We can also intuitively understand this concept: mathematical modeling is a process that makes pure mathematicians (mathematicians who only know mathematics but don't know its application in practice) become physicists, biologists, economists and even psychologists.
A mathematical model is generally a mathematical simplification of actual things. It often exists in an abstract form close to the real thing in a sense, but it is essentially different from the real thing. There are many ways to describe an actual phenomenon, such as recording, video recording, metaphor, rumors and so on. In order to make the description more scientific, logical, objective and repeatable, people use a language that is generally considered rigorous to describe various phenomena. This language is mathematics. What is described in mathematical language is called a mathematical model. Sometimes we need to do some experiments, but these experiments often use abstract mathematical models as substitutes for actual objects and carry out corresponding experiments. The experiment itself is also a theoretical substitute for the actual operation.
Mathematics is a science that studies quantitative relations and spatial forms in the real world. In the long history of its emergence and development, it has always been closely related to various application problems. The characteristics of mathematics lie not only in the abstraction of concepts, the rigor of logic, the clarity of conclusions and the integrity of systems, but also in the universality of applications. Since the 20th century, with the rapid development of science and technology and the increasing popularity of computers, people's requirements for various problems have become more and more accurate. It makes the application of mathematics more and more extensive and in-depth, especially in the era of knowledge economy that is about to enter the 2 1 century. The status of mathematical science will change greatly, and it is moving from the national or economic, scientific and technological reserves to the forefront. With the globalization of economic development, the rapid development of computers and the continuous expansion of mathematical theories and methods, mathematics has become an important part and think tank of contemporary high technology and a technology that can be universally implemented. It is necessary to cultivate students' consciousness and ability of applying mathematics.
When applying mathematics to solve various practical problems, it is a very crucial and difficult step to establish a mathematical model. The process of establishing teaching model is the process of simplifying and abstracting complex practical problems into reasonable mathematical structure. Through investigation and data collection, observe and study the internal characteristics and laws of the actual object, grasp the main contradictions of the problem, and establish the quantitative relationship that reflects the actual problem. Then use mathematical theories and methods to analyze and solve problems. This requires a deep and solid mathematical foundation, keen insight and imagination, strong interest in practical problems and extensive knowledge. Mathematical modeling is a bridge between mathematics and practical problems, a medium in which mathematics is widely used in various leading machinery, and a main way to transform mathematical science and technology. The important role of mathematical modeling in the development of science and technology has been paid more and more attention by mathematics and engineering circles. It has become one of the necessary abilities for modern scientific and technological workers. In order to meet the needs of scientific and technological development and cultivate high-quality and high-level scientific and technological talents, mathematical modeling has been gradually carried out in university education. More and more universities at home and abroad offer mathematical modeling courses and participate in open mathematical modeling competitions, and regard mathematical modeling teaching and competitions as an important aspect of teaching reform and training high-level scientific and technological talents in colleges and universities. At present, many colleges and universities are combining mathematical modeling with teaching reform, trying to explore more effective teaching methods of mathematical modeling and new ideas of talent training for 2 1 century. Compared with other mathematics courses in colleges and universities in China, mathematical modeling has the characteristics of great difficulty, wide coverage, flexible form and high requirements for teachers and students. Mathematical modeling teaching itself is a process of continuous exploration, innovation, perfection and improvement. In order to change the traditional teacher-centered, classroom-based and knowledge-imparting teaching mode, the guiding ideology of mathematical modeling course is: organizing teaching work based on laboratory, student-centered, problem-oriented, and aiming at cultivating ability. Through teaching, students can understand the whole process of analyzing and solving problems by using mathematical theories and methods, and improve their ability to analyze and solve problems. Improve their interest in learning mathematics and their awareness and ability to apply mathematics, so that they can often think of using mathematics to solve problems in their future work, improve their awareness of making full use of computer software and contemporary high-tech achievements, and organically combine mathematics with computers to solve practical problems. Mathematical modeling focuses on students, and teachers use some pre-designed questions to inspire students to actively consult literature and learn new knowledge. Encourage students to actively carry out discussions and debates, cultivate students' active exploration and enterprising style of study, cultivate students' initial ability to engage in scientific research, cultivate students' spirit of unity and cooperation, and form a lively environment and atmosphere. The focus of the teaching process is to create an environment, induce students' desire for learning, cultivate students' self-study ability, enhance students' mathematics quality and innovation ability, improve students' enumeration quality, and emphasize students' ability to acquire new knowledge. It is a process of solving problems, not knowledge and results. Most students who take part in the pre-competition training of mathematical modeling contest need to learn "short courses" (or lectures) such as mathematical statistics, optimization, graph theory, differential equations, calculation methods, neural networks, analytic hierarchy process, fuzzy mathematics and the use of mathematical software packages. Most of them are enlightening to talk about some basic concepts and methods, which are mainly learned by students themselves. Fully mobilize students' enthusiasm and give full play to their potential. Discussion classes are widely used in training, and students can report, discuss and debate by themselves. Teachers mainly play the role of asking questions, answering questions and counseling. The competition must use computers and corresponding software, such as Mathematica, MATLAB, Mapple and even typesetting software.