[Abstract] Based on many years' experience in guiding the national college students' mathematical modeling competition, this paper makes an in-depth analysis of the preparation, answering requirements, judging basis and development trend of the competition, and puts forward some suggestions for future contestants.
[Keywords:] CUMCM competition preparation answer sheet requires judgment according to the development trend
[Author] Cui Zhiming (1965-), male, from Yanchang, Shaanxi, is an associate professor at the School of Mathematics and Computer Science of Yan 'an University. The main research direction is mathematical model. (Yan 'an, Shaanxi 7 16000)
【 China Library Classification Number 】 G642.46 【 Document Identification Number 】 A 【 Document Number 】1004-3985 (2006) 36-0191-02
The National Mathematical Modeling Competition for College Students, co-sponsored by People's Republic of China (PRC) Ministry of Education and China Institute of Industrial and Applied Mathematics, has been welcomed by students and universities. For more than ten years, the continuous expansion of the competition scale has its profound background, because the combination of mathematics and computer technology has formed a universal and realizable key technology-mathematical technology, and the view that "high technology is essentially mathematical technology" is increasingly recognized. Under this background, the mathematical modeling competition for college students came into being. The author has been engaged in mathematical modeling teaching and competition guidance for many years and has accumulated a lot of experience. Now I'll write it down for reference.
First, you should have a "bottom" in your heart.
First of all, it is really difficult to predict which actual territory the title comes from, but it is definitely not too "specialized". After all, it has been simplified. Most competition questions can only be understood by consciousness, and the actual background of a few competition questions may be unfamiliar. You only need to look up some information to understand the meaning of the question. Secondly, of course, all the competition questions need to use mathematical knowledge, but they must not be too advanced. Some theories and methods of operational research, probability statistics, calculation methods, discrete mathematics, differential equations, etc. Used more. These contents are all learned in pre-competition training and really used. I always know what materials to look for.
Second, if it is broken, it will be broken.
You can't decide which of the two things to do for a long time because you only have three days. Once you choose, don't hesitate, let alone repeat it. After selecting the competition questions, there will be arguments when discussing the modeling ideas and problem-solving methods, but you should learn to compromise instead of arguing endlessly. After the scheme is decided, the whole team wants Qi Xin and Qi Xin to work together to do it.
Third, we should be mentally prepared for difficulties.
"If you get the topic, you will have an idea and do it smoothly." How can it be so easy? Taking part in the competition can be said to be "asking for trouble and taking pleasure in suffering". After three days of training, I will never forget it and become my spiritual wealth. Many students said after the game, "You will regret it for three days, but you will regret it for a lifetime if you don't participate." Being a "bump gun" is not necessarily better than being a "layman". For example, players who study mechanics do mechanical problems, players who study investment do investment problems, and players who study statistics do statistical problems, all of which may be "smarter than them". These situations have happened in Shaanxi Division and National Division.
Fourth, there is no best, only better.
First of all, to complete the modeling competition, of course, we must be creative, but creativity has no peak, and every team must do its best. Taking the sales of 1994B lock packaging as an example, most of the answers sent to the whole country by each division have reached or even exceeded the reference answer requirements provided by the National Organizing Committee, so the marking team decided to immediately eliminate the answers that did not meet the answer requirements or were poorly expressed, thus brushing off nearly 1/3, and decided whether to give the first prize after the remaining answers exceeded the reference answer requirements. So every team should work hard on the word "better". Secondly, almost all the excellent answers given by the whole country every year are insufficient or even wrong. It is not surprising that the answer sheet with obvious mistakes is actually excellent, because the Excellence of the answer sheet is relative. It depends on what grade your team's answer sheet is in the whole competition. Third, some events can be said to be "endless". For example, the third question of 1999B drilling layout, even the champion team of Skyworth Cup (Dalian University of Technology) failed to draw a conclusion. The propositional reviewer of this competition also pointed out: "It involves more properties about the distribution of the whole point and deserves further study."
Fifth, the first task is to thoroughly understand the problem.
Don't worry about "how to do this problem" after you get the competition problem, but first find out "what does this problem want us to do?" A competition problem usually includes three parts: background, question type and data. The first two parts should be carefully scrutinized to find out what practical problems to solve and what the practical significance of the data is. Otherwise, it may deviate from the original topic. If we continue to do it, it will be meaningless.
When doing a problem, don't rush to find a mathematical method to solve it. First, focus on establishing a mathematical model, and we must grasp the main factors of practical problems. For example, 2000B "Steel Pipe Ordering and Transportation" is a discrete optimization problem, and its focus is obviously on the analysis and establishment of the model. The purchase and transportation plan, total cost and sensitivity analysis involved in the three problems in the topic can only be known through the solution and discussion of the model. However, some teams in Shaanxi Division did not give a clear model, but only gave numerical results in a "set" way. Although it is reasonable on the whole, this method is not universal and is not the correct mathematical modeling method at all.
Sixth, think about the relationship between using computers.
Mathematical modeling is inseparable from computers and software, but there is a bad phenomenon in the competition, which should be paid attention to, that is, not paying attention to the brain, but relying too much on computers, that is to say, weakening the ability of mathematical analysis and relying too much on advanced software. An excellent team should use computers and software reasonably on the basis of full brain. You know, computers and software are tools to make smart people more capable, and an excellent answer sheet always needs some math skills.
Seven, correctly handle the digital results
In most cases, the numerical results can't be absolutely accurate, as long as they are reasonable, but they can't be too outrageous. For example, two questions in 1996A "optimal fishing strategy" have total catch, and the more accurate answer is1:388,700 tons/year; Question 2: The annual output is 6.5438+0.605 million tons. Some teams in Shaanxi Division answered the first question: annual × 10,000 tons; Question 2: Annual ×× 10,000 tons.
Sometimes the accuracy of the numerical results will affect the ranking of the answer sheet, and sometimes the numerical results are unique and not much worse. The lesson of dealing with numerical results is that the designed algorithm should be universal and rigorous, and should not be too constrained by the specific data given by the competition questions. Be sure to check the numerical results carefully. We should strive for higher accuracy under reasonable premise. Even if the numerical results are absolutely accurate, don't sit back and relax and check whether there are any omissions in the algorithm.
Eight, "practical" requirements should be implemented from beginning to end.
It seems that the requirement of "facing reality" should not be ignored when making assumptions and establishing models, but it is not necessarily the case in the inspection, evaluation and improvement of models.
First of all, don't stick to the written description of the competition questions, but remember the basic requirements of the answer sheet. For example, the three-dimensional reconstruction of 200 1A blood vessel stated in the question: "Try to calculate the central axis and radius of the pipeline, give a specific algorithm, and draw the projection of the central axis in each coordinate plane." Of the 75 teams that did this question in Shaanxi Division, quite a few teams answered irrelevant questions. What's wrong with that? First of all, the title of the contest is "Three-dimensional reconstruction of blood vessels". Now that the central axis and radius of the pipeline have been calculated, why not rebuild the pipeline wall? Secondly, and more importantly, even if the pipeline wall has been rebuilt, why not check it? Because for this game, only by testing can we give a proper evaluation of the model and find out the direction of improvement.
Secondly, the answer sheet cannot be "anticlimactic". For example, the title of 1995B, "Operation Scheduling of Cranes and Smelters", requires that "suggestions should be made to increase the steel output of this workshop to 3 million tons/year". Originally, it was intended for participants to put forward specific suggestions to improve management scheduling and tap production potential on the basis of their own team's model algorithm. Surprisingly, some teams even proposed "adding one or even several smelting furnaces!" Do they know that a large converter with supporting equipment needs tens of millions or even hundreds of millions of yuan of investment? The team that made this suggestion is totally divorced from reality.
Nine, the development trend of mathematics will inevitably be reflected in the competition questions and increase the challenge of the competition questions.
In recent years, the development trend of international mathematics includes the expanding role of discrete mathematics, increasing attention to nonlinear problems, the expanding role of probability and statistics, and the further development of large-scale scientific calculation. Reflected in CUMCM's competition questions, there are few continuity problems, and most optimization problems are nonlinear. In recent years, there is at least one random question every year, and the calculation is getting bigger and bigger. It is not uncommon for a team to be busy with two computers.
The combination of mathematics, an ancient discipline, with some young disciplines, such as image processing, graphics and computer science, has effectively promoted the emergence of many new growing points ("computer three-dimensional reconstruction of sequence images" involved in 200 1A is one of these growing points). This cross process also promotes the development of mathematics itself. For example, many three-dimensional reconstruction methods of equal-diameter pipes are closely related to the concepts of equidistant line, equidistant surface, envelope surface and swept surface in mathematics. The problem 200 1A, which reflects the development trend of mathematics, is not only quite innovative, but also the trend predicted by this problem deserves the attention of participating institutions.
[References]
Li Daqian. Mathematical modeling competition for Chinese college students [M]. Beijing: Higher Education Press, 200 1.
[2] Ye Xiaoqi. Textbook of Mathematical Modeling Competition for College Students [M]. Changsha: Hunan Education Press, 1997