abstract
Writing is regarded as the core of a paper, so how and what should the abstract be written? From my personal experience, there is not much difference between the abstracts of the American Games and the Chinese Games, because they are both concise abstracts of a paper, but the first sentence of the Chinese Games is often to introduce the background of the problem, while the abstract of the American Games is more direct. At the beginning of the summary, USA said, "In view of the * * * problem, we propose the * * * model" or "We propose the * * model to solve the * * * problem". Looking at the abstract writing style of the grand prize paper, it can be summarized as "syllogism", but its abstract is not only three paragraphs, but consists of three parts (total-sub-total).
The first paragraph summarizes the paper in one or two sentences to prepare for the following summary; To treat each question in the topic, I personally suggest that there is a paragraph corresponding to it in the abstract, which is not so much a very traditional method as a very effective method to make the abstract level very clear; The last part is the summary of the model and the summary of the results, including the result analysis, the sensitivity analysis of the model and the advantages and disadvantages.
An important problem in writing is that the abstract should not talk about what model it uses, but must involve some core assumptions. Take this year's APMCM title as an example. The problem requires that the UAV search area cover the whole Yangpu District. How to turn the problem of regional coverage into an existing problem that can be solved better? The excellent team's treatment method is as follows: Assuming that the monitoring area of the UAV is circular, as long as the circular area can fill Yangpu District, the next problem is to extract the center of these circles and let the UAV traverse these points.
Then, through the above assumptions, the region coverage problem is transformed into a classical graph theory problem. This transformation step is very important, it is the basis of all your later work, so it must be reflected in the abstract, which is also a highlight of your paper.
If there are numerical results in the question, it is best to reflect them in the abstract. People may worry about the correctness of their results, which is totally unnecessary. For the United States, there is no definite answer to any question, which is also the difference from the national competition; However, don't be too convinced that the United States has not had a correct result. Mercer solves some practical problems, and there is no fixed answer, but your results also need to be realistic and not too outrageous.
There should be no formula or chart in the abstract. Some teachers may say it's best not to show up, but here I tell you for sure, no formulas, no charts. Why? If there is a formula in the abstract, you need to explain the symbols in the formula, otherwise the judges will not fully understand the meaning of your formula. In view of this, there should be no formula; Charts occupy a lot of space in the abstract, and the number of words in the original abstract is certain, so charts should not appear.
In a word, a good abstract needs to make readers understand the following points: 1. What is your team's solution? 2. Why the scheme is reasonable; 3. What is the solution to the problem? 4. Whether the model of the scheme is stable; 5. What needs to be improved in this scheme? The first one is about modeling, the second one is about core assumptions, the third one is about results, and the fourth and fifth ones are about model and result analysis.
Collection type
Typesetting mainly includes the following aspects: the overall structure of the paper (table of contents, title), formulas, charts and appendices.
In the process of referring to the overall structure of the grand prize paper, you may have some feelings, basically just a few big things. What I want to emphasize here is the contents and titles. American competition papers don't require a table of contents, but I want to tell you that it's best to make a table of contents, because the judges can see the structure of your papers very clearly through the table of contents, which saves them a lot of things. When the judges marked the papers many times, they became impatient. When they see a paper without a table of contents, they should feel uncomfortable because they have to browse your text without a table of contents, which may not be too cool. Besides, if all the papers in the judges' hands have catalogues, but not your own, they will definitely feel something is missing.
The title also deserves everyone's attention. Don't write too broad a topic, such as "model building" and "model solving". Be sure to give meaning to the topic, such as "analytic hierarchy process", so that the judges can know what you have done in this part after seeing the topic.
The size of the formula needs attention. When writing formulas in word, we often encounter a problem, that is, the line where the formula is located is relatively large from other lines. What should we do? The solution (taking word20 10 as an example) is to remove the check mark before "If the document grid is defined, align to the grid" in the paragraph.
In addition, be sure to pay attention to the number of the formula. The number of the formula is described in detail in the "Campus Tour Lecture of School of Mathematics and Science-Northwest University Station". Please participate in the video for details.
To make a chart, you can refer to the Mercer Prize papers and learn how other people's charts are made. Besides the form of the chart, you should also pay attention to the font and size of the characters in the chart. During the course of the lecture, some students asked how to make dynamic diagrams, such as Question B of the 20 14 National Competition. In this case, it is enough to paste four pictures selectively in the text, and there is no need to put many pictures in the text. Students who participate in numerical simulation for the first time often think that it would be more powerful to put more pictures or even codes in the appendix, but in fact it is just the opposite. As long as you can express the problem clearly, if you put the program, you must put it in the appendix (of course, the program can not be put in the appendix), and put the program in order so as not to be chaotic. What is in the appendix may not be important to everyone, but it is still important. The judges will not read the contents of your appendix, but there is a great chance to browse the appendix, because the appendix is at the back, and the things on the front and back of the paper are generally easy to see. Therefore, the contents in the appendix must be neat and tidy, which makes people feel neat and beautiful at first glance.