First, the main content is different.
1. Mathematical analysis: a relatively complete mathematical subject with the general theories of calculus and infinite series as the main content, including their theoretical basis (basic theories of real numbers, functions and limits).
2. Advanced Mathematics: a basic subject formed by calculus, algebra, geometry and their overlapping contents.
Second, the characteristics are different.
1. Mathematical analysis: the most important feature is continuity. Only with the continuity of real numbers can limit, continuity, differential and integral be discussed. It is in the process of discussing the legitimacy of various limit operations of functions that people gradually establish a strict theoretical system of mathematical analysis.
2. Advanced mathematics: high degree of abstraction, strict logic and wide application. Abstraction and calculation are the most basic and remarkable features of mathematics. Only with a high degree of abstraction and unity can we profoundly reveal its essential laws and make it more widely used.
Extended data
In the early days of ancient Greek mathematics, the results of mathematical analysis were given implicitly. For example, Zhi Nuo's dichotomy paradox implies the sum of geometric series. Later, ancient Greek mathematicians such as eudoxus and Archimedes made the mathematical analysis more explicit, but it was not very formal. When they calculate the area and volume of regions and solids by exhaustive method, they use the concepts of limit and convergence. In the early days of ancient Indian mathematics, Pashgaro, a mathematician in the12nd century, gave a second example of derivative.
The establishment of mathematical analysis began with the pioneering work represented by Newton (I) and Leibniz (G.W) in the17th century, and was completed with the pioneering work represented by Cauchy and Weierstrass in the19th century. Calculus and its related contents have been called analysis since Newton.
Since then, the field of calculus has been expanding, but many mathematicians still use this name. Today, although many contents have been separated from calculus and become independent disciplines, people still call it analysis. Mathematical analysis is also called analysis for short.