Looking at the two people in the classroom, Professor Liu Xiangping was slightly stunned, and asked with a smile, "Is there only two people?" I've heard there's another one. ”

“…… I'll give her a call and ask about it. Wang Xiaodong looked embarrassed and took the phone and went outside.

The teacher was not in a hurry, unscrewed the thermos cup, took a sip of hot water, walked slowly to Lu Zhou's side, and asked with a smile: "What is the configuration of your team?" ”

Lu Zhou put down his phone and replied with a smile: "I am responsible for modeling, Wang Xiaodong is responsible for programming, and Lin Yuxiang is responsible for writing the thesis and defense." ”

"Modeling, programming, writing, standard configuration," Mr. Liu smiled and continued, "Speaking of which, you are the Lu Zhou of the first and third sessions, I have read your paper, it is indeed a good article." ”

Lu Zhou's eyes lit up: "Teacher, you are also engaged in mathematics?" ”

"Sort of, but my research direction is biased towards physics, and I rarely publish mathematical papers." Teacher Liu squinted his eyes, looked at the door of the classroom, and continued with a smile, "You lesbians don't seem to be very reliable." ”

Lu Zhou smiled awkwardly but politely.

Teacher Liu also smiled, didn't say anything more on this issue, paused for a moment, and continued: "Regarding the configuration of your team, I suggest that you can adjust it slightly. The same person is responsible for the modeling and the thesis, and the other two are responsible for programming. The advantage of this is that the person in charge of modeling has a stronger grasp of the overall problem and writes more fluently. However, of course, there is a downside, that is, your burden will be heavy. The competition lasts for only three days, which means that you have to start writing your essay as soon as you've finished modeling. ”

Lu Zhou thought thoughtfully: "...... Are two people in charge of programming? ”

Teacher Liu took a sip of tea and said slowly, "That's right. ”

Lu Zhou smiled and didn't give an immediate reply: "I'll think about it again, after all, I have to discuss this matter with my teammates." ”

At this time, there was the sound of trotting footsteps outside the hallway, and the last teammate was finally late.

"I'm sorry, I'm a little late, I'm really sorry!" Walking into the classroom with Wang Xiaodong, Lin Yuxiang bowed his head to the teacher with an apologetic face and admitted his mistake.

"It's okay, now that everyone is here, let's start quickly." Teacher Liu Xiangping smiled casually, and didn't blame her for being late, turned around and walked to the podium, inserted the USB flash drive into the computer, and turned on the projector, and played his PPT.

"Before we get started, I want you to look at a sample problem. This problem is not difficult in itself, but it can be used as an example of mathematical modeling. I hope that through this set of cases, you can first understand what mathematical modeling is. ”

As he spoke, he pressed the mouse and flipped the PPT to the next page.

"Three merchants each took an attendant to cross the river by boat, and a small boat could only hold two people, and the attendants secretly made a secret agreement that on either side of the river, if the number of retinues was greater than the merchant, they would kill people and steal goods, but the power of how to cross the river by boat was in the hands of the merchants, and asked: How can the merchants cross the river safely?"

Indeed, there is no difficulty in this question.

Even without the power of the system, Lu Zhou quickly came up with an answer and replied.

"In the first round, two retinues go and one retinue returns."

"In the second round, two more followers will go over, and one will come back."

"In the third round, two merchants passed, and one retinue and one merchant returned."

"In the fourth round, two merchants passed, and one retinue returned."

"In the fifth round, two retinues go and one retinue returns."

"In the sixth round, the last two followers passed and successfully crossed the river!"

"Bang Bang!" Lin Yuxiang clapped his little hands and clapped quietly, his face full of adoration.

The expression on Wang Xiaodong's face was unmoved, and he looked like a master outside the world.

In his opinion, this question is really not difficult, although he didn't use his brain to calculate, but he believes in his IQ, and at most it takes a little time to solve it.

"Exactly." Teacher Liu smiled and continued, "Even if you don't need any mathematical knowledge, you can solve this problem through logical analysis alone. But what if the problem is extended to N merchants? ”

This problem is indeed a bit difficult, but the difficulty is not in mathematics, but in how to abstract the problem into a mathematical problem and solve it.

Lu Zhou thought seriously for a while, and already had a general idea in his mind.

"Can I use the blackboard?"

"Of course," Professor Liu Xiangping smiled and made a gesture of please.

Lu Zhou stepped forward, picked up the chalk and began to write on the blackboard.

[(1) The number of merchants on this bank before the k-th crossing of the river is Xk. The number of followers is Yk, k=1,2,......,Xk, Yk=0,1,2,3. The two-dimensional vector Sk=(Xk,Yk) is defined as the state, and the set of states under the condition of safe river crossing is the set of allowed states, which is denoted as S.

S={(X,Y)|X=0，Y=0，1，2，3； X=3，Y=0，1，2，3； X=Y=1，2}

(2) The number of merchants on the k-th ferry is Uk, and the number of retinues is Vk. Define the two-dimensional vector Dk=(Uk,Vk) as a decision. The decision set is allowed to be denoted as D, which can be seen from the capacity of the boat: D={(U,V)|1≤U+V≤V,U,V=0,1,2}

(3) Based on the above conclusions, the variation law of state Sk with Dk is: S(k+1)=Sk+(-1)^k*Dk

】

"It's amazing......" Looking at the board book on the blackboard with a blank face, Lin Yuxiang opened his mouth slightly, looked at Lu Zhou who walked down from the podium, and whispered in surprise, "Don't you even need to make drafts?" ”

"Fight it in your heart." Lu Zhou said with a smile.

Wang Xiaodong was also silent as always and did not speak.

However, judging from his expression, this arrogant scholar was completely convinced of Lu Zhou's mathematical ability.

Glancing at the process on the blackboard, Professor Liu Xiangping smiled and nodded: "Exactly right!" From a mathematical modeling point of view, however, this is only half the story. After the modeling is completed, we also need a program to implement the model. Of course, this model is very simple, and I believe that with our ability to do so, this level of program will definitely be at your fingertips, so I won't waste precious time here. ”

Wang Xiaodong pushed his glasses, the expression on his face was still indifferent, and he looked like he was of course.

Although he didn't have the opportunity to show his programming skills live, he had some regrets.

After a pause, Mr. Liu continued, "Data modeling is actually the process of simplifying a practical problem into a problem that can be expressed in data and very short language, and then solving the problem through mathematical tools. ”

"So the key is, what are the practical issues that your team is facing?"

"Modeling is not a test of a team's programming skills, nor is it a test of mathematical ability, but of the ability to translate real-world problems into data language and solve them, and you must remember that."

"I don't have much advice on modeling itself, and there are no shortcuts other than practicing and broadening your knowledge. As for programming, I would say two things. ”

"There are four main types of software commonly used, Matlab, Mathematica, lingo and SAS, you don't need to master all of them, at least one of them, the key is to be able to use your own software to solve practical problems." When he said this, Professor Liu Xiangping was looking at Wang Xiaodong.

Because this sentence is mainly addressed to him.

Wang Xiaodong pushed his glasses, nodded and said, "I have used Matlab and SAS, so it's not a big problem." ”

Professor Liu nodded: "Yes, these two software are basically enough." You need to educate yourself on these things, and what I can do is provide guidance when you don't understand. ”

"Finally, as for reference books, I recommend that you read some mathematical modeling cases and other books, such as "Mathematical Model", "Mathematical Modeling Algorithms and Applications" and "Mathematical Modeling Basic Course".

"I have some internal handouts and materials here, you can copy them back and read them, but remember that they must not be disseminated or uploaded online. Got it? ”

"Understood!" The three of them said in unison.

Professor Liu smiled and said, "Okay, then that's all for today, I don't have anything else to say, it's mainly up to you." If you need information, download it from me, and go back to review English when you're done. ”