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What are the main parts of advanced mathematics?
Yes It also includes advanced algebra.

I don't know how far the questioner is. If you majored in electricity in university, you must study complex variable function. If you are an engineering student, you should also learn the basic knowledge of field theory and mathematical transformation (Laplace transformation).

If you are a high school student, you only need to care about simple limit solutions and first derivative solutions and their main applications.

Higher algebra can include determinant, line generation, vector space, quadratic form, probability and group ring theory.

Analytic geometry and solid geometry have been decentralized to the scope of elementary mathematics in middle schools. Of course, after studying calculus, your horizons will be higher.