1. elementary mathematics knowledge: advanced mathematics is developed on the basis of elementary mathematics, so mastering the basic concepts, theorems and formulas of elementary mathematics is the basis for learning advanced mathematics. This includes the properties of numbers, algorithms, algebraic expressions, equations and inequalities, functions and images, geometric figures and other knowledge.
2. Calculus: Calculus is one of the core contents of higher mathematics, which mainly studies the concepts and properties of limit, derivative and integral of functions. Before learning advanced mathematics, we need to master the basic concepts and methods of calculus, such as the definition of limit, the law of derivative, the law of integral and so on.
3. Linear Algebra: Linear Algebra is a discipline that studies concepts such as vector space, linear transformation and matrix, and it is an important branch of higher mathematics. Learning linear algebra is helpful to understand some concepts and methods in higher mathematics, such as the basis of vector space, the representation of linear transformation, the operation of matrix and so on.
4. Probability theory and mathematical statistics: Probability theory and mathematical statistics are disciplines that study the regularity of random phenomena and occupy an important position in higher mathematics. Learning probability theory and mathematical statistics is helpful to understand some concepts and methods in higher mathematics, such as random variables, probability distribution, expected value, variance and so on.
5. Logical reasoning ability: Advanced mathematics involves many abstract concepts and complex calculations, so it is very important to have strong logical reasoning ability. By cultivating logical thinking ability, we can better understand and master the knowledge of advanced mathematics.
6. Self-study ability: The study of advanced mathematics often requires a lot of time and energy, so it is very beneficial to have strong self-study ability. Through self-study, you can better master the knowledge of advanced mathematics and improve your academic level.
In short, learning advanced mathematics requires a certain foundation in elementary mathematics knowledge, calculus, linear algebra, probability theory and mathematical statistics, as well as strong logical reasoning ability and self-study ability. With these foundations, we can better learn and master the knowledge of advanced mathematics.