After studying for so many years, I think the most useful thing is math class. I believe there are many people who have the same idea as me.

. Think back: What lessons have you learned from beginning to end? I thought for a moment, only math, and of course English.

Especially in college, when I was studying signal processing and communication, I felt the importance of math class. Computer:

Data structure, programming algorithm ... it doesn't need mathematical knowledge and ideas. There is a saying called the human planning of the Department of Mathematics.

Computers are the best. Signals and systems: this transformation and that transformation. Communication: This code is encoded by another code. Digital map

Image and pattern recognition: this kind of probability theory and mathematical statistics are everywhere. Linear algebra and matrix theory often appear.

2. Mathematics learning methods:

The most important thing is not to be afraid of problems before you know how others deal with similar problems. Is it okay?

Draw lessons from, and then compare the similarities and differences between our problems and existing problems. What are the disadvantages of the existing methods? we should

Where to start thinking about new methods. Thinking about the route is more important than specific deduction. Mathematics is not more mysterious and advanced.

The real understanding lies in grasping the essence. "If you still find something difficult, complicated and difficult to remember, it means that you are still heavy."

Clinging to the details, not grasping the essence, grasping the essence, everything will be simple. "This is the father of probability, Kolmogorov.

Famous words. When we study mathematics at ordinary times, we always ask ourselves, can you explain this to a layman?

If not, it means that we haven't really understood it ourselves. The effort of mathematical deduction should be through a lot of after-school work.

What you get from practice is that you spend much more time after class than in class.

3. Introduction of Mathematical Software:

In today's more than 30 math applications (with modifiers added to distinguish them from word processing and drawing)

The original kernel of software mathematical processing can be divided into two categories. One is numerical calculation (digital operation)

) software, such as Matlab, Xmath, MLAB, etc. This kind of software has strong management, calculation and operation ability for a large number of data.

Strong visualization ability and high operation efficiency. The other is software for mathematical analysis, such as Mathemati.

Ca, Maple, Macsyma, etc. They are good at symbolic computation and can get analytic symbolic solutions and arbitrary precision solutions, but

When dealing with a large number of data, the operation efficiency is low. After years of international competition, MATLAB has occupied the numerical software.

The dominant position in the market is that XmathMaple, Mathematica and Macsyma are symbolic software.

The top three (see IEEE spectrum). Among the international popular science and technology application software, Mathcad has its own characteristics. should

Mathsoft, a software developer, has taken teaching and office as the market goal of Mathcad from the beginning. treat cordially

Developers of numerical calculation, symbolic analysis, word processing and graphics capabilities do not pursue professional standards, but try their best to collect them.

Various functions are integrated. MathWorks company conforms to the trend of multi-function demand, and its excellent numerical calculation and graphics ability.

Basic quotient, and take the lead in developing its symbolic calculation, word processing, visual modeling and simulation and real-time control at the professional level.

System ability, carefully create a new generation of science and technology application software MATLAB suitable for multi-disciplinary and multi-departmental needs.

Matlab is the most commonly used software for electronic students, and it is basically the only mathematical software used. Matlab 5.3

Version (latest version, version 6.0) is completely installed, including help and various toolboxes. * * * Actually need 1G hard disk space.

. Of course, the capacity of this G is not filled with all kinds of junk files. On the contrary, it is composed of countless Matlab departments.

The function file running on the system is occupied. This shows how comprehensive the functions of Matlab are. 1984, calculation

Mathematicians Steve Bangert, Steve Kreman, John Little and Cliff Moore were in the original FORTRAN program.

On the basis of order, a C language program for solving linear system calculation problems was developed, and they gave it a resounding name.

Matrix laboratory. Since then, the Matlab system has been out of control.

Software engineers, computational scientists, and scientific and technological workers in various application fields have all joined the ranks of Matlab developers.

. They use the programming language provided by Matlab system to compile the commonly used algorithms in their respective scientific research and application fields.

Thus, a feature of Matlab came into being: "toolbox". There are probably dozens in Matlab5.3.

Toolbox, including communication, signal system analysis, discrete signal analysis, optimization, partial differential equation, wavelet transform.

Exchange, map, finance, power system, neural network, numerical calculation and so on. Every function in the toolbox is based on.

This paper introduces the most advanced and efficient algorithm in this field, and countless such function text files constitute a giant Matlab, which is composed of

This shows that Matlab is extremely superior in solving engineering problems. It is the favorite of our electronic students. Last/better/previous/last name

This paper introduces one of the main functions of Matlab: toolbox. Let's talk about another feature of it, that is, it is similar to other languages.

Interface between language and compiler. This problem has always been the hottest topic about Matlab. The reason is simple, 1.

Matlab is such a comprehensive and efficient algorithm and function that it can only run on the platform provided by Matlab, which limits it.

This paper introduces the application scope of these programs, that is, if you want to apply these programs, you must first install one on your computer.

Matlab has hundreds of megabytes, which brings inconvenience to use. In addition, because Matlab adopts the way of line-by-line explanation.

To execute the code, so the running speed is slower than the binary file compiled into exe. Therefore, using the compiler, the M text is

Changing the file into a binary exe or dll file will greatly shorten the calculation time. Although Matlab is a perfect system,

However, after all, the industry has specially studied the visual programming environment of various languages (such as VC, C++Builder, Delphi and so on). ) for the user.

System functions such as interface design are faster and more efficient than Matlab. Therefore, how to integrate Matlab?

The powerful numerical calculation function is combined with the visual programming integrated environment IDE, which is convenient for users to operate and complete the calculation function.

Preparing and running fast applications has become the greatest wish of program developers. Matlab contains a lot of matrix operations.

Calculation, numerical operation function, graphic operation function, user graphical interface function, etc. With it, he can write like C language.

Function flow, develop the user program of WIN graphical interface. Matlab's powerful function and convenient operation have won it.

Won the title of the most popular mathematical software in the world. No wonder on the Internet, everyone rushed to tell each other, "You must learn Matlab before going abroad.

Good. "

4. Introduction of other mathematical software (although it is basically not used, it is also an eye-opener (except the first one)):

1.Matcom: Matcom is an M-file interpreter developed by MathTools (the programming language in Matlab).

explain

Interpreted as C language), not only can the M file be compiled into an executable exe or dll file, but it can also be automatically generated.

C source code of other high-level language compilers. Matcom is written directly in C language, which is similar to that of horses.

The function of tlab statement brings the following obvious advantages: First, the program compiled by Matcom can be used anywhere.

Why not install Matlab system and run it on the computer? Second, the running speed is several times faster than that of M-gear; The third is to realize the horse.

The perfect combination of tlab's powerful computing function and various C compiler interface designs. What I like best now is in vc.

It is convenient for users to operate on the interface, and the algorithm calculation is realized by Matcom library, which complements each other and is written in this way.

The program operation is convenient and simple, and the calculation graph is powerful and fast.

2.Mathmatica: The most fascinating thing is its perfect symbolic operation function. The so-called symbolic operation refers to it

be at home

Logical objects are not just common numbers (such as 12 or 3. 14), but some expressions with algebraic symbols. we

In algebra, I learned to use the operation rules of algebra to carry out identity transformation on an expression containing symbols, while a

A function is a rule or a map. For example, if we define the following rule, we can use this rule to translate the following formula.

Change. Mathematica has this function similar to human thinking, and it can constantly learn and remember various changes.

Rules, and apply these changes to all kinds of expressions, no matter how complicated the form is, I can always get it.

The result of algebraic symbols that scientists want. In C language or other programming languages, for a symbol, you must first

Declare, and then assign it to. So its meaning is limited, and Mathematica completely abandoned it.

This restriction, a symbol can represent any object, there is no type restriction, and the word "generation" in "algebra" is truly realized.

Mathematica, like a tireless formulator, can make complex functions complicated in one second.

Tens of thousands of times, it can find the simplest of all kinds of complex expressions. Freshman and sophomore mathematics

Students may be a gospel, for everyone in advanced mathematics, linear algebra often encountered limits, micro-expression.

Fractions, definite integrals, indefinite integrals, series, vector algebra and so on all have internal functions that can be directly calculated in Mathematica.

Result. Of course, I hope everyone can practice the basic skills of formula derivation by themselves and regard Mathematica as a

The inspection tool is understandable. In Mathematica4.0, system functions include calculus, linear algebra, probability,

The most commonly used branches of mathematics are geometry, graph theory, combinatorial mathematics, number theory mathematics and special functions.

3.MatheCAD 8.0, Maple 5: A famous symbolic arithmetic software, similar to Mathematica, with

Deposit management

Good management, SAS 6. 12 statistical professional software, compressed file 100 m (the most authoritative statistical software).

4. Others: SPSS 8.0 social science statistics software package; Lindo/Lingo 50 Linear and Nonlinear Programming Software

; A

Nsys 5.4 authoritative finite element calculation software, the installation file is about 200 ~ 300 m; Algo finite element method software

Packaging; Statistical software; Datafit numerical fitting professional software; Origin 6.0 Microsoft data

Analysis and drawing software, which can communicate with Excel database; Network parallel computing library; Isoft electromagnetic simulation software

Pieces; Automatic nonlinear dynamic system calculation software; Flexpde 2. 10 numerical software for solving partial differential equations; tellurium (Te)

Cplot 8.0 flow velocity and value line hydrodynamics; RATS numerical analysis software.

First, it is a mathematical modeling competition.

This is a mathematical modeling contest. It's called mathematics. Of course, it needs mathematical knowledge, but it's not the same as the previous number.

Learning competitions (pure math competitions) are different. It needs a computer, even without it, but it is not pure.

Computer competition, which involves physics, chemistry, biology, electronics, agriculture, management and other disciplines and knowledge fields,

But it is not a pure knowledge contest of these disciplines. It involves various disciplines and fields, but it is not influenced by any one.

Limitations of physical education disciplines and fields. It needs comprehensive knowledge in all aspects, but it is not limited to this. The contestants not only have to

Have all kinds of knowledge, but also have the ability to drive the field and apply these knowledge to deal with practical problems. Knowledge is nothing.

Endless, you must also have the ability to acquire new knowledge. In short, the mathematical modeling competition is to compete in all aspects.

Comprehensive knowledge is also the comprehensive ability of all aspects of the game. Its characteristic is synthesis, and its advantage is also synthesis. in this

In a sense, it is different from any knowledge contest in any subject field, which is characterized by impure and has its advantages.

That is impure, and comprehensive is impure. Pure mathematics competitions, such as the International Mathematical Olympiad for Middle School Students, or the United States.

Putnam Mathematics Competition for college students has a long history, and everyone is familiar with it. Especially in recent years, I

China athletes achieved good results in the middle-aged group of the International Mathematical Olympiad, which made the competition a household name in China.

Degree, widely carried out in the national high-quality middle schools. The pure mathematics competition mainly examines the basic knowledge of mathematics of the players.

Understanding of the situation, the ability and skills of logical reasoning and proof, whether the thinking is agile, the strength of calculation ability, etc. The test questions are

It is a pure math problem, and the examination method is a closed-book exam. Students will be alone for a specified time (usually three hours at a time)

Do exercises, don't talk to each other, don't read any books and reference materials, and don't use the computer. examination

All questions have standard answers. Of course, the player's solution method can be different from the standard answer, but its solution method is correct and

Nothing is also absolute, especially the number of calculation questions must be the same as the standard answer. Test results of each player

The answer gives a score, and the pros and cons are judged according to the score. Although you have to participate in the competition (representing a country or region)

Or school) to calculate the total score of the group, but the total score of the group is also obtained by adding the scores of the players in each group.

Players in the same group are not allowed to help each other in the competition. So this kind of competition is essentially a personal competition.

It doesn't help. So this kind of competition is essentially an individual competition rather than a team competition. The team's victory mainly depends on.

Each player's level is high or low, and there is no problem of mutual cooperation (of course, they can help each other in the training process).

This kind of competition is very important to attract young people to love mathematics, embark on the road of mathematical research and train mathematicians and mathematicians.

Learning specialized talents has played a great role.

With the development of society, mathematics is more and more widely used in all fields of society, and its role is getting bigger and bigger, not only for

Natural science is all fields and disciplines, and it permeates into economy, military affairs, management and even social science and social activities.

In all fields. However, the social demand for mathematics is not only good for people engaged in practical work in various departments.

Using mathematical knowledge and mathematical thinking to solve a large number of practical problems they face every day, and get economic benefits.

And social welfare. They don't look for practical problems in order to apply mathematical knowledge (just like doing mathematical application problems at school)

But in order to solve practical problems, we need to use mathematics. And it's not just math, it's probably something else.

Knowledge of disciplines and fields requires work experience and common sense. Especially in modern society, to truly solve a real

Almost all international problems are inseparable from computers. It can be said that the problems encountered in practical work are completely pure use.

There is almost no ready-made mathematical knowledge to solve the problem. All you can meet is math mixed with other things.

The problem together is not "clean" math, but "dirty" math. The mystery of mathematics is not there.

Waiting for you to solve it, but hiding in the depths waiting for you to find it. In other words, you have to analyze complex problems.

Find the relationship or law that can be described in mathematical language and turn this practical problem into a mathematical problem, which

It is called mathematical model, and the process of establishing mathematical model is called mathematical modeling. The word model means nothing to us.

No stranger, it can be said to be an imitation of something. For example, airplane models are made by imitating airplanes.

. Since it is imitation, it is not true. It can only be "imitation", not "fake". It must truly reflect imitation.

Property of an aspect of an object. If you just imitate the appearance of an airplane, such an airplane model only needs to look like an airplane.

Just put it in the exhibition hall for people to visit and take pictures, but you can't fly. If you want to imitate the flight principle of an airplane, you should

It is necessary to build a flying model plane, such as the works of model airplane competition, its flying principle and flying in the air.

Machines have something in common. But of course, it doesn't fly by burning fuel like an airplane, and it doesn't have to look like an airplane.

The model imitates only one aspect of the real thing. And the mathematical model, is to use mathematical language (possible

Including mathematical formulas, to describe and imitate the quantitative relationship and spatial form in practical problems. This imitation is of course approximate.

Yes, but as realistic as possible. There are many factors in practical problems that you can't and don't have when you build a mathematical model.

We need to consider everything, only the most important factors, and the secondary ones can be discarded.

The main factor is that mathematical tools and methods can be used to transform practical problems into mathematical problems after the mathematical model is established.

Come and answer. If only there were ready-made mathematical tools. If there are no ready-made mathematical tools, it will prompt mathematicians (also

Including those who build mathematical models, discover and develop new mathematical tools to solve them, which in turn promotes the development of mathematics itself.

Exhibition. For example, Kepler summed up Kepler's three theorems from the observation data of planetary motion (this is the mathematical model of planetary motion)

Type), Newton tried to explain it with his own mechanical theorem, but the mathematical tools at that time were not enough, which made

The invention of calculus. In addition to mathematical reasoning, we usually have to deal with a lot of data and carry out it.

A lot of calculations. This was difficult to achieve before the invention of electronic computers. Therefore, many mathematical models, although from mathematics.

Theoretically, it was solved, but due to the large amount of calculation, no useful results could be obtained, so it had to be shelved. And calculation

The appearance and rapid development of computers have opened up a broad road for solving practical problems with mathematical models. Now, tell the truth.

Without computers, it is almost impossible to solve practical problems. A mathematical model is established and mathematical methods are used.

Or the data method. Is everything all right? I can't. Because the mathematical model can only approximately reflect the reality.

Whether the relationship and legal response in international issues are good or not needs to be tested. If the mathematical model is not established

Well, if you don't describe the given practical problem correctly, the correct mathematical solution will be useless. Therefore, in

After the mathematical solution is worked out, the conclusion should be actually tested to see if it is reasonable and feasible. otherwise

In line with the reality, we should try to find out the reason, modify the original model, solve it again, and test it again until it is more reasonable and feasible.

To get an answer, you can put it into practice first, but there is no perfect answer, you have already got it.

There must be room for improvement in the answer, which can also be based on the actual situation, or continue to study and improve; Or pause for a while.

In autumn, wait until there are new situations and requirements, and then make progress.

The process of establishing mathematical models to solve problems mentioned above is very much needed in all walks of life and fields, and it is also mine.

What we students often do after work. Doing such a thing requires much more than mathematical knowledge.

The ability to understand and solve mathematical problems requires comprehensive abilities in many aspects. The demand of society for people with this ability is higher than that of others.

There is much more demand for math professionals. Therefore, efforts should be made to accompany and improve students' ability in this respect at school.

Ability. Of course, there are many forms to achieve this goal. For example, offering courses in mathematical models; Let students have more contact.

Practical work, exercise knowledge, etc.) to participate in the whole process of solving problems. These realities

International issues are not limited to one aspect, but can involve a very broad and uncertain scope. This will promote people's application.

Training of talents.

Second, the basis of mathematical model

1. Definition of mathematical model

At present, there is no uniform and accurate definition of mathematical model, because different angles can have different definitions.

. But we can give the following definition. Mathematical models are part of the real world and are made for special purposes.

Abstract and simplified structure of. ":Specifically, mathematical models use letters and numbers for a certain purpose.

Learning and others: equations or inequalities established by mathematical symbols, and charts, images, block diagrams, etc. to describe the characteristics of objective things.

The expression of mathematical structure of symbols and their internal relations.

2. Methods and steps of establishing mathematical model

First, model preparation (problem statement and analysis)

First of all, we should understand the actual background of the problem, clarify the purpose of modeling, collect all kinds of necessary information, and try our best to understand the characteristics of the object

Sign.

Second, model hypothesis and symbolic interpretation.

According to the characteristics of the object and the purpose of modeling, it is necessary and reasonable to simplify and assume the problem with accurate language.

, is a key step in modeling. If we consider all the factors of the problem, this is undoubtedly a brave but effective method.

Poor behavior: Therefore, excellent modelers can give full play to their imagination, insight and judgment, and are good at distinguishing priorities.

Moreover, in order to make the processing method simple, we should linearize and homogenize the problem as much as possible.

Thirdly, the establishment and solution of the model

Through the analysis of the problem and the hypothesis of the model, the mathematical model is established (the model is described by mathematical symbols and mathematical language)

, and through the design algorithm, the use of computer realization and other ways (determined according to the characteristics and requirements of the model) to solve the model! this

Technology is the most important part of integer: digital module technology, which needs to be treated with caution!

Fourth, the type of testing.

That is, the rationality and accuracy of the model can be judged by the data provided by the problem or relative to the real life situation.

Advantages and disadvantages of other models! Can be done by computer simulation and other means!

Fifth, the improvement and popularization of the model.

This step can be based on the specific situation when modeling!

The steps of modeling do not have to follow the above steps. Interested colleagues can refer to related books on modeling.

Third, the mathematical modeling reference:

1, Mathematical Model Basis Wang Shuhe University of Science and Technology Press 1996.

2. Mathematical model Tan Yongji, Yu Wen Fudan University Press 1997.

3. Mathematical Modeling Competition Course: Li Shangzhi Jiangsu Education Press 1996.

These books can be borrowed from the library or bought at Jiuzhang Bookstore. There are many other books, and there is enough time to go.

The information about the national mathematical modeling competition for college students can be found on the China Industrial and Applied Mathematics website.

Please visit the home page of CSIAM:/. Annual Mathematical Modeling Competition

Held in late September, registered in June every year, a team of three. Students who want to take part in the competition should study mathematics.

The department is auditing the course of mathematical model or taking the course of "mathematical model".

Jimmy Dovich's Mathematical Analysis Problem Set

This book is only suitable for super Daniel. The library has borrowed it, and Haidian Bookstore has sold it in Jiuzhang Mathematics Bookstore.

Typical problems and methods in mathematical analysis

Pei, Higher Education Press. This book is a classic holy book. Suitable for ordinary students. There are not many libraries, but nine.

This book is available in a bookstore.

Analysis and Selection of Test Questions in College Students' Mathematics Competition

The second edition, edited by Li Xincan, Higher Education Press. Everyone in the extracurricular group of the Association for Science and Technology wants a copy. Collect in it

Over the years, the real questions of Beijing college students' mathematics competitions are better, and they are interested in students above the medium level.

Justice. Chapter 9 is available in the Mathematics Bookstore.

The Solution and Guidance of Higher Mathematics Review

Chen Wendeng, two books, beijing institute of technology press: This book is very detailed and suitable for students at all levels.

It's very helpful. Hematemesis recommended! ! ! Chapter 9 is available in the bookstore.

Mathematics review guide

Science and engineering, Chen Wendeng is waiting. The high number content of this book is basically the same as that of the last book. But this book also includes linear algebra and probability theory.

And other parts, very comprehensive. The library has been borrowed. They are available in all major bookstores. Suitable for students of all levels.

Analysis and research on the process of solving problems in higher mathematics

Author Qian Changben. This book mainly introduces the thinking method of advanced mathematics. This example is very enlightening. The library has been borrowed. Jiuzhangshu

You can buy it in the store.

Starting from ordinary differential equations, mathematics has become a bottomless thing, and every topic is a matter of mathematical research.

A big chunk. How to say a basic course has been under discussion. Let's start talking about reference books, without any.

Doubts still have to start with our powerful northern neighbors.

Lecture notes on ordinary differential equations

Petrovsky held a very special position as the president of Moscow University in the history of mathematics in the 20th century.

. Academically, he has a very good job in the micro field. In the 1950s, when Gu Kailai went to the Soviet Union to study for a degree.

I also attended the seminar hosted by him. He has been engaged in administrative work since the late 1930s. Among his early students

There are many senior officials in the Soviet Union, so he used his relationship with these former students to build a model for the Soviet mathematics community.

Umbrella, his books have been standard textbooks for a long time.

ordinary differential equation

Pontryagin. With the encouragement and help of his mother, Academician Pontryagin 14 was blinded by a chemical experiment accident.

Next, he embarked on the road of mathematics with amazing perseverance, if nothing else, just look at the "continuous group" he left to future generations, "the most

The mathematical theory of good process ",you have to admire him, and the six bodies have also been thrown down. His book.

This textbook was translated by Mr. Li and them. This book has influenced many of our teachers' personalities.