Higher algebra is a branch of algebra, including polynomial theory and linear algebra. Without the concept of "higher function", I guess you might say "transcendental function". Advanced mathematics is engineering mathematics, including all calculations of mathematical analysis, and a little knowledge of analytic geometry and ordinary differential equations, all of which are calculations, and there is almost no theoretical proof. Mathematical analysis is a branch of analysis, which studies classical analysis, that is, limit, differential and integral in continuous function space. Real variable function is directly developed from mathematical analysis.