Counting two is the most difficult in science and engineering.
Number one and number two are integrated, and number two is simpler than number one.
Then the number three (economic mathematics) is simpler than the first two.
The simplest thing is to count to four.
The number three can be said to be integrated with the number four.
A Summary of the Changes of Mathematics Syllabus for Postgraduate Entrance Examination in 2007
-author:
Count one
Test paper structure: no change
Content proportion: advanced mathematics has changed from about 60% in 2007 to about 56%, linear algebra from about 20% in 2007 to about 22%, and probability theory and mathematical statistics from about 20% in 2007 to about 22%.
The proportion of questions: Fill-in-the-blank questions and multiple-choice questions have changed from about 40% in 2007 to about 45%, and the answers (including proof questions) have changed from about 60% in 2007 to about 55%.
Advanced mathematics
I. Function, Limit and Continuity
Examination requirements: 8. From the initial "understanding the concepts of infinitesimal and infinitesimal, mastering the comparison method of infinitesimal and finding the limit with equivalent infinitesimal" to "understanding the concepts of infinitesimal and infinitesimal, mastering the comparison method of infinitesimal and finding the limit with equivalent infinitesimal" in 2007.
Second, the differential calculus of unary function
Examination requirements: 7. From the initial "simple application of grasping the maximum and minimum values of functions" to "application of grasping the maximum and minimum values of functions" in 2007.
3. Integral calculus of unary function
Exam content: delete "expressing and calculating the center of mass with definite integral" in the 2006 syllabus.
Four, multivariate function integral calculus
Examination content: from the original "original function of known total differential" to "original function of total differential of binary function" in 2007.
Examination requirements: 5. From the initial "original function that can be fully differentiated" to "original function that can be fully differentiated with binary function" in 2007.
6. From the initial "knowing how to calculate surface integral and curve integral with Gaussian formula and Stokes formula" to "mastering the method of calculating surface integral with Gaussian formula and curve integral with Stokes formula" in 2007.
Five, infinite series
Examination requirements: 5. From the initial "relationship between absolute convergence and conditional convergence" to "relationship between absolute convergence and convergence" in 2007.
7. From the original "item-by-item differentiation" to the "item-by-item derivation" in 2007.
Sixth, ordinary differential equations
Examination content: From the original "variable separable equation" to the "variable separable differential equation" in 2007.
linear algebra
Second, the matrix
Examination requirements: 4. From the initial "mastering the elementary transformation of matrix" to "understanding the concept of elementary transformation of matrix" in 2007.
Third, the vector
Examination requirements: 3. From the initial concept of "understanding the rank of maximum linearly independent group and vector group" to the concept of "understanding the rank of maximum linearly independent group and vector group" in 2007.
Eigenvalues and eigenvectors of verb (abbreviation of verb) matrix
Examination requirements: 2. From the initial "understanding the concept and properties of similar matrix and the necessary and sufficient conditions for matrix similarity diagonalization" to "understanding the concept and properties of similar matrix and the necessary and sufficient conditions for matrix similarity diagonalization" in 2007.
Probability and mathematical statistics
Second, random variables and their distribution
(A) random events and probability
Examination content: from the original "random variable and its probability distribution" to "random variable" in 2007.
(3) Multidimensional random variables and their probability distribution
Examination content: from the original "independence and correlation of random variables" to "independence and irrelevance of random variables" in 2007. From the initial "probability distribution of common two-dimensional random variables" to "distribution of common two-dimensional random variables" in 2007.
(D) the digital characteristics of random variables
Examination requirements: 2. From the initial "finding the mathematical expectation of the function of a random variable according to its probability distribution" to "finding the mathematical expectation of the function of a random variable" in 2007.
(vi) Basic concepts of mathematical statistics
Examination content: from the original "some common sampling distributions of normal population" to "common sampling distributions of normal population" in 2007.
Examination requirements: 3. From the initial "understanding some common sampling distributions of normal population" to "understanding common sampling distributions of normal population" in 2007.
The second item
Test paper structure
Content proportion: from the original "advanced mathematics is about 80%, linear algebra is about 20%" to "advanced mathematics is about 78%, linear algebra is about 22%" in 2007.
The proportion of questions: from "about 40% fill-in-the-blank questions and multiple-choice questions, about 60% answer questions (including proof questions)" to "about 45% fill-in-the-blank questions and multiple-choice questions, about 55% answer questions (including proof questions)" in 2007.
Advanced mathematics
I. Function, Limit and Continuity
Examination content: from the original "the establishment of functional relationship of simple application problems" to "the establishment of functional relationship" in 2007.
Examination requirements: 1, from the original "can establish functional relations in simple application problems" to "can establish functional relations in application problems" in 2007.
4. From the initial "understanding the basic concept of elementary function" to "understanding the concept of elementary function" in 2007.
8. From the initial "understanding the concepts of infinitesimal and infinitesimal, mastering the comparison method of infinitesimal and seeking the limit with equivalent infinitesimal" to "understanding the concepts of infinitesimal and infinitesimal, mastering the comparison method of infinitesimal and seeking the limit with equivalent infinitesimal" in 2007.
Second, the differential calculus of unary function
Examination requirements: 4. From the initial "knowing the first and second derivatives of piecewise function" to "knowing the derivatives of piecewise function" in 2007.
5. From the initial Understanding Cauchy Mean Value Theorem to Understanding and Applying Cauchy Mean Value Theorem in 2007.
7. From the initial "finding the maximum and minimum of the main function and its simple application" to "finding the maximum and minimum of the main function and its application" in 2007.
3. Integral calculus of unary function
Examination requirements: Delete "6". Understand the "approximate calculation method and centroid of definite integral" in the 2006 syllabus.
Four, multivariate function calculus
Examination content: From the original "Concept and Calculation of Partial Derivatives of Multivariate Functions" to "Partial Derivatives and Total Differentials of Multivariate Functions" in 2007.
linear algebra
Second, the matrix
Examination requirements: 1, from the original "understanding orthogonal matrix" to "understanding orthogonal matrix and its properties" in 2007.
Fourth, linear equations.
Examination requirements: 3. Delete the concept of "understanding and solving space" in the 2006 syllabus.
Eigenvalues and eigenvectors of verb (abbreviation of verb) matrix
Examination content: delete the concept and nature of similarity transformation from the 2006 syllabus.
Six, quadratic form (new)
Examination content: Quadratic form and its matrix represent the rank inertia theorem of contract transformation and the quadratic form of contract matrix. The canonical form and canonical form of quadratic form are transformed into canonical quadratic form and the positive definiteness of its matrix by orthogonal transformation and matching method.
Examination requirements: 1. Understand the concept of quadratic form, express quadratic form in matrix form, and understand the concepts of contract transformation and contract matrix.
2. Understand the concept of rank of quadratic form, the concepts of standard form and standard form of quadratic form, and inertia theorem, and transform quadratic form into standard form by orthogonal transformation and collocation method.
3. Understand the concepts of positive definite quadratic form and positive definite matrix, and master their discrimination methods.
Changes of Mathematics (III) Outline in 2007
Examination subjects: no change.
Test paper structure:
Content change: (2) Content ratio: stones increased from about 50% to about 56%; Linear algebra is reduced from about 25% to about 22%; Probability theory and mathematical statistics dropped from about 25% to about 22%.
(3) the proportion of questions: the proportion of fill-in-the-blank questions and multiple-choice questions increased from about 30% to about 45%; The proportion of solving problems (including proof questions) has dropped from about 70% to about 55%.
calculus
I. Function, Limit and Continuity
Examination content: "The concept and relationship between infinitesimal and infinity" was changed to "The concept and relationship between infinitesimal and infinitesimal"
Change "the nature of infinitesimal and the comparison of infinitesimal" to "the nature of infinitesimal and the comparison of infinitesimal"
Examination requirements:
1. Change "Function relation of simple application problem will be established" to "Function relation of application problem will be established".
6. Change "can apply two important limits" to "master the method of using two important limits to find the limit".
7. "Understand the concept and basic properties of infinitesimal and master the comparison method of infinitesimal. Understand the concept of infinity and its relationship with infinitesimal. " Understand the concept and basic properties of infinitesimal and master the comparison method of infinitesimal. Understand the concept of infinity and its relationship with infinitesimal. "
Second, the differential calculus of unary function
Examination content: no change.
Examination requirements: No change.
3. Integral calculus of unary function
Examination content: no change.
Examination requirements: write generalized integral as generalized integral. Nothing else has changed.
Four, multivariate function calculus
Examination content: no change.
Examination requirements: 4. "Can solve some simple application problems" was changed to "Can solve simple application problems".
Nothing else has changed.
Five, infinite series
Examination content: no change.
Examination requirements: No change.
Six, ordinary differential equations and difference equations
Examination content: no change.
Examination requirements: No change.
linear algebra
I. Determinants
Examination content: no change.
Examination requirements: No change.
Second, the matrix
Examination content: no change.
Examination requirements: No change.
Third, the vector
Examination content: no change.
Examination requirements: No change.
Fourth, linear equations.
Examination content: no change.
Examination requirements: No change.
Eigenvalues and eigenvectors of verb (abbreviation of verb) matrix
Examination content: no change.
Examination requirements: No change.
Sixth, quadratic form
Examination content: no change.
Examination requirements: No change.
To sum up, the examination content and requirements of linear algebra have not changed.
Probability and mathematical statistics
I. Random events and probabilities
Examination content: no change.
Examination requirements: No change.
Second, random variables and their distribution
Examination content: no change.
Examination requirements: No change.
2. Added "Mastering geometric distribution and its application".
Nothing else has changed.
Thirdly, the distribution of multidimensional random variables.
Examination content: no change.
Examination requirements: No change.
Fourth, the numerical characteristics of random variables
Examination content: no change.
Examination requirements: No change.
Law of Large Numbers and Central Limit Theorem
Examination content: no change.
Examination requirements: No change.
Basic concepts of mathematical statistics of intransitive verbs
Examination content: no change.
Examination requirements: No change.
Seven. parameter estimation
Examination content: no change.
Examination requirements: No change.
Eight, hypothesis testing
Examination content: no change.
Examination requirements: No change.
To sum up, the part of probability theory and mathematical statistics only adds the requirement of "mastering geometric distribution and its application", and nothing else has changed.
Changes in the syllabus of Mathematics Band 4 Examination in 2007
Test paper structure
Content proportion: calculus 50% linear algebra 25% probability theory 25% in 2006.
In 2007, calculus 56% linear algebra 22% probability theory 22%
Proportion of questions: in 2006, fill-in-the-blank questions and multiple-choice questions accounted for 40%, and answers (including proof) accounted for 60%.
In 2007, 45% filled in the blanks and 55% answered multiple-choice questions (including proof).
calculus
1. Function, Limit and Continuity
Will use two important limits to master the method of using two important limits to find the limit.
Understanding the properties (boundedness, maximum theorem and mean value theorem) of continuous functions on closed intervals and their simple applications will be changed to understanding the properties (boundedness, maximum theorem and mean value theorem) of continuous functions on closed intervals and applying these properties.
2. Differential calculus of unary function
Examination content: the concept of derivative is changed to the concepts of derivative and differential;
Increase the tangent and normal of plane curve;
The four operations of derivative become the four operations of derivative and differential;
The derivative of compound function, inverse function and implicit function is changed to the differential method of compound function, inverse function and implicit function; Rolle theorem and Lagrange daily mean value theorem and their applications are changed into differential mean value theorem;
Discriminating the Transformation from Monotonicity of Function to Monotonicity of Function
Examination requirements: add tangent and normal equations of plane curves; Increase the understanding of Cauchy's mean value theorem and master the simple application of the theorem; Mastering the discrimination method and application of function monotonicity, mastering the solution of function extreme value, maximum value and minimum value, changing solving simple application problems into the discrimination method of function monotonicity, understanding the concept of function extreme value, mastering the solution and application of function extreme value, maximum value and minimum value;
Finding the oblique asymptote of the function is changed to finding the asymptote of the function;
3. Integral calculus of unary function
Examination requirements: use definite integral to calculate the area of plane figure and the volume of rotating body, instead of using definite integral to calculate the area of plane figure, the volume of rotating body and the average value of functions;
4. Multivariate function calculus
Examination requirements: to understand the intuitive meaning of limit and continuity of binary function, we should change to understand the concepts of limit and continuity of binary function.
5. Ordinary differential equations have not changed.
linear algebra
1. Determinant: No change.
2. Matrix addition of main matrix transposition
Knowing the power of square matrix, mastering the properties of determinant of square matrix product is changed to knowing the properties of determinant of square matrix power and square matrix product.
3. Vector: No change
4. Linear equation: invariant
5. Eigenvalues and eigenvectors of the matrix: no change.
6. Quadratic type (new)
Examination content: Quadratic form and its matrix represent the rank inertia theorem of contract transformation and the quadratic form of contract matrix. The canonical form and canonical form of quadratic form are transformed into canonical quadratic form and the positive definiteness of its matrix by orthogonal transformation and matching method.
Examination requirements:
1. Understand the concept of quadratic form, express quadratic form in matrix form, and understand the concepts of contract transformation and contract matrix;
2. Understand the concept of rank of quadratic form, the concepts of standard form and standard form of quadratic form, and inertia theorem, and transform quadratic form into standard form by orthogonal transformation and collocation method; 、
3. Understand the concepts of positive definite quadratic form and positive definite matrix, and master their discrimination methods.
probability theory
1. Random events and probabilities: unchanged.
2. Random variables and their probability distribution: unchanged.
3. The distribution of multidimensional random variables
The joint probability distribution, edge distribution and conditional distribution of discrete random variables are changed into the joint probability distribution, edge distribution and conditional distribution of two-dimensional discrete random variables.
4. Numerical characteristics of random variables: no change.
5. Central limit theorem
Test content: Chebyshev's law of large numbers, bernhard's law of large numbers and Sinchin's law of large numbers were added.
Examination requirements: increase the understanding of Chebyshev's law of large numbers, bernhard's law of large numbers and Sinchin's law of large numbers, and use relevant theorems to approximately calculate the probability of random events.