Looks at the two people in classroom, Professor Liu Xiangping gawked slightly, asked with a smile: „Only has two people? I heard that also has one.” 看着教室里的两人,刘向平教授微微愣了下,笑着问道:“只有两个人吗？我听说还有一个。” „...... I call to ask her.” The Wang Xiaodong expression was awkward, takes the telephone to go to outside. “……我打个电话问一下她。”王晓东表情尴尬,拿着电话去了外面。 The teacher does not worry, twists off the insulated cup, sipped a hot water, arrived by Lu Zhou slowly, was asking: „What situation is the disposition of your team?” 那老师也不着急,拧开保温杯,抿了口热水,慢悠悠地走到了陆舟旁边,笑着问:“你们队伍的配置是什么情况？” Lu Zhou puts down cell phone, replied with a smile: „I am responsible for the modeling, Wang Xiaodong am responsible for programming, Lin Yuxiang is responsible for writing the paper and reply.” 陆舟放下手机,笑着回答道:“我负责建模,王晓东负责编程,林雨湘负责撰写论文和答辩。” „Modeling, programming and writing, the standard configuration,” Teacher Liu smiles , to continue, „said that you are 13 that Lu Zhou, your paper I looked, truly is a good article.” “建模、编程、写作,标准配置啊,”刘老师笑了笑,继续说,“说起来,你就是一三届的那个陆舟吧,你的那篇论文我看了,确实是篇好文章啊。” Lu Zhou eye one bright: „Teacher you also do the math?” 陆舟眼睛一亮:“老师您也是搞数学的？” „Is, my research direction deviation physics, the mathematical paper rarely sent actually.” Teacher Liu narrowed the eye, looked at the classroom entrance, continued with a smile, „your woman comrades, were not as if reliable.” “算是吧,不过我的研究方向偏向物理,数学论文倒是很少发了。”刘老师眯了眯眼睛,看了眼教室门口,笑着继续说,“你们这位女同志,似乎不怎么靠得住啊。” Lu Zhou does not lose awkwardly smiles politely. 陆舟尴尬而不失礼貌地笑了笑。 Teacher Liu also smiles, without said anything in this issue, stopped the moment, then continued: „About the disposition that you form a team, I suggested that you can adjust slightly. The modeling and paper are under the charge to the same person, other two people are responsible for programming. Such advantage is, the person who is responsible for the modeling has the strong assurance to the entire topic in the overall situation, the issue document mentality is smoother. However the fault also has certainly, that will be your burden/shoulder pole will be very heavy. The playing time altogether is only three days, this means that you after completing modeling, must start the paper writing immediately.” 刘老师也笑了笑,没在这个问题上多说什么,停顿了片刻,便继续说:“关于你们组队的配置,我建议你们可以稍微调整。建模和论文由同一个人负责,其余的两个人负责编程。这样的好处是,负责建模的人对整个题目在全局上有着较强的把握,行文思路更加流畅。然而坏处当然也有,那就是你的担子会很重。比赛时间总共只有三天,这就意味着你在完成建模之后,必须立刻开始论文写作。” Lu Zhou looking pensive: „...... Are two people responsible for programming?” 陆舟若有所思:“……两个人负责编程吗？” Teacher Liu sipped a tea, said slowly: „Right.” 刘老师抿了口茶,慢悠悠地说道:“没错。” Lu Zhou smiles, has not given the answer immediately: „I considered again, this matter also discussed with the teammate after all.” 陆舟笑了笑,没有立刻给出答复:“我再考虑考虑吧,毕竟这事儿也得和队友商量下。” At this time, outside the corridor heard the sound of footsteps that slightly ran, the last teammate finally was the long in coming. 这时候,走廊外传来小跑的脚步声,最后一位队友总算是姗姗来迟。 „Excuse me, I get up to be late slightly, really really sorry very much!” Enters the classroom with Wang Xiaodong, a Lin Yuxiang face was sorry that admits mistakes to the teacher. “不好意思啊,我稍微起晚了点,真的真的很对不起！”和王小东一起走进教室,林雨湘一脸抱歉地向老师低下头认错。 „All right, since the person arrived in full, we start quickly.” Teacher Liu Xiangping smiles amiably, has not blamed her late issue, turned around to arrive on the platform, inserted the computer the USB, and turned on the projecting apparatus, emitted his PPT. “没事儿,既然人到齐了,咱就赶快开始吧。”刘向平老师随和地笑了笑,也没责怪她迟到的问题,转身走到了讲台上,将U盘插进了电脑,并打开了投影仪,放出了他的PPT。 „Before starting to teach, I hope that you first come to see together the sample question. This writes has no difficulty, but can actually as a case of mathematical modeling. I hope that through this set of case, can make you first understand that actually the mathematical modeling is what?” “在开始讲课之前,我希望你们先来看一道例题。这道题本身没什么难度,不过却可以作为一道数学建模的案例。我希望通过这套案例,能让你们先明白数学建模究竟是什么？” Saying, he presses down the mouse, turned the next page ppt. 说着,他按下鼠标,将ppt翻到了下一页。 „Three merchant various belt/bring accompany to go by boat to cross river, small ships can accommodate two people, accompany secret approximately, in any shore of river, the population of once accompanying are more than merchant, kills a person and takes his possessions, the power how but to go by boat to cross the river grasps in the merchants hand, asked: How can the merchants cross the river safely?” “三名商人各带一个随从乘船过河,一只小船只能容纳二人,随从们秘约,在河的任一岸,一旦随从的人数比商人多,就杀人越货,但是如何乘船渡河的大权掌握在商人们手中,问:商人们怎样才能安全渡河呢？” Truly, this problem has no difficulty. 确实,这道题没有任何难度。 Even if not rely on the system the strength, Lu Zhou still soon found out the answer, replied. 即便不凭借系统的力量,陆舟也很快想出了答案,回答道。 „The first round, two accompany, accompanies.” “第一轮,两个随从过去,一个随从回来。” „The second round, two accompany again, accompanies.” “第二轮,再两个随从过去,一个随从回来。” „The third round, two merchants in the past, accompanied with a merchant comes back.” “第三轮,两个商人过去,一个随从和一个商人回来。” „The fourth round, two merchants in the past, accompanied.” “第四轮,两个商人过去,一个随从回来。” „The fifth round, two accompany, accompanies.” “第五轮,两个随从过去,一个随从回来。” „The sixth round, final two accompany, successfully crosses the river!” “第六轮,最后两个随从过去,成功渡河！” „pa pa!” Lin Yuxiang pats the small hand to applaud low voice, on the face full is the worship. “啪啪啪！”林雨湘拍着小手小声鼓起掌,脸上满是崇拜。 The expression on Wang Xiaodong face remains unmoved, an appearance of extra mundane person of high skill. 王晓东脸上的表情不为所动,一副世外高人的模样。 In his opinion this problem truly has no difficulty, although has not used the brain to calculate, but he believes that oneself intelligence quotient, the spend some time can also solve at most slightly. 在他看来这道题确实没什么难度,虽然没动脑去算,可他相信自己的智商,顶多稍微花点时间同样解得出来。 „Absolutely correct.” Teacher Liu smiles , to continue, „even without arriving at any mathematical knowledge, can solve this problem through the logic analysis purely. But if promotes the issue to N merchants?” “完全正确。”刘老师笑了笑,继续说,“即便不用到任何数学知识,单纯通过逻辑分析也能解决这个问题。可如果将问题推广到N个商人呢？” This issue truly some difficulties, but difficult is actually not difficult in mathematical, but how is difficult to become the mathematical problem to solve this topic abstractly. 这个问题确实有些难度,不过难却不是难在数学方面,而是难在如何将这道题目抽象成数学问题进行解决。 Lu Zhou seriously thought deeply about a while, in the brain has an approximate mentality. 陆舟认真思索了一会儿,脑子里已经有了一条大致的思路。 „Can I use the blackboard?” “我可以用下黑板吗？” „Sure,” Professor Liu Xiangping gave the hand signal of invitation with a smile. “当然可以,”刘向平教授笑着做了个请的手势。 Lu Zhou walks up, takes the chalk to start the blackboard writing on the blackboard. 陆舟走上前去,拿起粉笔开始在黑板上板书。 【 ① records for the k th time before fording , the merchant number that this shore is Xk. Accompanying the number is Yk , k = 1,2,......, Xk , Yk = 0,1,2,3. Defines two-dimensional vector Sk = ( Xk , Yk ) as the condition, the condition set under security fording condition is the set of admissible states, making S. 【①记第k次渡河前此岸的商人数为Xk。随从数为Yk,k=1，2,……,Xk,Yk=0，1，2，3。将二维向量Sk=(Xk,Yk)定义为状态,安全渡河条件下的状态集合为允许状态集合,记做S。 May result in S = \ { ( X , Y ) | X = 0 , Y = 0,1,2,3 ; X = 3 , Y = 0,1,2,3 ; X = Y = 1,2 } 可得S=\{(X,Y)|X=0,Y=0，1，2，3;X=3,Y=0，1，2，3;X=Y=1，2} ② records the merchant number on k th ferry is Uk, accompanying the number is Vk. Defines two-dimensional vector Dk = ( Uk , Vk ) as the decision. The set of admissible decisions to record to make D, may know by the small ship's capacity: D = \ { ( U , V ) | 1 ≤ U + V ≤ V , U , V = 0,1,2 } ②记第k次渡船上的商人数为Uk,随从数为Vk。将二维向量Dk=(Uk,Vk)定义为决策。允许决策集合记做D,由小船容量可知:D=\{(U,V)|1≤U+V≤V,U,V=0，1，2} ③ synthesizes the above conclusion, condition Sk along with the Dk rules of changes is: S ( k + 1 ) = Sk + (-1 ) ^ k * Dk ③综合以上结论,状态Sk随Dk的变化规律是:S(k+1)=Sk+(-1)^k*Dk 】 】 „Good fierce......” bewildered looks at the blackboard writing on blackboard, Lin Yuxiang is opening mouth slightly, looks Lu Zhou that walks from the platform, asked with amazement low voice, „you do not need the rough draft?” “好厉害……”一脸茫然的看着黑板上的板书,林雨湘微微张着嘴,看着从讲台上走下来的陆舟,惊讶地小声问,“你都不需要打草稿的吗？” „Is hitting at heart.” Lu Zhou smiles to say. “在心里打好了。”陆舟笑了笑说道。 Wang Xiaodong as is always very also silent, without speech. 王晓东同样一如既往很沉默,没有说话。 However from his expression, this arrogant study tyrant regarding the Lu Zhou ability in mathematics, was convinced thoroughly. 不过从他的表情来看,这位高傲的学霸对于陆舟的数学能力,算是彻底服气了。 Looked at process on the blackboard, Professor Liu Xiangping nods with a smile: „Is absolutely correct! However from the perspective of mathematical modeling, this work can only calculate that completed half. After completing modeling, we also need a procedure/program, realizes this model. Naturally, this model is very simple, I believe that by our Fellow student Wang ability, the procedure/program of this rank definitely has words at fingertips and writes with facility, did not waste the precious time here.” 看了眼黑板上的过程,刘向平教授笑着点了点头:“完全正确！不过从数学建模的角度来看,这项工作只能算完成了一半。在完成了建模之后,我们还需要一个程序,将这个模型进行实现。当然了,这个模型很简单,我相信以咱们王同学的能力,这种级别的程序肯定是信手拈来,就不在这里浪费宝贵的时间了。” Wang Xiaodong pushed the eyeglasses, a expression face on face is still faint, a that is the natural appearance. 王晓东推了推眼镜,脸上的表情依旧一脸淡漠,一副那是当然的样子。 Although does not have opportunity to show his procedure draw up technique, lets his some small regrets and that's the end. 虽然没机会现场展现他的编程技术,让他有些小遗憾就是了。 Stopped the moment, Teacher Liu continues saying that „data modeling in fact is one can very brief language can express with the data an actual issue simplification issue that then solves this problem through the mathematical instrument the process.” 停顿了片刻,刘老师继续说道,“数据建模实际上就是将一个实际的问题简化为一个可以用数据和很简短的语言能表示出来的问题,然后通过数学工具解决这个问题的过程。” „Therefore, what the key is the actual problem that your team must face is?” “因此,关键是你们队要面临的实际问题是什么？” „Modeling does not inspect the programming ability of team, is not the inspection ability in mathematics, but is the inspection transforms the ability of the data language and solution the actual problem, this point you must remember.” “建模既不是考察团队的编程能力,也不是考察数学能力,而是考察将实际问题转化成数据语言和求解的能力,这一点你们一定要记住。” „About modeling's words, I too had not suggested, this besides practices and expands the aspect of knowledge much not to have more shortcuts. As for programming this aspect, I can say two actually.” “关于建模本身的话,我并没有太多建议,这个除了多练和拓宽知识面之外没有更多的捷径。至于编程这方面,我倒是可以说两句。” „Commonly used software main four types, Matlab, Mathematica, lingo and SAS, do not need you to grasp completely, at least can grasp one type was good, the key can utilize to suit own software to solve the actual problem.” Said this saying time, Professor Liu Xiangping is looking at Wang Xiaodong. “常用的软件主要四种,Matlab、Mathematica、lingo和SAS,不需要你全部掌握,至少能掌握其中一种就行了,关键是能够运用适合自己的软件来解决实际问题。”说这话的时候,刘向平教授在看着王晓东。 Because of these words, mainly listens to him i.e . 因为这句话,主要就是说给他听的。 Wang Xiaodong pushed the eyeglasses, the nod said: „Matlab and SAS I have used, the issue is not big.” 王晓东推了推眼镜,点头道:“Matlab和SAS我用过,问题不大。” Professor Liu nods: „Met these two software basically enough. These things need you to study independently, I can do is also when you do not understand provides the instruction.” 刘教授点了点头:“会这两个软件基本够了。这些东西都需要你们自学,我能做的也就是在你们不懂的时候提供指导。” „Finally about the reference book, I recommends you to look at some mathematical modeling cases and other books, for example «Mathematical model», «Mathematical modeling Algorithm And Application» as well as «Mathematical modeling Foundation Course» these three books.” “最后是关于参考书,我推荐你们可以看一些数学建模案例等书,比如《数学模型》、《数学建模算法与应用》以及《数学建模基础教程》这三本。” „Some here also schools printed lectures and materials, you can the copy go back to look, but cannot remember leak, cannot on pass to online. Understood?” “我这里还有一些学校内部的讲义和资料,你们可以拷贝回去看,但记住不得外传,更不能上传到网上。明白？” „Understood!” Three people said with one voice. “明白！”三个人异口同声道。 Professor Liu smiles, said: „Ok, that today arrived here, I did not have other anything to say that mainly depended on you. Needs the material comes my downloading, got down to hurry to review English.” 刘教授笑了笑,说:“行了,那今天就到这里,我也没别的什么可说的,主要还是靠你们自己。需要资料的来我这下载,下完了就赶紧回去复习英语吧。”