1. Set: Set is one of the most basic concepts in mathematics, and it is a whole composed of things with certain properties. A set can be finite or infinite, discrete or continuous.
2. Function: A function is a corresponding relationship that maps elements in one set to elements in another set. Functions can be used to describe the relationship between variables, such as linear function and quadratic function.
3. Series: A series is a series of numbers arranged in a certain order. Series can be used to describe time series data, financial data and so on.
4. Matrix: A matrix is a rectangular array consisting of m×n numbers, which can represent linear equations and linear transformations.
5. Vector: A vector is a quantity consisting of two elements: size and direction. Vectors can be used to describe physical phenomena, such as force and velocity.
6. Space: Space is a three-dimensional geometric structure consisting of points, lines and surfaces. Space can be used to describe the shape and position of objects.
7. Calculus: Calculus is a branch of mathematics that studies the rate of change and cumulative quantity. It includes the concepts of derivative, integral and differential equation.
8. Probability theory and statistics: Probability theory and statistics is a branch of mathematics that studies the regularity of random phenomena. Including the concepts of probability distribution, expected value, variance, etc.