I am no native speaker and always confused about the comma in introductory phrases, in particular in prepositional phrases. Is there any hard rule when a comma must be set? If I make a google search for certain phrases, I often find both variants. Typical examples where I am not sure whether a comma must be set are:
- In this case[,] we must...
- For simple problems[,] the algorithm...
- From Lemma 1.2[,] we obtain...
- For a typical user[,] the algorithm...
- In our theory[,] we...