First of all, the commonly used mathematical model is optimization model (mainly statistical regression, including data processing, fitting, difference and so on. ), differential equation model (mostly ordinary differential, less partial differential), difference equation model (that is, discrete model, can not take derivative differential) and so on. ), probability theory model, and some messy graph theory (what I said above are all very basic models, and almost all complex models are based on simple models. There are three main steps in mathematical modeling, 1. Turn practical problems into mathematical problems (this is usually the work two days before the competition); 2. Solve mathematical problems with mathematical knowledge and computer knowledge (mainly MATLAB); 3. Finishing and perfecting, thesis writing I think the most important step in mathematical modeling is to turn practical problems into mathematical problems, because the latter two steps are often not difficult. The point is 1. You should be flexible, think boldly and consider factors comprehensively. However, you can't model immediately after you come up with a model, because you have to consider many issues, such as feasibility (mainly practical issues, such as cooperation mode, where everyone's interests are greater than or equal to everyone's non-cooperation interests). For example, whether the established mathematical model is easy to solve (for example, if you set up a set of ordinary differential equations, this problem seems to have never been solved by mathematicians in general, then you can imagine whether you and the computer can solve it. At this time, you should consider cleverly transforming or simplifying the problem. The second point is to find the intermediate and core problems in practical problems, and then expand through this or these cores (preferably not too many cores). For example, the core problem of rocket three-stage boost is to explore the law of rocket mass change. Then, after studying the core issues, think about the real problems. For example, it is still a problem of rocket boosting. Is it necessary to use infinite boosters after discovering the rule that more boosters are better? Obviously not, this is a follow-up optimization problem. You can find a class to listen to or borrow a book to read. (I mainly recommend Jiang Qiyuan's Mathematical Modeling), and then try to model it yourself, taking your time. Then learn some knowledge, of course, mathematics is essential (mainly you have to learn operations research, optimization and so on. If you want to stand out from the rest in styling), and you have to form a team early and do a good job of division of labor. Papers are generally nothing, mainly to express their ideas clearly and concisely, combined with graphics, tables and so on. Then the language should be rigorous, accurate and vivid. Of course, the math competition in the United States requires you to have a relatively high level of English. You can study some excellent papers, which will be of great help to you. I hope I can help you ~