Mathematics for postgraduate entrance examination mainly includes advanced mathematics, linear algebra and probability and mathematical statistics.

Arc differentiation is to approximate the length of an arc by the length of a segment. Let the function f(x) have a continuous derivative in the interval (a, b), take a fixed point Mo(xo, f(xo)) on the curve Y=f(x) as the base point for calculating the arc length of the curve, and M(x, y) as any point on the curve.

Curvature is a quantity that describes the degree of geometric bending, such as the degree to which a surface deviates from a plane or a curve deviates from a straight line. In different fields of geometry, the specific definition of curvature is not exactly the same. Curvature can be divided into external curvature and internal curvature, and there are important differences between them. The former definition needs to embed geometry into Euclidean space, while the latter is directly defined on Riemannian manifold.