What exactly is mathematical modeling? What is mathematical modeling for?

This cat has participated in the national competition and the American competition. You don't know what you've learned until you've experienced it.

The first is thinking and insight. Use mathematical thinking to solve problems that you wouldn't even dare to think of, and when you do, you'll be amazed.

Then there is the ability, mathematical modeling is mainly done to use computers to solve problems. You can learn MATLAB

mathematics, and other mathematical software. (Mainly matlab, after all, it is so powerful that you can do anything except have children). There are also various algorithms, particle swarm algorithms, BT neural network algorithms, Bayesian algorithms, and so on.

Contemporary popular artificial intelligence, the core of artificial intelligence is mathematical algorithms.

Finally, there is the experience, no matter what kind of work you do after many years, maybe you have no connection with mathematics anymore, but when you look back and find that the most recent time mathematics and you were not in the classroom, but in the time when you were younger, you participated in mathematical modeling and struggled with your brain, and that is enough.

Mathematical modeling is the process of describing actual phenomena in mathematical language. The actual phenomena here include both concrete natural phenomena, such as the phenomenon of free fall, and abstract phenomena, such as the value tendency of customers to a certain commodity. The description here includes not only the description of the external form and the internal mechanism, but also the content of **, experimenting and explaining the actual phenomenon.

We can also intuitively understand this concept in this way: mathematical modeling is a process that turns pure mathematicians (mathematicians who only understand mathematics but do not understand the application of mathematics in practice) into physicists, biologists, economists, and even psychologists.

Mathematical modeling is to build a mathematical model based on a practical problem, solve the mathematical model, and then solve the practical problem according to the results. Mathematical model is a kind of simulation, which is an abstract and concise description of the essential attributes of a practical topic by using mathematical symbols, mathematical formulas, subroutines, graphics, etc.

Features of mathematical modelingConstruction of creative and empirical models: given an implementation scenario, learning to identify problems, making hypotheses and collecting data, proposing models, testing hypotheses, refining the model if necessary, seeing if the model and data are consistent when appropriate, and analyzing the basic mathematical structure of the model to evaluate the sensitivity to conclusions when the assumptions are not fully satisfied.

Model AnalysisGiven a model, learn to analyze reverse reasoning to reveal fundamental assumptions that are not necessarily explicitly represented, critically assess the degree to which these assumptions fit into the scenario at hand, and estimate the sensitivity to conclusions if the assumptions are not fully and accurately satisfied.

Mathematical modeling is to establish a mathematical model according to the actual problem, solve the mathematical model, and then solve the practical problem according to the results. When it is necessary to analyze and study a practical problem from a quantitative point of view, people should use mathematical symbols and language to establish a mathematical model on the basis of in-depth investigation and research, understanding the object information, making simplified hypotheses, and analyzing the internal laws.

Understand the actual background of the problem, clarify its practical significance, and grasp various information about the object. Mathematical ideas are used to contain the essence of the problem, and mathematical ideas run through the whole process of the problem, and then the problem is described in mathematical language. It is required to conform to mathematical theories, conform to mathematical habits, and be clear and accurate.

Based on the characteristics of the actual object and the modeling and dispersion purposes, the problem is simplified as necessary, and some appropriate assumptions are made in precise language.

On the basis of assumptions, appropriate mathematical tools are used to delineate the mathematical relationships between the constants of each variable and establish the corresponding mathematical structures (try to use simple mathematical tools as much as possible). Using the data obtained, Qingfian calculates (or approximates the calculation) of all parameters of the model.

The idea of the model to be established is elaborated, and the results obtained are mathematically analyzed. The accuracy, reasonableness, and applicability of the model are verified by comparing the results of the model analysis with the actual situation. If the model is in good agreement with reality, the actual meaning of the calculation results should be given and explained.

If the model does not match well with reality, you should revise your assumptions and repeat the modeling process again.

Mathematical modeling refers to the process of abstracting practical problems into mathematical problems and solving them through mathematical analysis, calculation, and simulation. In the study of mathematical modeling, the following knowledge is required:

1.Advanced Mathematics: Calculus, Linear Algebra, Probability Theory and Mathematical Statistics, etc.

2.Operations Research and Optimization Theory: Conventional Optimization Methods, Nonlinear Programming, Integer Programming, Dynamic Programming, etc.

3.Computer Science: Computer Programming Languages, Algorithm Design and Analysis, Semi-structured and Unstructured Data Mining, etc.

4.Statistical analysis, regression analysis, polynomial coefficient regression, time series**, factor analysis, etc.

6.Thinking logic: It is the key to the success of mathematical modeling, learning how to formulate hypotheses reasonably, find solutions, test and validate models, etc.

Through the above learning and practice, mathematical modelers can master the basic mathematical modeling methods and be able to analyze and solve complex practical problems. <>

Advanced mathematics, linear algebra, C language, fuzzy mathematics (partial), and learn to talk about the use of software such as Sakura MATLAB and Lingo in the modeling process.

Concept: Mathematical modeling is to establish a mathematical model according to the actual problem of Xian Shishou, solve the mathematical model, and then solve the practical problem according to the results. When it is necessary to analyze and study a practical problem from a quantitative point of view, people should use mathematical symbols and language to establish a mathematical model on the basis of in-depth investigation and research, understanding the information of the number of brothers, making simplified assumptions, and analyzing the internal laws.

Application: Mathematics is the study of real-world quantitative relations and spatial forms, and has been closely related to a variety of applied problems throughout its long history. The characteristics of mathematics lie not only in the abstraction of concepts, the rigor of logic, the clarity of conclusions and the integrity of the system, but also in the wide range 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 precise, making the application of mathematics more and more extensive and deep, especially in the 21st century, the era of knowledge economy, the status of mathematical science will undergo great changes, and it is moving from the reserve of the national economy and science and technology 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 mathematics has become a technology that can be widely implemented. Cultivating students' awareness and ability to apply mathematics has become an important aspect of mathematics teaching.