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Is applied mathematics just advanced mathematics?
No. Are concepts in two different categories. Advanced mathematics is a definite academic name, which refers to a large class of mathematics based on calculus, generally including mathematical analysis, differential equations, advanced algebra, complex variable functions and integral transformation. The content is more rigorous and the level requirements are more solid.

Applied mathematics is an uncertain popular term, sometimes called engineering mathematics. Like an all-inclusive basket, everything can be put in, and it can be increased or decreased as needed. In addition to calculus, there are statistics, probability theory, calculation methods, projection geometry and so on. Many theorems can be used directly without strict proof, as long as they can be used.