Mathematics 3 is a mathematics subject in the postgraduate examination, which mainly examines the knowledge points of calculus, linear algebra, probability theory and mathematical statistics. Specifically, the content of the Mathematics 3 exam mainly includes the following aspects:
1. Calculus.
Calculus is an important part of Mathematics 3, which mainly examines the concepts and properties of limits, derivatives, integrals, etc., as well as their operations and applications. Specifically, it includes the following:
Limit Theory: It mainly examines the definition, properties and operations of limits, as well as the theorem of limit existence, infinitesimal quantities, etc.
Derivatives and Differentiation: It mainly examines the definition, properties, and operations of derivatives, as well as the concepts and operations of differentiation.
Integralism: It mainly examines the definition, properties and operations of integrals, including definite integrals, indefinite integrals and anomalous integrals.
Calculus of multivariate functions: It mainly examines the limit, continuity, partial derivative, and full differentiation of multivariate functions, as well as the concept, properties, and operations of double integral.
Infinite series: It mainly examines the concepts, properties, and operations of number series, power series, and Fourier series.
2. Linear algebra.
Linear algebra mainly examines concepts and properties such as determinants, matrices, vectors, and systems of linear equations, as well as their operations and applications. Specifically, it includes the following:
Determinants and matrices: This course mainly examines the concepts, properties, and operations of determinants, as well as the operations of matrices, inverse matrices, and elementary transformations.
Vectors: This course mainly examines the concepts, properties, and operations of vectors, as well as the linear combination and representation of vectors.
Linear equations: The solutions of linear equations are mainly investigated, including Gaussian elimination method, Kramer's rule, etc.
Eigenvalues and eigenvectors: This paper mainly examines the concepts, properties and operations of eigenvalues and eigenvectors, as well as the diagonalization of matrices.
3. Probability Theory and Mathematical Statistics.
Probability theory and mathematical statistics mainly examine the basic concepts of probability theory, the distribution of random variables, numerical characteristics, etc., as well as the basic concepts of mathematical statistics and the methods of parameter estimation and hypothesis testing. Specifically, it includes the following:
Random Events and Probability: It mainly examines the concept of random events, the definition and calculation methods of probability, as well as conditional probability and independence.
Random variables and their distributions: This paper mainly examines the concept, distribution function and distribution law of random variables, as well as the distribution of common random variables.
Multidimensional random variables and their distributions: This paper mainly examines the concept, joint distribution and marginal distribution of two-dimensional random variables, as well as the independence of random variables.
Numerical characteristics of random variables: This paper mainly examines the calculation and application of numerical features such as mathematical expectations, variance and covariance of random variables.