simple, but Xu Ling solved it with ease.

Even when Xu Ling finished all the test questions, there was still half an hour left.

Xu Ling did not waste half an hour. He checked it over and over again and finally found a calculation error.

When the bell rang to end the exam, Xu Ling was very confident. He handed in his paper and left without any delay.

The remaining theoretical mechanics, thermodynamics and statistical physics were also completed within the same day, and Xu Ling hurried to the next examination room.

……

The whole day was spent in intensive examinations. When Xu Ling walked out of the last examination room, it was already evening.

However, Xu Ling did not get any time to breathe. Because——

The deadline for the system assessment of another glory mission is also on this day.

Arriving at the library, Xu Ling found a quiet corner, then opened the taskbar and clicked on the words "accept the assessment".

"Ding!"

"Are you sure you want to start the assessment? Please ensure the surroundings are quiet!"

"Confirm!" Xu Ling did not hesitate.

"The assessment begins! The assessment is mostly about understanding concepts. After hearing the question, the host can just recite it in his mind."

Hearing this, Xu Ling breathed a sigh of relief.

"Question 1: Please briefly explain the conjecture on the estimation of the remainder of the Fourier series."

“The convergence rate of the Fourier series is related to the Fourier coefficients, and the envelope of the remaining terms can be approximated as a secant function.

However, currently, the Abel lemma can only produce results similar to secx/2 or cscx/2 when an and bn are monotone. The coefficient 1/2 in the front is difficult to prove, so this conjecture has not yet been confirmed.

The first question is not difficult, it is just a repetition of the content of the material.

"Question 2: Please list several mathematical physics equations related to the small initial value global solution conjecture."

The second question wasn't difficult either, but it was very detailed. Xu Ling had to think for a long time before finally coming up with as many answers as possible:
In four-dimensional Euclidean space, it is conjectured that under small initial conditions, a unique global smooth solution exists for the Yang-Mills equation. If proven, this would deepen our understanding of gauge field theory and provide a more solid mathematical foundation for theoretical physics research such as quantum field theory. In general relativity, Einstein's equations describe the relationship between the curvature of spacetime and the distribution of matter. It is conjectured that under certain special small initial conditions and reasonable assumptions about the distribution of matter, solutions exist in global time with favorable properties. This is of great significance for studying the evolution of the universe.
While global solutions to the three-dimensional incompressible Navier-Stokes equations have been proven to exist in two dimensions for small initial values, this finding remains unresolved in three dimensions. It is conjectured that under appropriate small initial values ​​and smoothness conditions, the equations possess a unique global canonical solution, which is crucial for understanding the long-term behavior of fluids and the mechanisms that shape turbulence.

......"

Xu Ling recited seven or eight physical equations in one breath until he could not think of any more.

The system asked a total of ten questions. The subsequent questions became more difficult than the last. It was no longer a simple repetition of the data. Xu Ling thought about many questions for a long time before he could stutter out his answers.

"Ding!"

"Passed the assessment!"

"Reward 10 motivation points and start the second stage of the "One Small Step Towards Scientific Research" series of tasks. Please check it promptly."

The second round of tasks! Xu Ling quickly opened the taskbar.

【Ordinary tasks

……

Glory Mission
(1) Prove yourself
……

(2) A small step towards scientific research (Second Ring) Please choose a specific question and watch the customized explanation of the system at 10:00 every night. No latecomers will be accepted.

Task reminder: Please make your choice before 10 o'clock tomorrow night. Once selected, it cannot be modified.

Completion reward: After reading all the explanations, it is considered completed, and 10 motivation points will be awarded, and the final task will be unlocked.

Failure penalty: 10 motivation points will be deducted and the final mission will not be able to be started.

Rejectable: Yes]

Is that how it is? Xu Ling suddenly realized that the system first gave a general overview of the broader issues before targeting a specific breakthrough.

What will be the ultimate goal? Will it be to prove a conjecture?
Thinking of this, Xu Ling was pleasantly surprised. However, he still needed to carefully consider the next choice.

Putting this question aside for the time being, Xu Ling began to study his own motivational points.

With motivation points, all the functions of the system were unlocked, and Xu Ling checked them one by one.

The plus sign after the subject level in the personal panel is still there, but there is an additional experience value data in front of the plus sign.

Mathematics - Level 0 (30/100) (+)
b.Physical——lv.0 (20/100)(+)
c. Chemistry——lv.0 (0/100)(+)
d. Biology and Medicine——lv.0 (0/100)(+)
e. Informatics lv.0 (0/100)(+)
f. Engineering lv.0 (0/100)(+)
g. Linguistics lv.0 (0/100)(+)】

Xu Ling tried clicking the plus sign, and a line of text popped up.

[Do you want to exchange for experience points? Inspiration points and experience points are exchanged at a 1:1 ratio. (First reminder)]

There was no rush to exchange experience points, because Xu Ling still remembered that motivation points also played a role in the academic lottery pool.

After entering the top student lottery pool, Xu Ling clicked on the "add bet" button that had puzzled him before.

[You can use motivation points to add to the learning points lottery to increase the probability of winning high-quality prizes.]

【Please enter the additional amount:】

So far, Xu Ling has fully mastered all the functions of the system.

It is precisely because of this that Xu Ling is full of confidence in the future of his scientific research.

The next thing to consider is the topic of the glory mission.

(End of this chapter)