Scholar’s Advanced Technological System

Looking at the two people in the classroom, Professor Liu Xiangping stunned slightly and asked with a smile: “Are there only two people? I heard there was another one. ”

“… I'll call her.” Wang Xiaodong looked embarrassed and went outside with his phone.

The teacher was not in a hurry, unwrapped the thermos cup, sipped the hot water, slowly walked to the side of the ark, smiled and asked: “What is the configuration of your team? ”

Ark dropped his phone and replied with a smile: "I am responsible for modeling, Wang Xiaodong is responsible for programming, Lin Yuxiang is responsible for writing papers and answers. ”

“Modeling, programming, writing, standard configuration,” Teacher Liu laughed and continued, "By the way, you're the 13-year-old ark. I read your paper, it's a good article indeed. ”

The ark's eyes lit up: “Teacher, do you do math too? ”

“Sort of, but my research is oriented towards physics, and mathematical papers are rarely distributed.” Teacher Liu squinted her eyes and looked at the door of the classroom. She continued with a smile. “You lesbians don't seem to be very reliable. ”

The ark was embarrassed and laughed politely.

Teacher Liu smiled too. Without saying much on this issue, he paused for a moment and continued: “I suggest you adjust the configuration of your team slightly. Modelling and dissertation are the responsibility of the same person, while the other two are responsible for programming. The advantage is that those responsible for modeling have a stronger overall grasp of the topic and a smoother grammar. But of course there's also the downside, which is that you're going to be very burdened. The game lasts only three days in total, which means you have to start writing as soon as you finish modeling. ”

The Ark thought something: "… are the two people in charge of programming? ”

Teacher Liu sipped tea and said slowly: "Yes. ”

Ark laughed and didn't immediately reply: “I'll think about it, after all, I'll have to discuss this with my teammates. ”

At this point, the footsteps of a small run came from outside the corridor, and the last teammate was finally late.

“Sorry, I'm a little late. I'm really, really sorry!” Walking into the classroom with Wang Xiaodong, Lin Yuxiang looked sorry and bowed his head to the teacher to make a mistake.

“It's okay, now that we're all here, let's get started.” Teacher Liu Xiangping laughed and didn't blame her for being late. She turned to the podium, plugged the USB drive into the computer, turned on the projector and released his PPT.

“Before I begin my lecture, I would like you to take a look at a routine. The question itself is not difficult, but it can serve as an example of mathematical modelling. I hope this set of cases will give you an idea of what mathematical modeling really is. ”

He pressed his mouse and turned the ppt to the next page.

“Each of the three businessmen carries one attendant across the river by boat. A small boat can only accommodate two people. The attendant promises to kill more people on either side of the river than the businessman, but how can the power to cross the river by boat be in the hands of the businessman? How can the businessman safely cross the river? ”

Indeed, there is no difficulty in this question.

Even without the power of the system, the ark quickly came up with an answer, answering.

“Round one, two follow the past, one follow back. ”

“Round two, two more to follow, one to come back. ”

“Round three, two businessmen past, one attendant and one businessman back. ”

“Round four, two businessmen past, one following back. ”

“Round five, two follow the past, one follow back. ”

“Round six, the last two followers, successfully crossed the river! ”

“Pfft, pfft!” Lin Yuxiang clapped his hands and clapped his hands. His face was full of admiration.

Wang Xiaodong's expression on his face was immobile. He looked like a tall man.

In his view, the problem was really not difficult, although he didn't have the brain to calculate it, but he believed in his IQ and took a little time to figure it out as well.

“Exactly.” Teacher Liu laughed and continued, "Even without any mathematical knowledge, it can be solved simply by logic analysis. But what if we spread the problem to N merchants? ”

The problem is a bit difficult, but it's not difficult in mathematics, it's difficult to solve the problem by abstracting it into a mathematical problem.

After a while of careful reflection, the Ark had a general idea in mind.

“Can I use the blackboard? ”

“Sure,” Professor Liu Xiangping laughed and made a gesture.

The ark went up and picked up the chalk and started placing books on the blackboard.

① Remember that the number of merchants on this bank before the K th crossing is XK. The number of adherents is Yk, k = 1, 2, …, Xk, Yk = 0, 1, 2, 3. Define the two-dimensional vector Sk = (Xk, Yk) as a state, and the set of states under safe crossing conditions as a set of allowed states, recorded as S.

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

② Remember the number of merchants on the kth ferry is Uk and the number of attendants is Vk. Define the two-dimensional vector Dk = (Uk, Vk) as decision making. Allow decision sets to be recorded as D, as can be seen from small boat capacity: D = {(U, V) | 1 ≤ U + V ≤ V, U, V = 0, 1, 2}

③ Combining the above conclusions, the state Sk changes with Dk law is: S (k +1) = Sk + (-1) ^ k * Dk

“Awesome...” Looking at the board book on the blackboard, Lin Yuxiang opened her mouth slightly and looked at the ark coming down from the podium, surprised to whisper, "Don't you need to write a draft? ”

“Strike it in your heart.” The Ark laughed and said.

Wang Xiaodong was as silent as ever and did not speak.

But from the look on his face, this arrogant schoolmaster was completely overwhelmed by the mathematical ability of the ark.

Looking at the process on the blackboard, Professor Liu Xiangping nodded with a smile: “Absolutely correct! From a mathematical modelling point of view, however, this work can only be halved. Once we've finished modeling, we'll also need a program to implement this model. Of course, this model is very simple, I believe that with the ability of our Wang classmates, this level of program must be hands-on, not to waste valuable time here. ”

Wang Xiaodong pushed his glasses. The expression on his face was still indifferent. One pair looked natural.

Although he didn't get a chance to show his programming skills on the spot, it just made him feel a little sad.

Paused for a moment, Teacher Liu continued, "Data modeling is actually about simplifying a real problem into one that can be represented in data and very short language, and then solving the problem through mathematical tools. ”

“The key, therefore, is what are the practical issues facing your team? ”

“It is important to remember that modeling is neither the programming nor the mathematical skills of the study team, but the ability to translate practical problems into data language and solving. ”

“With regard to modelling itself, I do not have many suggestions, and there are no shortcuts beyond more practice and broadening the knowledge base. As far as programming is concerned, I can say two words. ”

“There are four main types of software that are commonly used, Matlab, Mathematica, lingo, and SAS, and you don't need to master them all, at least one of them. The key is to be able to solve real problems with the software that suits you.” While saying this, Professor Liu Xiangping looked at Wang Xiaodong.

Because the main thing is to give it to him.

Wang Xiaodong pushed his glasses and nodded: “I have used Matlab and SAS and the problem is not great. ”

Professor Liu nodded: "Yes, these two pieces of software are basically enough. These things need to be self-taught, and what I can do is give guidance when you don't understand. ”

“Finally, regarding reference books, I recommend that you read some examples of mathematical modeling, such as Mathematical Models, Mathematical Modeling Algorithms and Applications, and Basic Mathematical Modeling Tutorials. ”

“I also have some handouts and materials from inside the school that you can copy back to see, but don't forget to pass them on, let alone upload them online. Understood?”

“Understood!” the three spoke in unison.

Professor Liu smiled and said, "Well, that's it for today. I have nothing else to say, mainly on your own. If you need information, please download it to me and go back to English. ”