1. 微分几何（微分几何是研究光滑曲线、曲面等，它以数学分析、微分几何为研究工具。在力学和一些工程问题（如弹性壳结构、齿轮等方面）中有广泛的应用）
2. 拓扑学（拓扑学是研究几何图形在一对一的双方连续变换下不变的性质，这种性质称为“拓扑性质”）
3. 数论（数论是研究整数性质的一门学科。按研究方法的不同，大致可分为初等数论、代数数论、几何数论、解析数论等）
4. 近世代数（近世代数是把代数学的对象由数扩大为向量、矩阵等，它研究更为一般的代数运算的规律和性质，它讨论群、环、向量空间等的性质和结构）
5. 微分方程（微分方程是含有未知函数的导数或偏导数的方程）
6. 函数论（函数论是实函数论（研究实数范围上的实值函数）和复变函数（研究在复数平面上的函数性质）的总称）
7. 泛函分析（泛函分析是综合运用函数论、几何学、代数学的观点来研究无限维向量空间（如函数空间）上的函数、算子和极限理论，它研究的不是单个函数，而是具有某种共同性质的函数集合）

The main majors for basic mathematics recruitment are as follows:

1. Differential geometry (differential geometry is the study of smooth curves, curved surfaces, etc. It uses mathematical analysis and differential geometry as research tools. It has a wide range of applications in mechanics and some engineering problems (such as elastic shell structures, gears, etc.))
2. Topology (topology is the study of the invariable properties of geometric figures under one-to-one continuous transformations between two parties. This property is called "topological properties")
3. Number theory (number theory is a subject that studies the properties of integers. According to different research methods, it can be roughly divided into elementary number theory, algebraic number theory, geometric number theory, analytic number theory, etc.)
4. Modern algebra (modern algebra expands the object of algebra from numbers to vectors, matrices, etc. It studies the laws and properties of more general algebraic operations, and it discusses the properties and structures of groups, rings, vector spaces, etc.)
5. Differential equation (differential equation is an equation containing the derivative or partial derivative of an unknown function)
6. Function theory (function theory is the general term of real function theory (studying real-valued functions on the real number range) and complex variable functions (studying the properties of functions on the complex number plane))
7. Functional analysis (functional analysis is a comprehensive application of the viewpoints of function theory, geometry, and algebra to study functions, operators and limit theories on infinite dimensional vector spaces (such as function spaces). It does not study a single function. But a collection of functions with a certain common property)

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