As one of the compulsory subjects in the graduate school entrance examination, Mathematics I is an insurmountable difficulty for the majority of candidates. In order to help the majority of candidates better understand the content of the Postgraduate Mathematics I exam, what are the contents of the Postgraduate Mathematics I exam? This article will provide a detailed analysis of the content of the Mathematics I exam for the postgraduate entrance examination, hoping to help candidates review and prepare for the exam.
1. Linear algebra
Linear algebra is the first part of Mathematics I, which mainly includes matrices and vectors, determinants, systems of linear equations, eigenvalues and eigenvectors, quadratic forms, etc. This section tests the candidate's ability to understand and apply the basic concepts, properties, and methods of linear algebra.
1.Matrices and vectors: the basic operations of matrices, the rank of matrices, the inner product of vectors, vector spaces, etc.
2.Determinant: The nature of the determinant, the calculation method of the determinant, etc.
3.Systems of linear equations: Gaussian elimination, structure of solutions to systems of linear equations, etc.
4.Eigenvalues and eigenvectors: definitions, properties, and methods of eigenvalues and eigenvectors.
5.Quadratic type: definition of quadratic type, standard form, positive definite quadratic form, etc.
2. Probability theory and mathematical statistics
What are the contents of the Postgraduate Mathematics Exam? Probability Theory and Mathematical Statistics is the second part of Mathematics I, which mainly includes random events and probability, random variables and their distributions, multidimensional random variables and their distributions, the law of large numbers and the central limit theorem, parameter estimation, hypothesis testing, etc. This part mainly tests the candidates' understanding and application ability of the basic concepts, properties and methods of probability theory and mathematical statistics.
1.Random Events and Probabilities: Definition of Random Events, Definition of Probability, Conditional Probability, Independence, etc.
2.Random variables and their distributions: definition of random variables, discrete random variables and their distributions, continuous random variables and their distributions, etc.
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3.Multidimensional random variables and their distributions: definition, joint distribution, marginal distribution, etc. of multidimensional random variables.
4.The Law of Large Numbers and the Central Limit Theorem: The Law of Large Numbers, the Central Limit Theorem, etc.
5.Parameter estimation: point estimation, interval estimation, etc.
6.Hypothesis testing: the basic ideas, steps, and common testing methods of hypothesis testing.
3. Calculus
Calculus is the third part of Mathematics I, which mainly includes functions and limits, derivatives and differentiation, median theorem and Taylor's formula, indefinite integrals, definite integrals and their applications, ordinary differential equations, etc. This part mainly tests the candidate's understanding and application ability of the basic concepts, properties and methods of calculus.
1.Functions and Limits: The concept of functions, the concept of limits, continuity, etc.
2.Derivatives and Differentiation: The concept of derivatives, the concept of differentiation, the calculation methods of derivatives, etc.
3.Median Theorem and Taylor's Formula: Median Theorem, Taylor's Formula, etc.
4.Indefinite integral: the concept of indefinite integral, basic integral table, commutation integral method, partial integral method, etc.
5.Definite integrals and their applications: the concept of definite integrals, the properties of definite integrals, the application of definite integrals, etc.
6.Ordinary differential equations: the basic concepts of ordinary differential equations, the solution of first-order differential equations, etc.
What is the content of the Postgraduate Mathematics First Exam? You already have the answer, the content of Mathematics I for graduate school involves linear algebra, probability theory and mathematical statistics, calculus and other aspects, and the exam is more difficult. Therefore, in the process of reviewing and preparing for the exam, candidates need to systematically grasp the basic concepts, properties and methods of each part, and improve their problem-solving ability through a lot of practice. At the same time, candidates also need to pay attention to past past questions and understand the type and difficulty of the exam questions in order to better cope with the exam. I hope this article will be helpful to candidates in their review and preparation, and I wish you all a smooth exam!