高等数学课程大纲英文

2024年1月23日发(作者：四川的数学试卷)

高等数学课程大纲英文

OUTLINE OF A COURSE IN ADVANCED MATHEMATICS

I. Introduction

A. Nature of Mathematics

B. Learning Objectives

II. Algebra

A. Linear Algebra

1. Matrix Algebra

2. Vector Spaces

B. Advanced Structures

1. Groups

2. Rings and Fields

III. Calculus

A. Differential Calculus

1. Limits and Continuity

2. Derivatives

3. Integrals

B. Multivariable Calculus

1. Vector and Parametric Equations

2. Partial Derivatives

3. Several Variable Integrals

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IV. Analysis

A. Series

1. Convergence Tests

2. Power Series

3. Fourier Series

B. Differential Equations

1. Ordinary Differential Equations

2. Partial Differential Equations

V. Probability and Statistics

A. Probability

1. Random Variables and Processes

2. Probability Distributions

3. Mathematical Expectation

B. Statistics

1. Descriptive Statistics

2. Inferential Statistics

VI. Geometry and Topology

A. Euclidean Geometry

1. Analytic Geometry

2. Transformations

B. Non-Euclidean Geometry

1. Hierarchical Geometry

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2. Topology

VII. Computer Science

A. Programming

1. Algorithms

2. Complexity Theory

B. Databases

1. Entity-Relationship Model

2. Query Languages

VIII. Applications

A. Modeling

1. Operations Research

2. Computer Graphics

B. Other Applications

1. Cryptography

2. Number Theory。

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