Wendengmu hotel

Personally, if you can use the information of a former master, then his summary and induction in the book will be helpful to you.

Very helpful); First of all, let's talk about reviewing exam books. At present, there are two popular versions in the market: A Guide to Mathematics Review edited by Wendeng Chen and A Book of Mathematics Review edited by Fan Peihua, Yuan Yintang and Li Yongle. It should be said that these two books have their own merits, but in recent years, especially since the 2003 exam, the complete works have played a stronger role in counseling the exam. This book pays more attention to the foundation and the improvement of ability on this basis, which is very consistent with the questions of the postgraduate entrance examination. Because the problems of postgraduate entrance examination are basically the deformation of basic questions, the master is that he can turn a complex mathematical problem into two or three simple problems, which is the value of books. Wendeng Chen's book emphasizes skills too much, so it is not easy to improve everyone's ability;

If we must choose numbers, it is generally accepted that Chen's probability is the weak link, but Chen's linear algebra is not.

Chang Hao (but some people call him "the king of the line"), some people think that Chen's advanced mathematics is the essence, but I just think this is a cliche.

Chen's failure, in advanced mathematics, he used too many unrealistic skills, and the high number part exceeded the standard and concentrated.

In the comparison and proof of definite integral, double integral and its application, series, and teacher Chen's proof column, it is simply too

Focus on skills, you'd better look at these parts and compare them carefully with the exam outline;

The key point is that Mr. Chen has not participated in the postgraduate entrance examination proposition and is too famous (mainly for the first time)

Li Er, a math tutor, is a few years behind him, and he is still a little level.

Six full marks came from Wendeng School, and his propaganda angered the proposition group everywhere, which led to the problem in 2003.

Deliberately opposed), became the target of the proposition group;

2. If the evaluation of reference books is still controversial, it is generally acknowledged that Yuan Yintang and Li Yongle are the best editors of simulation questions.

"400 Classic Simulation Questions" (published by National School of Administration Press), these 20 sets of simulation questions basically summarize the latest.

The prediction of the test questions of the year is also more accurate. It is recommended that all students with middle and upper grades buy one. no

The disadvantage of reading this book is that it is sometimes too difficult and it is easy to undermine everyone's confidence (my grades are basically concentrated in 105-

-120), so personal advice is best to do it early, find your weak links in time, and review in a targeted manner.

; Another good mock exam was last year's Bourne mock exam (edited by Fan Peihua). The characteristics of this group of questions are

The difficulty of the test questions in 2008 is basically close, which can be used as a tool to test your true level; In addition, it is also famous for Chen Wen.

The simulated test questions edited by Deng, but the personal feeling is average and the questions seem to continue the habit of teacher Chen Chaogang, so I won't share them with you.

Recommend;

3. The final sprint book: Generally speaking, every year at the end of 1 1, all famous writers have to publish a final sprint book, which is personal.

I don't think I can buy it, because mathematics focuses on the foundation, and it is basically impossible to get it by surprise; If you must buy it.

Personally, I suggest using Wendeng Chen's formula 21 of mathematical thinking. In fact, I personally think that this book has verified Chen.

Wendeng's mathematical attainments are really not high. He tried to solve all the math problems by thinking mode (on the first page of this book).

There is an advertisement: "the key to solving any problem"), which completely reverses the essence of mathematics. This book was used in 2003.

Books are really useless in the exam (although the math problems in 2003 are not difficult, the focus is on strangeness, especially the probability problems, which are actually all

It is the basic concept of examination, but the examination method is really strange, like the first high probability problem of Math 3 and Math 4, finding the distribution of Y.

Function, although simple, contains a profound theorem in number theory: "the distribution function of all random variables."

The distribution functions all obey the uniform distribution of 0- 1. "If you don't understand what I'm talking about, your probability base is really a bit.

However, personally, I think this book is still useful for dealing with general routine problems, and in 2003,

After the year was destroyed by the proposition group, it is estimated that it will no longer attract the attention of the subject; The other is Chong, edited by Li Yongle.

Sting 135 points, you don't have to read books!

In addition, if the master wants to get high marks, he needs to read the following books:

1: Mathematical Examination Analysis (Higher Education Edition), including the original questions in the past three years, the average score and variance of each question.

, as well as the ideas of the questioner and the common mistakes in the marking process, as well as the comments of the questioner on the test questions;

2. Case Analysis of Mathematics Test Questions in National Postgraduate Entrance Examination and National Postgraduate Entrance Examination.

An analysis of the examples of compiling mathematics test papers (second edition) (higher education edition), it is said that the previous book (published in 2000) included 20.

0 1, 2002, 2003, all probability questions, its guiding role for everyone is beyond doubt, these two books are on the market.

If we can't see it at all, we will try our best to get it (the book is very thin and the price is only 8.5 yuan);

3. Reference Book for the 2003 Postgraduate Entrance Examination (both Math III and Math IV are applicable), which was the first book in 2002.

For the second time, it should be said that the content system is not perfect and there are some mistakes. But this book is for the examination center to get extra money.

It was written by an expert who quickly edited the exam outline, so it has a certain guiding role. And in order to open the fame, 20

Part of the original questions were used in the 2003 exam (it is said that there are two big questions in Mathematics IV). If you want to get high marks, you must be right.

I have a deep grasp of the above questions (personally, I suggest reading books instead of reading the knowledge system, but for example 1.

Be sure to study it carefully), and at the same time, read the problem-solving ideas and specific methods and steps carefully, which is the most important.

Orthodox!

Second, review methods

As a basic subject, mathematics attaches great importance to the foundation. In fact, the problems of postgraduate entrance examination are basically the deformation of basic questions.

As mentioned earlier, the ability of a master lies in turning a difficult problem into several simple basic problems, so everyone should master it.

Certain skills, but focus on the foundation, from so many years of postgraduate entrance examination questions, even if you can't use skills, be honest.

Although it may take time to use the basic method, it can certainly be done. Here I combine the postgraduate mathematics.

Several components to talk about specific review methods.

It should be said that the simplest part of postgraduate mathematics is linear algebra, and the difficulty of this part lies in many concepts.

And interrelated (we must be clear about the concepts of relevance, similarity, contract, equivalence, etc.), but line generation runs through.

The main line is to find the solution of the equation, as long as the concept and general method of the solution of the equation are thoroughly understood, and then look back.

The surface content is simple. At the same time, judging from the examination content, the examination content is basically the same, which can be said to be the most dead part.

In fact, the exam questions issued in recent years are all copies of previous exam questions. Let's take a closer look at the previous questions.

The most beneficial. In the 150 scale, linear algebra accounts for about 38 points. Personally, I think as long as the foundation is slightly better.

34 points is not a problem;

The other part is probability statistics, which should be said to be more complicated, because advanced mathematics can be combined with line.

The contents of sex algebra are all tested together, especially finding the distribution function is to a large extent a double integral, and it is almost the same.

The rate is closely related to daily life, which invisibly increases the difficulty of postgraduate entrance examination; But personally, I think this part

The key is to study methods and concepts carefully. For example, in 2003, the two major problems of postgraduate entrance examination were to find the probability density through distribution function.

Degree is actually the concept of distribution function. You'd better find a good textbook to review, such as Cai Daming Allianz.

It is better to teach textbooks than to use the textbooks recommended by the Ministry of Education compiled by Yuan Yintang of the National People's Congress. Another part of statistics should be said to be public.

There are many formulas, but it is actually the simplest part. The key is to understand three distribution types: X2, t and f.

After understanding, the statistical part is actually to send sub-questions. Personally, I think that a big statistical problem in the third grade of mathematics will be big.

Drums should be played at home to celebrate.

The most difficult part of the math postgraduate entrance examination is the high number, which may be partly because everyone learns this in freshman year.

I don't think I will study too hard. In fact, it is hard to say that the advanced mathematics part (Mathematics I) is difficult in mathematics of science and engineering.

The difficulty of linear algebra is almost the same as the number three and the number four, and its probability and statistics part is definitely simpler than the number three and the number four.

If you get this part, you must grasp the basic questions and try to lose as few points as possible. I made three big mistakes in the exam, all of which were calculation errors.

It should be said that it is a pity. Personally, I think we should seriously grasp the following issues. These problems are relative.

Simple questions, don't lose points.

First of all, the third question of the postgraduate entrance examination generally examines the continuity of functions, and these 8 points are simply points (unfortunately, I was wrong); sequence

The four questions are generally for investigation and guidance, and this is also a sub-question; The fifth question is generally to investigate the definite integral, which is a bit difficult, but it is also better than

Simple; There is still a series problem left, in fact, the series part is the simplest in higher mathematics (provided that

Learn to understand), which is equivalent to distributing points; Then there is the differential problem. The differential part is actually a bit difficult, but on the whole, as long as

Memorizing several types is also a relatively simple part (generally speaking, the types of exams are relatively simple, and sometimes you can read one.

You will know the special solution if you guess); Then there is a question of proof. Judging from the situation in recent years, it is basically an investigation.

Rolle theorem and mean value theorem, but in 2002 and 2003, the mean value theorem was added, which is actually relatively simple.

Generally speaking, you can basically solve the problem by using these three theorems first. If not, then this proof is established.

It must be a bit difficult; Generally speaking, the last question is either an application question. It should be said that there are only a few kinds, which are difficult but not counted.

It is extremely difficult to calculate, but the average number of application problems in Math 4 in 2003 is a bit out of class. If it is not an application problem, then

Most of them are comprehensive questions that integrate several parts of higher mathematics. This kind of problem is more difficult, and everyone should work hard.

If you can't do it, you have to write a few more steps, and sometimes you will give one or two points of hard work!

, recommended bibliography

The following is just a part of the guidance book for postgraduate review that I have always thought is good, and there are many good new books that I don't know. I should learn more from those who have just passed the exam.

(1), mathematics

When reviewing for the first time, you can use Zhejiang University's own advanced mathematics (calculus) textbook. For other students who don't use the textbook of Zhejiang University or Advanced Mathematics compiled by Tongji University (the first and second volumes of higher education edition), you should use this Advanced Mathematics compiled by Tongji University (it should be noted that this book of Tongji University is written for science and engineering majors, and many contents are for those who study economic management, so they don't need to read everything), so you should support it. Advanced Mathematics Tutoring edited by Zhang Yuande (Volume I), ***3 1.5 yuan, Tsinghua University Publishing House. This book is especially useful for those students with poor foundation in advanced mathematics.

The textbook of linear algebra can be Zhejiang University. If you find it difficult to understand, you can also read Linear Algebra published by Tsinghua University Publishing House (edited by Yu Ma and others, 15 yuan). It is said that people who take the postgraduate entrance examination unanimously recommend the book Linear Algebra. The supporting counseling book can be "Guidance on Linear Algebra" (second edition) edited by Hu Jinde Wang, 15 yuan, Tsinghua University Publishing House, which is excellent!

Tsinghua undergraduates have also published a tutorial book on advanced mathematics, Calculus Learning Guide edited by Han, Wang Yanlai and Wu Jiehua. The price is 18 yuan, which should be very good, relatively thin and easy to read (I have never used it, but it is widely used in Tsinghua, so it should be good).

The classic textbook of Probability Theory and Mathematical Statistics should be the one compiled by Zhu Sheng of Zhejiang University (Higher Education Edition), and many people use this textbook to prepare for the postgraduate entrance examination. I use this book for class and review. I did all the exercises at the back of the book in the first review, and I thought those topics were not bad.

In the second comment, most people recommended Chen Wendeng's tutorial books and supporting exercises.

Seeing a person recommending the mathematics in the "Golden Edition" postgraduate entrance examination series published by Academy Press (divided into three books: advanced mathematics, linear algebra and mathematical statistics of probability theory), he said it was very helpful to him.

Tsinghua University Publishing House and springer Publishing House jointly published Tsinghua University Teaching Reference Book and Postgraduate Entrance Examination Teaching Book, and Yu, Wang, Alfred and Zhao Hengxiu edited College Mathematics: Concept. Methods and Skills (Volume I Calculus, Volume II Linear Algebra and Probability Theory), Volume I 29 yuan and Volume II 24 yuan can be purchased separately.

Outline of Mathematics Band 4 Examination

[examination subjects]

Calculus, linear algebra, probability theory

calculus

I. Function, Limit and Continuity

Examination content

The concept of function and its expression: boundedness, monotonicity, periodicity and parity of function, inverse function, composite function, implicit function and piecewise function, properties of basic elementary function, concepts of left limit and right limit of graphic elementary function, concepts of infinitesimal and infinity and their relationship, basic properties of infinitesimal and comparison limit of order, four operations, two important limit functions, and properties of continuous function on continuous closed interval of elementary function.

Examination requirements

1. Understand the concept of function and master the representation of function.

2. Understand the boundedness, monotonicity, periodicity and parity of functions.

3. Understand the concepts of compound function, inverse function, implicit function and piecewise function.

4. Grasp the nature and graphics of basic elementary functions and understand the concept of elementary functions.

5. The functional relationship in simple application problems will be established.

6. Understand the concepts of sequence limit and function limit (including left and right limits).

The concept and basic properties of ternary infinitesimal are introduced. This paper introduces the comparison method of mastering infinitesimal order, and understands the concept of infinity and its relationship with infinitesimal.

8. Understand the nature of limit and two criteria for the existence of limit (monotone bounded sequence has limit and pinch theorem), and master four algorithms of limit, and two important limits will be applied.

9. Understand the concept of function continuity (including left continuity and right continuity).

10. Understand the properties of continuous functions and the continuity of elementary functions. Understand the properties of closed interval continuous function (boundedness, maximum theorem, minimum theorem, intermediate value theorem) and its simple application.

Second, the differential calculus of unary function

Examination content

The relationship between derivability and continuity of derivative concept function; Four operations of derivative of basic elementary function: the concept and operation rule of derivative differentiation of higher derivative of inverse function and implicit function; Rolle theorem and Lagrange mean value theorem and their applications: hospital rules; The concavity and convexity of extremum function graph of monotone function: inflection point and maximum and minimum value of asymptote function graph.

Examination requirements

1. Understand the concept of derivative and the relationship between derivability and continuity, and understand the geometric and economic significance of derivative (including the concepts of margin and elasticity)?

2. Master the derivation formula of basic elementary function, the four operation rules of derivative and the derivation rules of complex variable function; Master the derivation methods of inverse function and implicit function, and understand logarithmic derivative.

3. If you understand the concept of higher derivative, you will find the second derivative and n derivative of simpler function.

4. Understand the concept of differential, the relationship between derivative and differential, and the invariance of first-order differential test; Master differential method.

5. Understand the conditions and conclusions of Rolle theorem and Lagrange mean value theorem, and master the simple application of these two theorems.

6. Will use the Lobida rule to find the limit.

7. Master the discriminant method and simple application of monotonicity of function, and master the solution of extreme value, maximum value and minimum value (including solving simple application problems).

8. Master the judgment method of curve convexity and inflection point and the solution method of curve asymptote.

9. Master the basic steps and methods of drawing functions, and be able to draw some simple functions.

3. Integral calculus of unary function

Examination content

The concept of original function and indefinite integral, the basic properties of indefinite integral, the concept and basic properties of basic integral formula, the substitution integral method of indefinite integral and the legal integral mean value theorem of partial integral, the Newton-Debeney formula defined by variable upper limit integral and its derivative, the concept of substitution integral method, the integral of partial generalized integral and the application of calculating definite integral.

Examination requirements

1. Understand the concepts of original function and indefinite integral, and master the basic properties and basic integral formula of indefinite integral; Master the substitution integral method and partial integral method for calculating indefinite integral.

Law.

2. Understand the concept and basic properties of definite integral; Master Newton-Leibniz formula, substitution integral method and integration by parts of definite integral; Will find the derivative of the upper limit integral of the variable.

3. I will use definite integral to calculate the area of plane figure and the volume of rotator, and I will use definite integral to solve some simple economic application problems.

4. Understand the concept of convergence and divergence of generalized integral, master the basic method of calculating generalized integral, and understand the conditions of convergence and divergence of generalized integral.

Four, multivariate function calculus

Examination content

Concept of multivariate function, geometric meaning of bivariate function, limit and continuity of bivariate function, properties of bivariate continuous function in bounded closed region (maximum theorem and minimum theorem), concept and calculation of derivative of multivariate composite function, derivative of implicit function, extreme value and conditional extreme value, maximum value and minimum value of high-order partial derivative fully differential multivariate function. The concept, basic properties and calculation of simple double integral on unbounded domain

Examination requirements

1. Understand the concept of multivariate function, and understand the representation and geometric meaning of binary function.

2. Understand the intuitive meaning of limit and continuity of binary function.

3. Understand the concepts of partial derivative and total differential of multivariate function, and master the solution of partial derivative and total differential of composite function; You can use the derivative rule of implicit function.

4? Understand the concepts of multivariate function extreme value and conditional extreme value, master the necessary conditions for the existence of multivariate function extreme value, and understand the sufficient conditions for the existence of binary function extreme value, and you will find the extreme value of binary function. Lagrange multiplier method will be used to find conditional extremum. Can find the maximum and maximum j, value of simple multivariate function, and can solve some simple application problems.

5. Understand the concept and basic properties of double integral, and be able to calculate simple double integral (including calculation in polar coordinates); Simple double integrals on unbounded domains can be calculated.

linear algebra

I. Determinants

Examination content

The concept and basic properties of determinant Using the determinant expansion theorem of row (column) Clem rule

Examination requirements

1. Understand the concept of determinant of order n..

2. Mastering the properties of determinant will apply the properties of determinant and the expansion theorem of determinant line by line (column) to calculate determinant.

3. Will use Cramer's rule to solve linear equations.

Second, the matrix

Examination content

The concepts of matrix identity matrix, diagonal matrix, quantized matrix, triangular matrix and symmetric matrix, the concepts and properties of transposed inverse matrix and matrix adjoint matrix of matrix product, the elementary transformation of block matrix of elementary matrix and the rank of its operation matrix.

Examination requirements

1. Understand the concept of matrix, and understand the definitions and properties of several special matrices.

2. Master the addition, multiplication and multiplication of matrices and their algorithms; Master the properties of matrix transposition; Master the properties of determinant of square matrix product.

3. Understand the concept of inverse matrix and master the properties of inverse matrix. Will use the adjoint matrix to find the inverse of the matrix.

4. Understand the elementary transformation of matrix and the concept of elementary matrix; In order to understand the concept of rank of matrix, we will use elementary transformation to find the inverse sum rank of matrix.

5. Understand the concept of block matrix and master the algorithm of block matrix.

Third, the vector

Examination content

The concept and properties of the concept vector of vector and the linear combination of the product vector of vector and the linear representation vector group are linearly related and linearly independent, and the rank of the largest linearly independent vector group of the normal vector group.

Examination requirements

1. Understand the concept of vector. Master the operations of vector addition and number multiplication.

2. People's understanding of the concepts of linear combination and linear representation of vectors, linear correlation of vector groups and linear element correlation. And master the correlation properties and discrimination methods of linear correlation and linear independence of vector groups.

3. Understand the concept of maximal unrelated group of vector group and master the solution of maximal childless group of vector group.

4. Understand the concept of the rank of vector group, understand the relationship between the rank of matrix and the rank of its row (column) vector group, and find the rank of vector group.

Fourth, linear equations.

Examination content

The solution of linear equations and the determination of the solution and special solution of linear equations; the basic solution system of homogeneous linear equations and the relationship between the solution of nonhomogeneous linear equations and the solution of corresponding homogeneous linear equations (derivative group) General solution of nonhomogeneous linear equations

Examination requirements

1. Understand the concept of solutions of linear equations, and master the judgment method of solutions and non-solutions of linear equations.

2. Understand the concept of basic solution system of homogeneous linear equations, and master the solution and general solution of basic solution system of homogeneous linear equations.

3. Master the solution of the general solution of non-homogeneous linear equations, and express the general solution of non-homogeneous linear equations with its special solution and the basic solution system of the corresponding derivative group.

Eigenvalues and eigenvectors of verb (abbreviation of verb) matrix

Examination content

Eigenvalues and eigenvectors of matrices Similar diagonal matrices Eigenvalues and eigenvectors of real symmetric matrices

Examination requirements

1. Understand the concepts of matrix eigenvalues and eigenvectors and master the properties of matrix eigenvalues. Master the method of finding eigenvalues and eigenvectors of matrices.

2. Understand the concept of matrix similarity and master the properties of similar matrices; Understand the necessary and sufficient conditions of matrix diagonalization and master the method of transforming matrix into similar diagonal matrix.

3. Understand the properties of eigenvalues and eigenvectors of real symmetric matrices.

probability theory

I. Random events and probabilities

Examination content

The relationship between random events and sample space events; Operation of events and their attributes; Independence of events; Definition of complete event group probability; Basic properties of probability; Classical probability; Conditional probability; Addition formula; Multiplication formula; Total probability formula; And Bayesian formula; Independent repeat test.

Examination requirements

1. Understand the concept of sample space, understand the concept of random events, and master the relationship and operation between events.

2. Understand the concepts of probability and conditional rate, master the basic properties of probability and calculate classical probability; Master the addition and residue formulas of probability, as well as the total probability formula and Bayesian formula.

3. Understand the concept of event independence and master the probability calculation with event independence; Understand the concept of independent repeated test and master the calculation method of related event probability.

Second, random variables and their probability distribution

Examination content

The concept and properties of distribution function and its probability distribution of random variables; probability distribution of discrete random variables; probability density of continuous random variables; probability distribution of common random variables and its joint (probability) distribution; joint probability distribution and edge distribution of two-dimensional discrete random variables; joint probability density and edge density of two-dimensional continuous random variables; probability distribution of independent random variable function of common two-dimensional random variables.

Examination requirements

1. Understand the concept of random variables and their probability distribution; Understand the concept and properties of distribution function F(x)=P{X≤x}; Calculate the probability of events related to random variables.

2. Understand the concept of discrete random variables and their probability distribution; Master 0- 1 distribution, binomial distribution, hypergeometric distribution, poison distribution and its application.

3. Understand the concept of continuous random variables and their probability density; Master the relationship between probability density and distribution function; Master uniform distribution, exponential distribution and their applications.

4. Understand the concept of two-dimensional random variables and the concept, properties and two basic forms of joint distribution of two-dimensional random variables: discrete joint probability distribution and edge distribution, continuous joint probability density and edge density; Will use two-dimensional probability distribution to find the probability of related events.

5. Understand the concept of independence of random variables and master the conditions of independence of discrete and continuous random variables.

6. Grasp the two-dimensional uniform distribution, understand the density function of the two-dimensional normal distribution, and understand the probability meaning of the parameters.

7. Master the basic method of finding the probability distribution of its simpler function according to the probability distribution of independent variables.

Third, the numerical characteristics of random variables

Examination content

Mathematical expectation, variance, standard deviation and their basic properties of random variables; Mathematical expectation of random variable function; Covariance of two random variables and its properties: correlation coefficient of two random variables and its properties.

Examination requirements

1. Understand the concept of digital characteristics of random variables (expectation, variance, standard deviation, covariance, correlation coefficient), use the basic properties of digital characteristics to calculate the digital characteristics of specific distributions, and master the digital characteristics of common distributions.

2. The mathematical expectation eG(X) of the function g (x) will be obtained according to the probability distribution of random variables.

Fourth, the central limit theorem

Examination content

Poisson theorem, DE MOIVRE (Laplace) theorem, binomial distribution with normal distribution as the limit distribution, Levi-Lindberg theorem (central limit theorem of independent and equal distribution).

Examination requirements

1. Grasp the conclusion and application conditions of Poisson theorem, and use Poisson distribution to approximately calculate the probability of binomial distribution.

2. Understand the conclusions and application conditions of Lemov-Laplacian central limit theorem and Levi-Lindbergh central limit theorem, and use relevant theorems to approximately calculate the probability of random events.

[Test Paper Structure]

(1) content ratio

Calculus is about 50%

Linear algebra accounts for about 25%

Probability theory is about 25%

(B) the proportion of questions

Fill in the blanks and multiple-choice questions about 30%

Answer questions (including proof questions) about 70%