Professor Liu Xiangping looked at the two people in the classroom and smiled as he asked, "Only two people? I heard there's one more. "
"… I'll call her," said Wang Xiaodong awkwardly. He took his phone and walked outside.
The teacher was not in a hurry. He opened his vacuum flask and took a sip of hot water. He slowly walked next to Lu Zhou and asked, "What's your team configuration?"
Lu Zhou put down his phone and said, "I'm responsible for modeling, Wang Xiaodong is responsible for programming, and Lin Yuxiang is responsible for writing the thesis and defending."
"Modeling, programming, writing, standard configuration," said Professor Liu with a smile. He then said, "Speaking of which, you're Lu Zhou from the class of 2013, right? I read your thesis, it's a good one."
Lu Zhou's eyes lit up as he asked, "Teacher, you're also in mathematics?"
"Sort of, but my research direction is more towards physics, so I rarely publish mathematics theses." Professor Liu squinted his eyes and looked at the classroom door. He then smiled and said, "Your female comrade doesn't seem to be very reliable."
Lu Zhou smiled politely and awkwardly.
Teacher Liu also smiled and didn't say anything more on this question. He paused for a moment and then continued, "As for the configuration of your team, I suggest you make some slight adjustments. The same person will be responsible for the modeling and thesis, and the other two people will be responsible for programming. The advantage of this is that the person responsible for modeling will have a strong grasp of the overall situation and will be able to write the thesis more smoothly. However, of course, there are also disadvantages, which is that you will have a heavy burden. The competition is only three days in total, which means that after you finish modeling, you must immediately start writing the thesis. "
Lu Zhou said, "… Two people in charge of programming?"
Professor Liu took a sip of tea and said, "That's right."
Lu Zhou smiled and did not immediately reply, "I'll think about it. After all, I have to discuss this with my teammates."
At this time, the sound of running footsteps came from outside the corridor. The last teammate had finally arrived.
"Sorry, I woke up a little late, I'm really sorry!" said Lin Yuxiang as she walked into the classroom with Wang Xiaodong. She bowed her head and apologized to the teacher.
"It's alright. Since everyone is here, let's get started." Mr. Liu Xiangping smiled amiably and didn't blame her for being late. He turned around and walked to the podium, plugged the USB into the computer, turned on the projector, and played his PowerPoint.
"Before I start, I want you to look at an example. This question itself was not difficult, but it could be used as a mathematical modeling case. I hope that through this set of cases, you can understand what mathematical modeling is. "
He clicked the mouse and flipped the PowerPoint to the next page.
"Each of the three merchants brought a follower to cross the river. A small boat could only accommodate two people. The followers secretly agreed that if the number of followers outnumbered the merchants on either side of the river, they would kill the merchants and rob them of their goods. However, the decision on how to cross the river was in the hands of the merchants. Question: How could the merchants cross the river safely?"
Indeed, this question was not difficult at all.
Even without the power of the system, Lu Zhou quickly came up with an answer.
"In the first round, two followers will go, and one follower will come back."
"In the second round, two followers will go, and one follower will come back."
"In the third round, two merchants will go, and one follower will come back."
"In the fourth round, two merchants will go, and one follower will come back."
"In the fifth round, two followers will go, and one follower will come back."
"In the sixth round, the last two followers will go, and they will successfully cross the river!"
"Clap clap clap!" Lin Yuxiang clapped her hands. Her face was full of admiration.
Wang Xiaodong's expression was unfazed. He looked like he was an expert.
In his opinion, this question was not difficult at all. Although he did not use his brain, he believed that with his IQ, he could solve it with a little bit of time.
"Completely correct." Mr. Liu smiled and continued, "Even without any mathematical knowledge, this problem can be solved through logical analysis. But what if I apply the problem to N merchants? "
This question was indeed difficult, but it was not difficult in mathematics. It was difficult in abstracting this question into a mathematical problem.
Lu Zhou thought for a while and had a general idea in his mind.
He then asked, "Can I use the blackboard?"
"Of course." Professor Liu Xiangping smiled and made an inviting gesture.
Lu Zhou walked forward and picked up a piece of chalk. He began to write on the blackboard.
[① Record the number of merchants before the k crossing is Xk. The number of followers is Yk, k = 1, 2, …, Xk, Yk = 0, 1, 2, 3. Define the two-dimensional vector Sk = (Xk, Yk) as the state. The set of states under the condition of safe crossing is the set of allowed states, which is recorded as S.
S = {(X, Y) | X = 0, Y = 0, 1, 2, 3; X = 3, Y = 0, 1, 2, 3; X = Y = 1, 2}
② Record the number of merchants on the k ferry is Uk, and the number of followers is Vk. Define the two-dimensional vector Dk = (Uk, Vk) as the decision. The set of allowed decisions is recorded as D, which is known from the boat capacity: D = {(U, V) | 1 ≤ U + V ≤ V, U, V = 0, 1, 2}
③ Combining the above conclusions, the law of state Sk with Dk is: S (k + 1) = Sk + (-1) ^ k * Dk
】
"Amazing …" Lin Yuxiang looked at the blackboard with a blank face. She opened her mouth slightly and looked at Lu Zhou walking down from the podium. She whispered in surprise, "You don't even need to write a draft?"
"I just need to write it in my mind," said Lu Zhou with a smile.
Wang Xiaodong was also silent as usual.
However, from his expression, this arrogant genius student was completely convinced by Lu Zhou's mathematical ability.
Professor Liu Xiangping looked at the process on the blackboard and smiled as he said, "Completely correct! However, from a mathematical modeling point of view, this work is only half done. After the modeling is completed, we still need a program to implement this model. Of course, this model is very simple. I believe that with Wang Xiaodong's ability, this level of program will be easy, so I won't waste my precious time here. "
Wang Xiaodong pushed his glasses up his nose. His expression was still indifferent as if it was a given.
Even though he did not have the opportunity to show his programming skills, he was still a little disappointed.
Professor Liu paused for a second and continued, "Data modeling is actually the process of simplifying a practical problem into a problem that can be expressed with data and a very short language. Then, using mathematical tools to solve this problem.
"Therefore, the key is, what is the practical problem your team is facing?
"Modeling is neither a test of a team's programming ability nor a test of mathematical ability. It is a test of the ability to transform a practical problem into a mathematical language and solve it. You must remember this.
"As for the modeling itself, I don't have much advice. There are no shortcuts other than practicing and broadening your knowledge. As for programming, I can say a few words.
"There are four types of commonly used software, Matlab, Mathematica, Lingo, and SAS. You don't need to master all of them, just master at least one of them. The key is to be able to use the software that suits you to solve practical problems," said Professor Liu Xiangping as he looked at Wang Xiaodong.
This was mainly because this sentence was mainly for him to hear.
Wang Xiaodong pushed his glasses up and nodded as he said, "I've used Matlab and SAS, it's not a big problem."
Professor Liu nodded and said, "These two software are enough. You need to learn these things on your own. All I can do is provide guidance when you don't understand.
"Finally, regarding reference books, I recommend you to read some mathematical modeling case books, such as' Mathematical Model ',' Mathematical Modeling Algorithms and Applications', and 'Basic Mathematical Modeling Course'.
"I also have some internal school handouts and materials here. You can copy them back, but remember, don't leak them, and don't upload them online. Understood? "
"Understood!" said the three people in unison.
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