  We study the strong rates of the Euler-Maruyama approximation for one
dimensional stochastic differential equations whose drift coefficient may be
neither continuous nor one-sided Lipschitz and diffusion coefficient is
H\"older continuous. Especially, we show that the strong rate of the
Euler-Maruyama approximation is 1/2 for a large class of equations whose drift
is not continuous. We also provide the strong rate for equations whose drift is
H\"older continuous and diffusion is nonconstant
