The nine basic equivalent infinitesimals of high numbers are: when x->; 0，sinx~x，tanx~x，sinx~tanx， 1-cosx~x？ /2，tanx-sinx~x？ /2,e^x- 1~x,√( 1+x)- 1~x/2,√( 1-x)- 1~-x/2,ln( 1+x)~x。

Higher mathematics refers to a more complicated part of mathematical objects and methods compared with elementary mathematics.

In a broad sense, all mathematics except elementary mathematics are advanced mathematics, and some call algebra, geometry, simple set theory and logic in middle school intermediate mathematics, which is the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities.

Generally speaking, advanced mathematics is a basic subject formed by calculus, algebra, geometry and their intersection.

The main contents of advanced mathematics include: series, limit, calculus, spatial analytic geometry and linear algebra, series, ordinary differential equations.