With the development of society, mathematics is used more and more widely in various fields of society, and its role is growing. It is not only used in various disciplines and fields of natural science, but also penetrates into economics, military, management to all fields of social sciences and social activities. However, society’s demand for mathematics is not only for mathematicians and talents specializing in mathematical research, but also for people engaged in practical work in various departments who are good at using mathematical knowledge and mathematical thinking methods to solve the problems they face every day. solve a large number of practical problems and achieve economic and social benefits. They are not looking for practical problems in order to apply mathematical knowledge (like doing math word problems in school), but they need to use mathematics in order to solve practical problems. And not only mathematics will be used, but also knowledge from other subjects and fields, as well as work experience and common sense will be used.
There are almost no problems encountered in actual work that can be solved purely using existing mathematical knowledge. The mathematical secrets are not out there waiting for you to solve, but hidden deep in the world waiting for you to discover. That is to say, you have to analyze complex practical problems, discover the relationships or rules that can be described in mathematical language, and turn this practical problem into a mathematical problem. This is called a mathematical model. This process of establishing a mathematical model It's called mathematical modeling.
Mathematical Model is to use mathematical language (may include mathematical formulas) to describe and imitate the quantitative relationships, spatial forms, etc. in actual problems. For the prototype in reality, for a specific purpose, make some necessary simplifications and assumptions, and use appropriate mathematical tools to obtain a mathematical structure.
Mathematical Modeling: Refining practical problems in the real world, abstracting them into mathematical models, finding solutions to the models, verifying the rationality of the models, and using the answers provided by the mathematical models To explain real-life problems, we call this application process of mathematical knowledge mathematical modeling. It can also be said that mathematical modeling is a model that uses mathematical language (symbols, formulas and images) to simulate reality. Abstracting and simplifying the real model into a certain mathematical structure is the basic feature of mathematical models. It can either explain the actual state of a specific phenomenon, predict the future condition of the object, or provide optimal decision-making or control for handling the object.
Now that the mathematical model has been established and the solution has been obtained using mathematical or numerical methods, is everything going to be fine? no. Since a mathematical model can only approximately reflect the relationships and laws in actual problems, whether it reflects it well or not needs to be tested. If the mathematical model is not well established and does not correctly describe the actual problem given, no matter how correct the mathematical solution is, Useless. Therefore, after the mathematical solution is obtained, the conclusion must be subjected to actual testing to see whether it is reasonable, feasible, etc. If it is not realistic, we should try to find out the reason, modify the original model, and re-solve and test it until it is more reasonable and feasible.
Every item in middle school mathematics is a mathematical model. It mainly includes concepts such as functions, equations, inequalities, sequences, triangles, quadratic curves, polyhedrons, solids of revolution, sets, permutations and combinations. The content of mathematical modeling in middle schools is quite rich, covering issues such as interest, growth rate, environmental protection, planning, economic charts, market forecasts, supply and demand and storage, as well as subjects such as physics, chemistry, biology, geography, medicine, population, and life sciences. aspects of the problem.
An excellent paper must first capture "good" problems and choose meaningful problems suitable for your own solution. The topic selection is very creative. We do things we have never done before, and even solve problems that have not been solved by our predecessors. This is the basis for our success.
Topic selection can be done from different directions and angles.
Such as
Social life issues: the design of traffic lights at traffic intersections, product packaging, bicycle speed changes,...
School life issues: the design of blackboards, classroom lighting layout, bicycle swings Put,...
Family life issues: house purchase loan issues, moving issues, how to save gas, water and electricity, etc....
Others, such as diabetes testing, transformer testing Design, how the placement of goods in the store attracts customers, pricing of goods to cater to customers' psychology, how the growth of plants is affected by light, from jigsaw puzzles to the Human Genome Project,...
What we proposed The problem is not like the problems in previous books. The known conditions and required data are all available. This requires us to obtain evidence data through information review, social surveys, experiments and practice. We may spend days or weeks observing the traffic flow conditions at a certain intersection; going to a certain store to investigate the purchasing power and shopping psychology of customers; going to different shopping malls to investigate the relationship between the pricing and packaging of a certain brand of goods. ;We can also personally plant plants under different experimental conditions and record the impact of light on plant growth rate;…. During this time, we need to observe carefully, measure and record carefully, and also organize and analyze data or experimental results, establish hypotheses, use mathematical language to describe the development rules of things, and then conduct scientific inferences and verifications to arrive at solutions or solutions that fit the situation. Build reasonable solutions.
This process is a process of testing and exercising our patience, perseverance to overcome difficulties (we may experience multiple failures), and careful thinking about problems. It also cultivates our spirit of mutual cooperation. Learn to get along with others, learn to cooperate, learn to express and communicate. While we understand society, we also better understand and enrich ourselves.