In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono Phys. Rev. Lett., 73 (1994), pp. 1311–1315; Phys. Rev. E, 54 (1996), pp. 376–394 is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum. The method is illustrated by some linear and nonlinear singular perturbation problems.